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A decision support tool for accepting or rejecting donations in humanitarian relief organizations

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Title:
A decision support tool for accepting or rejecting donations in humanitarian relief organizations
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English
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Ruiz-Brand, Francisco Javier
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University of South Florida
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Subjects / Keywords:
disaster management
decision making
disaster relief
humanitarian assistance
decision under uncertainty
Dissertations, Academic -- Engineering Management -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Summary:
ABSTRACT: With the increase in the occurrence of disasters (natural and man-made) that leave people injured, handicapped or dead, the disaster management theory is gaining more importance. As a consequence, human assistance and disaster relief organizations are managing increasingly more inventories anticipated to help people in need. Donations are the common means used by humanitarian relief organizations for procuring commodities to support some of their programs. Previous experiences have indicated that donations become a burden instead of offering relief when they do not match actual victims' needs. Accepting or rejecting donations is a key issue that can produce not only economic losses but loss of lives as well. The objective of this thesis is to provide a means of assessing acceptance or rejection decisions using decision tree analysis theory and utility theory. The proposed model considers the inputs that a decision-maker may face when accepting or rejecting a donation. Such inputs include these categories: the probability of the occurrence of disaster, the need for and further use of a commodity, the unit price and holding cost of the item, the benefit provided by the donation, and the probability of having subsequent donations when the initial donation is initially rejected. Various scenarios are simulated in Excel&reg environment through the Monte Carlo process. This will assess the varied impacts from the alternative inputs in the decision making process; a sensitivity analysis will evaluate the effects of various decisions. The results obtained from the simulation of the diverse scenarios indicate that the decision of accepting or rejecting donations is driven more by the possibility of the use of the commodity than by the probability of occurrence of the disaster. The findings from the model also indicate that the decision of accepting or rejecting is more sensitive to the relationship of sale price to benefit deployment of the commodity than to sale price alone. The simulation of the expected monetary benefit of the relief provided results in the development of graphs that can affect the decision making process when accepting or rejecting donations.
Thesis:
Thesis (M.S.E.M.)--University of South Florida, 2004.
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Includes bibliographical references.
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by Francisco Javier Ruiz-Brand.
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Title from PDF of title page.
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Document formatted into pages; contains 141 pages.

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oclc - 56564271
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usfldc doi - E14-SFE0000457
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A Decision Support Tool for Accepting or Rejecting Donations in Humanitarian Relief Organizations by Francisco Javier Ruiz-Brand A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering Management Department of Industrial and Management Systems Engineering College of Engineering University of South Florida Major Professor: Ali Yalcin, Ph.D William A. Miller, Ph.D Paul McCright, Ph.D Date of Approval: June 30, 2004 Keywords: decision under uncertainty, humanitarian assistance, disaster relief, decision making, disaster management Copyright 2004, Francisco Javier Ruiz-Brand

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Dedication To my parents, my wife and my dearest daughters Natalie and Isabella, who were born during the preparation of this thesis.

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Acknowledgments The author wants to express his gratitude to Dr. Ali Yalcin for his judicious advice and guidance during this thesis. Thanks, indeed, to Dr. Anita L. Callahan and Dr. Paul Givens for their priceless help during my studies. Special thanks go to Dr. Callahan for encouraging me to pursue this research. The author also wants to thank committee members Dr. Paul McCright and Dr. William A. Miller for their kind and opportune suggestions and corrections to this thesis. Thanks indeed to Holly Alderman and JoNette LaGamba for their revision and edition of this thesis. Additionally, special thanks go to J. Ke vin Smith, Emergency Disaster Services Director of Florida Division of the Salvati on Army, and Eric. E. Matos, Deputy Director of the Global Center for Disaster Management and Humanitarian Action at the University of South Florida. Mr. Smith and Mr. Matos were very supportive in providing an insight of the current donation problems in disaster management organizations.

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TABLE OF CONTENTS LIST OF TABLES .............................................................................................................iv LIST OF FIGURES ...........................................................................................................vi ABSTRACT .......................................................................................................................ix CHAPTER 1 .......................................................................................................................1 INTRODUCTION ..............................................................................................................1 1.1 Motivation of this Research ..........................................................................................1 1.2 Thesis Outline ...............................................................................................................2 1.3 Background of the Problem ..........................................................................................3 1.3.1 Introduction ................................................................................................3 1.3.2 Natural Disasters ........................................................................................4 1.3.3 Man-made Disasters ...................................................................................5 1.3.4 Trend of Peoples Vulnerability .................................................................6 1.3.5 Counter Measurement to the Disaster Situation ........................................7 CHAPTER 2 .....................................................................................................................11 RESEARCH OBJECTIVES .............................................................................................11 2.1 Problem Statement ......................................................................................................11 2.2 Problem Description ...................................................................................................11 2.3 Scope ...........................................................................................................................14 2.4 Assumptions ................................................................................................................14 2.5 Importance of this Study .............................................................................................15 CHAPTER 3 .....................................................................................................................16 BACKGROUND AND LITERATURE REVIEW ..........................................................16 3.1 Procurement Methods: Donations ...............................................................................16 3.2 Inventories for Humanitarian Relief Operations .........................................................17 3.3 The Cost of Human Life .............................................................................................20 3.4 Assessing the Benefits of the Deployment of Commodities ......................................22 3.5 Decision Trees Analysis .............................................................................................23 3.5.1 Decision Variables ................................................................................25 CHAPTER 4 .....................................................................................................................27 FORMULATION OF THE MODEL ...............................................................................27 4.1 Notations .....................................................................................................................27 4.2 Equalities .....................................................................................................................28 4.3 Building the Model .....................................................................................................28 4.4 Description of the Model ............................................................................................32 4.5 Assumptions ................................................................................................................35 i

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4.6 The Scenarios ..............................................................................................................36 4.6.1 Notation for the Different Scenarios ........................................................37 4.6.2 Uncertainty Space of the Scenarios .........................................................37 4.7 Simulation of the Different Scenarios .........................................................................40 4.8 Generating the Random Numbers ...............................................................................40 4.9 Assessing the Input Data to the Model .......................................................................41 4.9.1 Probability of the Use of the Commodity ................................................41 4.9.2 Probability of the Occurrence of the Disaster ..........................................43 4.9.3 Probability of Having a Later Donation ...................................................46 4.9.4 Eliciting of the Ratio Holding Cost-sale Price () ...................................47 4.9.5 Eliciting of the Ratio Sale Price-benefit () ............................................47 4.10 Summary of the Model .............................................................................................48 CHAPTER 5 .....................................................................................................................50 THE MODEL ....................................................................................................................50 5.1 Assessment of the Best Decision ................................................................................50 5.2 Sensitivity Analysis ....................................................................................................52 5.3 Deduction of the EMV ................................................................................................62 5.3.1 Expected Monetary Value for the Acceptance Decision .........................62 5.3.2 Expected Monetary Value for the Rejection Decision .............................65 5.4 Discussion of the Model .............................................................................................67 CHAPTER 6 .....................................................................................................................73 CASE STUDY ..................................................................................................................73 6.1 Introduction .................................................................................................................73 6.2 The Situation ...............................................................................................................74 6.2.1 Inputs to the Model ..................................................................................75 6.3 Results of Case Study .................................................................................................80 CHAPTER 7 .....................................................................................................................87 HOW TO IMPLEMENT THIS METHODOLOGY IN HUMANITARIAN RELIEF ORGANIZATIONS ..........................................................................................................87 7.1 Create an Influence Diagram ......................................................................................87 7.1.1 Influence Diagram of the Decision of Accepting/Rejecting Donations ..87 7.1.2 Governmental/External Influence ............................................................88 7.1.3 Donors Influence ....................................................................................88 7.1.4 Peoples influence ....................................................................................89 7.1.5 Relief Organization Influence ..................................................................89 7.2 Assess the Type of Disaster and its Probability of Occurrence ..................................91 7.3 Assess the Possible Need of the Donation ..................................................................92 7.4 Find the Costs .............................................................................................................92 7.5 Evaluate the Values of the PWTP ...............................................................................92 7.6 Review What may be of Interest to the Stakeholders and Assess the P(LD) .............93 7.7 Estimate the Values of and and Obtain the Graphs .............................................93 ii

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CHAPTER 8 .....................................................................................................................95 RESULTS, CONCLUSIONS, AND FURTHER RESEARCH .......................................95 8.1 Summary of the Results ..............................................................................................95 8.2 Conclusions .................................................................................................................97 8.3 Contribution ................................................................................................................98 8.4 Scope for Future Research ........................................................................................100 REFERENCES ...............................................................................................................102 APPENDICES ................................................................................................................107 APPENDIX A .................................................................................................................108 Visual Basic Codes for Generating the Random Numbers and the Charts.....................108 A.1 VBA Code for Generating the Random Numbers ...........................................108 A.2 VBA Code for Generating the MSD and the Charts ........................................108 APPENDIX B .115 Different MS and Graphs for P(D) vs. P(U|D), P(D) vs. P(U|ND), and P(D) vs. P(LD). Cases When HC=0 .......................................................................115 iii

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LIST OF TABLES Table 1: Top U.S. Private Charities by Donations for the Year 2000 ..............................10 Table 2: Advantages and Disadvantages of Donations for Humanitarian Relief .............16 Table 3: Possible Scenarios and Consequences if the Donation is Accepted ...................38 Table 4: Possible Scenarios and Consequences if the Donation is Rejected ....................38 Table 5: Short Term Effects of Major Disasters. Source: Pan American Health Organization (2001p. 8) ............................................................................................43 Table 6: Matrix of Expected Monetary Value (EMV) ......................................................53 Table 7: Matrix of Strategic Decision (MSD) ..................................................................57 Table 8: Matrix of Expected Monetary Value for Different Probabilities of P(D) and P(U|D). Case of PWTP=$10 .....................................................................................58 Table 9: Matrix of Strategic Decision for the PWTP=$10 ...............................................58 Table 10: Summary of the Inputs for Running the Model ................................................80 Table 11: Matrix of Strategic Decision P(D) vs. P(U|D) for the Case Study ...................82 Table 12: Matrix of Strategic Decision P(D) vs. P(U|ND) for the Case Study ................82 Table 13: Matrix of Strategic Decision P(D) vs. P(LD) for the Case Study ....................83 Table 14: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 .................115 Table 15: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 .................117 Table 16: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 ..............119 Table 17: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0.5, and =0 ..............121 Table 18: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=1.0, and =0 ..............123 iv

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Table 19: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=1.0, and =0 ..............125 Table 20: MS for P(D) vs. P(LD) Given P(U|D)=0.5, P(U|ND)=0.5, and =0 ..............127 v

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LIST OF FIGURES Figure 1: Decisions and Events when Accepting or Rejecting Donations .......................29 Figure 2: Graph of the Decision Tree Model ....................................................................30 Figure 3: Layout of the Decision Tree Diagram ...............................................................31 Figure 4: Decision, Events, and Cash Flow for the Donation Process .............................34 Figure 5: Layout of Probabilities and Cash Flow of the Decision Tree Diagram ............39 Figure 6: Geographical Distribution of Major Hazards in the US ....................................45 Figure 7: EMV of P(D) from 0.0 to 1.0 When P(U|D)=0.5 ..............................................54 Figure 8: EMV for Different Probabilities of the Occurrence of Disaster .......................54 Figure 9: EMV for P(D) vs P(U|D). Case of PWTP = $903,915,574 ..............................55 Figure 10: Threshold of P(D) vs. P(U|D) for Accepting or Rejecting the Donation when =0 ..................................................................................................................60 Figure 11: Graph of Different Thresholds for P(D) vs. P(U|D) for from 0.0 to 1.0 ...................................................................................................................60 Figure 12: 3-D View of the Threshold of the Graph P(D) vs P(U|D) vs that Yields the Highest EMV ....................................................................................61 Figure 13: Layout of the Model Proposed ........................................................................63 Figure 14: Flood Data Map for the Area along the Red River, Grand Forks, ND. Source: ISRI/FEMA Project Impact Hazard Map (Federal Emergency Management Agency, 2003) ...................................................76 Figure 15: Strategic Factors for Evaluating the PWTP (Case Study) ...............................79 Figure 16: Chart of P(D) vs. P(U|D) for the Case Study ..................................................84 vi

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Figure 17: Chart of the P(D) vs. P(U|ND) for the Case Study .........................................85 Figure 18: Chart of the P(D) vs. P(U|LD) for the Case Study ..........................................85 Figure 19: Influence Diagram of Accepting /Rejecting Donations ..................................90 Figure 20: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 ...................................................................................................................116 Figure 21: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 ...................................................................................................................116 Figure 22: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 ...................................................................................................................118 Figure 23: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 ...................................................................................................................118 Figure 24: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 ...................................................................................................................120 Figure 25: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 ...................................................................................................................120 Figure 26: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0.5, and =0 ...................................................................................................................122 Figure 27: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=05, and =0 ...................................................................................................................122 Figure 28: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=1.0, and =0 ...................................................................................................................124 Figure 29: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5,P(LD)=1.0, and =0 ...................................................................................................................124 Figure 30: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=1.0, and =0 ...................................................................................................................126 Figure 31: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5,P(LD)=1.0, and =0 ...................................................................................................................126 Figure 32: Graph of MS of P(D) vs. P(LD) Given P(U|D)=0.5, P(U|ND)=0.5, and =0 ...................................................................................................................128 vii

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Figure 33: 3-D Graph of the P(D) vs. P(LD) Given P(U|D)=0.5, P(U|ND)=0.5, and =0 ............................................................................................128 viii

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A DECISION SUPPORT TOOL FOR ACCEPTING OR REJECTING DONATIONS IN HUMANITARIAN RELIEF ORGANIZATIONS Francisco Javier Ruiz-Brand ABSTRACT With the increase in the occurrence of disasters (natural and man-made) that leave people injured, handicapped or dead, the disaster management theory is gaining more importance. As a consequence, human assistance and disaster relief organizations are managing increasingly more inventories anticipated to help people in need. Donations are the common means used by humanitarian relief organizations for procuring commodities to support some of their programs. Previous experiences have indicated that donations become a burden instead of offering relief when they do not match actual victims needs. Accepting or rejecting donations is a key issue that can produce not only economic losses but loss of lives as well. The objective of this thesis is to provide a means of assessing acceptance or rejection decisions using decision tree analysis theory and utility theory. The proposed model considers the inputs that a decision-maker may face when accepting or rejecting a donation. Such inputs include these categories: the probability of the occurrence of disaster, the need for and further use of a commodity, the unit price and holding cost of the item, the benefit provided by the donation, and the probability of having subsequent ix

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donations when the initial donation is initially rejected. Various scenarios are simulated in Excel environment through the Monte Carlo process. This will assess the varied impacts from the alternative inputs in the decision making process; a sensitivity analysis will evaluate the effects of various decisions. The results obtained from the simulation of the diverse scenarios indicate that the decision of accepting or rejecting donations is driven more by the possibility of the use of the commodity than by the probability of occurrence of the disaster. The findings from the model also indicate that the decision of accepting or rejecting is more sensitive to the relationship of sale price to benefit deployment of the commodity than to sale price alone. The simulation of the expected monetary benefit of the relief provided results in the development of graphs that can affect the decision making process when accepting or rejecting donations. x

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CHAPTER 1 INTRODUCTION 1.1 Motivation of this Research From 1997 to 2000, this author served as the Operative Department Head of the Secretary of Development in a city populated by 2.7 million people. One of the many functions of the department was to assist people in need who were affected by the occurrence of disasters. Potential donors, inside and outside of the organization, contacted the department head to notify him of in-kind donations for humanitarian assistance purposes. While some of the donations were categorized as free use, which meant that the commodity might have been used for several purposes, other donations were categorized as single-purpose depending on the donors intention. The former category was for free use, however, it stipulated the money was for assisting people and these people incurred no personal expenses; the latter donation category stipulated that the department state the intention of the donor. At that time, decisions were made based on historical data collected from the warehouse where the donations were stored. It provided information about past commodity demands over time. The historical information was complemented with the 1

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recommendations obtained from expert personnel who worked for non-governmental humanitarian relief and nationwide humanitarian organizations. The decisions that were made at that time failed to address the uncertainty of the occurrence of the disaster and the uncertainty of the commodity use. Neither included the comparison of the commodity price nor the expected benefit gained after its deployment. Additionally, no one assessed the possible advantages or disadvantages of not accepting the donation, which then assumed the task of procuring the item after the disaster occurred. The decisions were based on personal judgment and the application of traditional economic order quantity for inventory control policy. No one considered the application of an analytical tool that included the possible scenarios that could result after the acceptance or rejection of the donation. This project incorporates the uncertainties that any director of a humanitarian relief organization may face when deciding whether to accept or reject donations into an analytical tool. Decision tree theory is used to consider the possible uncertainties (i.e., event nodes) and the subsequent decisions (i.e., decision node) that have to be considered when accepting or rejecting donations. 1.2 Thesis Outline Subsequent to this introductory chapter, this thesis is organized as follows. Chapter 2 contains the research objectives of this thesis. Chapter 3 contains a detailed review of the background of the problem and literature relevant to the thesis. Chapter 4 provides the formulation of the model. Chapter 5 focuses on the sensitivity analysis of the model, 2

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assessment of the best decision, and deduction of the analytical expression for the decision making process. Chapter 6 is concerned with a case study of the model proposed. Chapter 7 explains how to implement this methodology for humanitarian relief purposes. Chapter 8 contains the conclusions that can be drawn from the study, discussing the implications of the results and the directions for further research. Appendix A exhibits the Visual Basic Code used for running the simulation. Finally, Appendix B displays, as an example, some of the graphs for P(D) vs. P(U|D), P(U|ND), and P(LD). 1.3 Background of the Problem 1.3.1 Introduction This section incorporates current information regarding disasters and current trends of HRO, in the United States and worldwide. Natural disasters and man-made disasters continue to take their toll on the lives of people all around the world. Despite the vast efforts of non-governmental institutions and governmental agencies in mitigations, there are many factors that continue to increase the vulnerability of people and the likelihood of occurrence of disasters. Unfortunately, though most deaths are due to preventable causes (Brennan & Nandy, 2001), disasters continue to pose a threat to people because of unpredicted factors, precarious economical developments, careless human actions, or a combination of these three factors. 3

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1.3.2 Natural Disasters Acknowledging that there is no singular definition of disaster that is universally accepted (Journal of Prehospital and Disaster Medicine, 2002; Shaluf, Ahmadun, & Said, 2003), McEntire (2001) defines disaster as such: [] the disruptive and/or deadly and destructive outcome of triggering agents when they interact with, and are exacerbated by, various forms of vulnerability. (p. 190) While the triggering agent comes from the natural environment, human activity, or a combination of both; the likelihood is that an individual or group will be exposed to and adversely affected by a hazard (Cutter, 1993). Natural catastrophes caused the death of 10 million people in the U.S. during the 20th Century. During the 1990s, natural catastrophes such as hurricanes, floods, and fires affected more than two billion people, an average of 211 million people per year. During the 1990s, there were 86 great disastersmajor natural catastrophes requiring outside assistance due to extensive deaths or losses. And in the 1950s, there were 20; later during the 1970s, 47 natural catastrophes (Worldwatch Institute, 2003). Natural disasters in the 1990s caused over $608 billion US dollars in economic losses, fivefold the figure in the 1970s, and affected 15 times the amount of people as in the 1950s (Abramovitz, 2002). 4

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1.3.3 Man-made Disasters Shaluf et. al. (2003) defines man-made disasters as complex systems of interdependent impacts that entail consequences beyond geographical boundaries and sometimes produce trans-generational consequences (Worldwatch Institute, 2003). He asserts that man-made disasters occur due to interactions among human, organizational, and technological factors. These factors become triggering events; which depending on the level of regulation, infrastructure, and preparedness of an impacted zone or population; may interact alone or in combination to produce a disaster. Some authors call man-made disasters politically induced disasters (Albala-Bertrand, 2000:p. 215), socio-technical disasters (Shaluf et al., 2003:p. 25), and differentiate the term man-made disaster from natural disasters (Journal of Prehospital and Disaster Medicine, 2002). A man-made disaster sometimes brings about complex humanitarian emergencies (CHE). CHE are described as humanitarian crises because of political instability, population displacements, propagation of refugees, famines, collapse of health infrastructure, and social instability. CHE accounts for more deaths, diseases, and casualties than other types of disasters (Brennan & Nandy, 2001; Hansch & Burkholder, 1996). According to the International Federation of Red Cross and Red Crescent Societies (1999; 2000) the CHE cause between 320,000 and 420,000 deaths worldwide each year. From 1990 to 1999, an average of 59,200 people died worldwide due to natural and man-made disasters combined. 5

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1.3.4 Trend of Peoples Vulnerability The odds of people being affected by the occurrence of a disaster is raised by the increase of the population, the damage infringed to nature because of new settlements, and the changes in the ecosystem due to human habits. The world population continues to grow at an annual rate of 1.16%, an increase of 73,447,055 human beings per year, to yield the total world population of 6,302,309,691 persons for 2003. Hence, a net increase of 2.4 human beings is yielded every second. The situation is more critical in the worlds less affluent countries. Ninety-nine percent of global natural increase of the population occurs in the less developed nations of the world.(U.S. Census Bureau, 2003). U.S Census Bureau also asserts that according to recent projections, the world population will rise to a level of nearly 8 billion persons by the end of the next quarter century, and will reach 9.3 billion persons by the year 2050. The increase of the density of population per unit of area entails the degradation of the surrounding ecosystem. It contributes to many aspects of environmental stress. Factors such as unplanned development and overpopulation of existing settlements generate, for example, the following conditions: soil degradation and erosion, deforestation, water and air contaminations, and emissions and pollution.. The United Nations states that population growth, although not the only cause of environmental damage, is especially prominent as the main factor of several types of environmental stress over agricultural resources such as soil, water, forest, and air (United Nations, 2001). Every time the natural equilibrium of nature is altered because of unplanned development, the likelihood of disasters increases. 6

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Global warming due to human habits is another factor that drives changes in the agents that work together in the ecosystem. Increased levels of greenhouse gas concentrations, due to anthropogenic contributions, produce the following conditions: alterations of polar areas; increase of sea level, recurrent heat waves, alteration of humidity and precipitation patterns; and increase of floods, storms, hurricanes, and fires. The U.S. Department of State, in the U.S. Climate Action Report 2002, asserts that greenhouse gases are accumulating in the earths atmosphere as a result of human activities, producing the rise of the temperatures of both air and ocean water. The report asserts that the environment in the U.S. will be substantially changed over the next few decades. These environment changes will likely disrupt some human activities if they drive the occurrence of disasters. 1.3.5 Counter Measurement to the Disaster Situation Facing the increasing numbers of people affected by disaster, various worldwide organizations continually assist people affected by disruptive events. These events, natural or a man-made disasters, produce fatalities, injuries, and economic losses. Disaster management is the managerial techniques (i.e., planning, organizing, leading and controlling the allocation of resources (Schermerhorn, 2001)) applied to the prevention, mitigation, assistance, and relief of people that may be or have already been stricken by a disaster. Disaster management includes the activities to control disaster and emergency situations and to help people at risk to avoid or recover from the impact of a disaster (Disaster Management Center, 2003). 7

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International relief organizations assumed levels of disaster management techniques that made them operate efficiently when dealing with disaster prevention and victim assistance. However, when disaster strikes a region that subsequently requires assistance, most non-governmental organizations supply humanitarian assistance relief operations, either by deployment of commodities or by assistance with technical personnel. Some charities hold in-kind donations to be used for relief operations (U. S. Census Bureau, 2002). During the year 2000, in the U.S. alone, the amount of non-governmental nonprofit organizations with funds and programs was 56,582 (U. S. Census Bureau, 2002). Their goals are to maintain or aid social, educational or religious activities; to provide public or societal benefit; environmental/wildlife support; and international humanitarian assistance. This were two and a half times more organizations than in 1980 (22,088 organizations), and 75% more than in 1990 (32,401 organizations). According to the U. S. Census Bureau, the total population in the United States during the year 2000 reached the amount of 292,339 million (2003), meaning there was one non-governmental nonprofit organization with funds and programs for every 5,166 residents. It does not include either the governmental organizations or the profit organizations devoted to serve the common good. Non-profit organizations under the Internal Revenue Service tax code 501(c)(3), 501(c)(4), and religious congregations as well reached the amount of 1.23 million organizations in the U.S. during the year 1998 (Independent Sector, 2001). Gadd (2003) exhibited that private support to charities in the United States during the year 2000 alone 8

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accounted for a total of $12,955 million dollars for the top 25-ranked organizations. Table 1 depicts the top 25-ranked private organizations for the year 2000. Some of the organizations such as Salvation Army, Red Cross, and Second Harvest are public charities that strive for the common good and play an important role as humanitarian relief organizations. The affluence of donations is strengthened by the sort of incentives that donors have in exchange of the contributions, as is the case of the tax system. Consider that in the U.S., money and property supplied to federal, state, and local governments for non-profit, schools and hospitals or humanitarian relief organizations (HRO), such as Salvation Army, Red Cross, United Way, CARE, etc., are deductible in the tax report system (IRS, 2000:p, 2). This macroeconomic variable, along with the U.S. custom of giving to charities, is behind the affluence of donations to HRO. This affluence of charity organizations is not only in the U.S.; for example, in the U.K., there were more than 185,000 charity organizations during the year 2003 (Dean, 2003). Not-for-profit organizations in the U.S alone, also known as third sector, are recipients of money, in-kind donations, and social services in a massive demonstration. More than half of Americans volunteer time to nonprofit organizations or causes (Hodgkinson, Weitzman, Noga, Gorski, & Kirsch, 1996). 9

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Table 1: Top U.S. Private Charities by Donations for the Year 2000 2000-Rank CharityPrivate support1 (x 106 Dollar)1 Salvation Arm y $1,440.40 2 Fidelit y Investments Charitable Gift Fun d $1,087.70 3 YMCA of the US A $812.10 4 American Casncer Societ y $746.40 5 Lutheran Services in America$710.30 6 American Red Cross$637.70 7 Gifts in Kind International$601.90 8 Stanford Universit y $580.50 9 Harvard Universit y $485.20 10 Nature Conservanc y $445.30 11 Bo y s and Girls Clubs of America$425.10 12 America's Second Harvest$421.70 13 Catholic Charities US A $414.40 14 Duke Universit y $408.00 15 American Heart Associatio n $396.40 16 Feed the Childre n $395.60 17 World Visio n $372.00 18 Habitat for Humanit y International$371.10 19 Yale Universit y $358.10 20 AmeriCares Foundatio n $326.40 21 Cam p us Crusade for Christ International$325.80 22 Cornell Universit y $308.70 23 Johns Ho p kins Universit y $304.00 24 Columbia Universit y $292.30 25 University of Pennsylvania$288.20 Source: The Chronicle of Philanthropy, Nov. 1, 2001 1 Private support consists of donations from individuals, foundations, and corporations. Does not include government funding and fees charged. 10

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CHAPTER 2 RESEARCH OBJECTIVES 2.1 Problem Statement This research proposes a model for assessing the acceptance of donations for humanitarian relief operations. It also determines the assessment of refusal of these donations as well. 2.2 Problem Description In the United States alone, estimation of donations to community-involved organizations reached the amount of $212 billion during the year 2002 above state and federal public funds allotted for donations in the country and overseas (American Association of Fund-Raising Counsel, 2002). It accounts for about 2% of the Gross Domestic Product (GDP) for the same year [$10,446.2 billion dollars (U.S. Department of Commerce, 2003)]. Inventories are precious assets not only for private enterprises, but also for any humanitarian relief organization (HRO). The acceptance or rejection of donations by the HRO impacts the amount of inventories on hand; thus, it affects the holding costs of the inventory. 11

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If the donation is accepted, the HRO will incur holding costs until actual deployment of the commodities. If the disaster strikes after the acceptance of the donation, the HRO with inventories on hand for relief operations, may find itself in an advantageous position in immediately deploying the commodities Providing the commodity as soon as possible is especially vital in critical situations where the time lag remains crucial between the occurrence of the disaster and the provision of the suppliesmedical supplies, drinkable water, sheets, etc. When the various items are needed and both the infrastructureroads, buildings, harborsand the operative capacity of the HRO allows the deployment of the relief inventory, the benefits may be affected due to costs incurred from holding the inventory. In that situation, the donation is rejected and the HRO will not incur holding costs. However, if a disaster occurs and the HRO is committed to provide relief to disaster victims, the organization may incur only two alternatives: Ask for a donation from a donor whose initial donation was rejected Purchase the commodity in the market place The uncertainties for making correct decisions are increased for various scenarios when attempting to match inventory on hand with the peoples actual needs. For example, there are situations where the HRO has inventory on hand, but the community does not need the inventory. The Pan American Health Organization (1999) claims that when commodities do not match the needs of the people, instead of being a relief, they can become a burden. 12

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Whenever there is the possibility of alternate outcomes from varied scenarios, the problem involves uncertainty. The acceptance of donations is naturally characterized by complexity and uncertainty, as the events and decisions that may drive the need of the inventory and its subsequent use may or may not even occur. The uncertainty that results from the interaction of these variables that model alternate scenarios/outcomes has to be assessed studying extensive criteria to result in the most accurate decision. Some of the events to consider when accepting or rejecting donations include the occurrence of the disaster, the need and use of the commodity, and the uncertainty of having a posterior donation when the initial donation was already refused. Hence, one should consider how likely is it to receive the same donation if it was initially refused. Some of the decisions determining acceptance or rejection of donations include the acceptance of the donation the first time it is offered, the purchase of the inventory that is needed when not received as charity, the use of the commodity, and the decision to do nothing. For the events and decisions already mentioned, the negative occurrence has to be considered as well. Conditions such as the uncertainty of the demand, the uncertainty about future donations, and the uncertainty of fulfilling the donors intention include some issues that should be addressed when devising any model to solve the uncertainties of accepting or rejecting donations. In the case of donation for HRO, management science techniques in general and decision tree models, in particular, offer a means for assessing the acceptance or rejection of donations. However, the review of the literature indicates a lack of the use of such techniques in the acceptance or rejection of donations. 13

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2.3 Scope The scope of this study is to assess the different inputs that should be considered when accepting or rejecting goods considered as vital or critical donations for humanitarian relief purposes. Various scenarios are to be evaluated to appraise the impacts of the subsequent factors that emerge when making decisions. The scope of this study is limited to the assessment of whether to accept or reject donations before the occurrence of a specific disaster event.. 2.4 Assumptions The assumptions are as follows: There are organizations, companies, and individuals willing to donate a great amount of commodities An HRO is a significant organization with national and international recognition (e.g., Red Cross, Salvation Army, Gifts in Kind International, etc.); society expects them to provide humanitarian assistance relief to disaster victims The donation will be made by providing commodities other than cashin-kind donations There is only one item to be donated in considerable quantities After the occurrence of the disaster, the HRO has the choice of either requesting the commodity through donation channels or purchasing it 14

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2.5 Importance of this Study There exists an ever-increasing amount of donations in the last decade in the U.S. (U. S. Census Bureau, 2002); thus, the use of decision tree analysis to cope with uncertainty when accepting or rejecting donations will save money and increase the effectiveness of the HRO. Many HROs worldwide approach the decision process of accepting/rejecting donations through empirical estimations based on previous experiences. The use of quantitative techniques will improve the decision making process. As the donors intention (i.e., the expected use of the commodity as well as who is expected to be the recipient) is paramount for the HROs long-term existence, the donor would appreciate the HROs decision when it employs sound assessment techniques. Even a rejection, when properly explained from an analytical standpoint, will be acknowledged by the donor and may prepare for future donation requests. The decision process of accepting/rejecting donations in the aftermath of a disaster is an issue that has been covered by the literature reviewed in this research. In such circumstances, the identification of the needed items is determined by the shortage assessment from the organizations initiating the relief operations. After a disaster, using decision support systems already available in the market will expedite the tasks. These systems keep track of the commodities, match the commodities with the people in need, and assess when a new procurement is needed (PAHO, 2000). In this research, the issue of decision making under uncertainty applies to the acceptance or rejection of commodities aimed to aid people in need during humanitarian relief operations. 15

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CHAPTER 3 BACKGROUND AND LITERATURE REVIEW 3.1 Procurement Methods: Donations The procurement method for relief assistance entails the understanding of the characteristics of the disaster event. According to PAHO (2000), the procurement methods that humanitarian relief organizations (HRO) use to provide assistance to people in need before, during, and after the occurrence of a disaster include the following: Donations received from the national and international community Direct purchase from the local or external market Acquisitions of products and goods through temporal loans In Table 2 the same organization depicts the advantages and disadvantages of donations. Table 2: Advantages and Disadvantages of Donations for Humanitarian Relief Advantages Disadvantages Free or low-cost (note: every donation has a cost) Promotes national and international solidarity Frequently, items were not requested Supplies sent may not meet local needs If unusable, their handling leads to a waste of time and resources It is hard to reject them if they are useless Source: Logistics Guide to Emergency Supply Management. Draft. (PAHO, 2000: p, 44) 16

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3.2 Inventories for Humanitarian Relief Operations Some of the characteristics that entail donation decisions include these items: The demand is uncertain The commodities are stored until they are needed It is accepted before the disaster strikes (i.e. order at the beginning of the period) The amount of the donation has to be determined The objectives are both to minimize expected costs and to supply the demand Goods at the end of the period may or may not be sold or used for other purposes Costs associated with accepting the donations may or may not be present If the donation is refuse, there is a penalty cost associated because the commodity is needed and the demand may not be met. Considering humanitarian relief operations, the penalty cost is very high, as the commodity is intended to aid disaster victims. One of the reasons for any enterprise to keep inventory available is to allow a buffer between supply and demand (Waters, 1992). In the case of the HRO, the reason to maintain an inventory enables the organizations to immediately supply other the inventories upon demand. The demand of the commodities may occur before, during, and after the occurrence of the disaster. For any enterprise, as is the case of the HRO, uncertainties often play the main role in the decision of maintaining inventories (Nahmias, 2001). Some of the uncertainties are as follows: The type and the amount of inventory needed during and after the disruptive event 17

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The lead-time that elapses from the moment the HRO makes the decision to purchase and to order the commodities until the time when they arrive at the HROS warehouse Additionally, problems may arise with the supply of the needed items when the infrastructure (e.g., harbors, airports, roads, buildings, etc.) are damaged because of the disaster. HROs seek to provide humanitarian assistance in case of a disaster and maintain inventories as a way to satisfy needs that may arise. The inventory is maintained from the acquisition time until it is needed. The items provide relief of crucial necessities for disaster victims. The inability to provide the inventories after the occurrence of the disaster entails a risk for the people and incurs costs to the HRO. This is a penalty cost for not supplying the needed commodities. A tangible penalty cost is the monetary expense the HRO may incur for amending a situation due to lack of assistance for disaster victims, such as facing a sudden epidemic outbreak after a tragedy. Intangible penalty costs include the loss of prestige from criticism of watchdog organizations, anger of victims and non-victims, and complaints of donors. However, when the donations do not meet the peoples needs or the assistance has not been requested, instead of being a relief, the abundance of donations rapidly becomes a burden (PAHO, 1999). The same PAHO (2000) claims that: When they comprise items that have not been requested, are not a priority, or do not meet the needs generated by the emergency, they complicate unnecessarily the logistics of relief operations. (p. 42) 18

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Some of the available literature indicates that the in-kind donations in the aftermath of a disaster can lead to a secondary disaster. While donations help the people in the recovery process, there remains the problem when both the type and quantity might not be properly assessed in accordance with [] the real needs of the victims; they can overwhelm disaster managers, contribute to chaos, and lead to a secondary disaster (Bittner, 2003:p. 1). Even a financial donation can encounter several problems. For example, in the aftermath of the attack to the World Trade Center in New York on September 11, 2001, Red Cross donors were disappointed when they realized that the relief organization intended to use some of the contributions for needs unrelated to the attacks (Association Management, 2002). As a consequence, some changes were introduced in the fundraising Donor DIRECT (Donor Intent Recognition Confirmation and Trust) Program of the American Red Cross. Starting July 31, 2003, the revamp of the program assures that advertisements and donor solicitations will explain that donations to the Red Cross Disaster Relief Fund are used to help victims of all types of disasters besides the program that the donor is contributing to, e.g., earthquakes, floods, tornadoes, tropical storms, hurricanes, house fires, etc. (Orfinger, 2003). It will allow the Red Cross full freedom in deploying the donations wherever they are needed. According to Fiedrich et al. (2000), the extent to which computer-based decision systems are currently used appears to adequately enhance relief operation efficiency. Some of the software available is the GIS-based HAZUS (Natural Hazards Loss Estimation Tool) developed by the National Institute of Building Science (2003). Another 19

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computer database system for controlling and managing inventories, and matching them with the people in need is SUMA (Supply Management Project). SUMA was developed by PAHO (Pan American Health Organization) and by HRO and governments, which enhances government and organization capacity to handle supplies during a disaster situation (PAHO, 1999). Fiedrich et al.,(2000) states that the recent efforts in applying computational models to disaster situations are far from state of the art. He also claims that these computational models are solely information systems, and they do not give active support in the decision making process. There have been few direct studies about when to accept donations. The importance of deciding when to accept or refuse donations resides in the consequences of holding the inventory. The commodity may become key goods in alleviating disaster victims needs; however, if the commodity is not needed when donated, it may become a burden. 3.3 The Cost of Human Life For most people, assigning monetary value to a human life is unacceptable (Fuguitt & Wilcox, 1999); however, the monetary valuation of human life is necessary for cost benefit analysis. In doing so, one can compare the action of saving human lives, or providing relief to a disaster victims, with other competing policies where the resources might be allocated, such as improving public infrastructure, building heath centers, and boosting education programs. Two methods commonly used in assessing the value of human life include: 20

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The human capital method, introduced by Rice (1967), estimates the price of human life by assessing the present value of expected future earnings of an individuals lifetime. When the future personal expenditure is subtracted, the present net value is obtained. The value of mortality risk method, introduced by Schelling (1966), is currently known as the value of statistical life (VSL), the estimation of an individuals preference of saving a statistical life. It is the price that any individual is willing to pay (PWTP) or the cost he or she is willing to accept (CWTA) for a small change in the probability of death or mortality risk. The most relevant measure of determining the PWTP is the statistical death, which are unnamed individuals belonging to a subset of the society whom are expected to die. The assumption is that since the individual does not know if he or she belongs to the subset, the person will incur a PWTP for reducing the likelihood (risk) of being part of the subset. Though Federal agencies in the United States have their own guidelines for assessing health and safety costs and benefits, there have been situations where various values were employed even within the same agency (Krupnick, 2002). These values proposed for assessing the value of life, or VSL, vary among several authors who proposed different assessments. For example, the U.S. Environmental Protection Agency (1999) estimates the average VSL is worth $4.8 million with a standard deviation of $3.2 million (in 1990 dollars, $6 million in 1998 dollars), while Mrozek & Taylor (2002) exhibit a compendium of 33 studies with estimation of the VSL varying from $50,000 21

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dollars to $21.5 millions dollar (in 1998 dollars). The latter conclude their research by asserting that a reasonable assessment of the VSL, through past-labor market and meta analysis, ranges from $1.5 million to $2.5 million dollars (in 1998 dollars). 3.4 Assessing the Benefits of the Deployment of Commodities The difficulties of undertaking cost benefit analysis exist in assigning monetary units to all costs and benefits associated with particular alternatives (Levin, 1983). Assessing the benefit costs provided by the deployment of an item donated for disaster victims is a subjective assessment, unless there is a field calculation (i.e., after the disaster occurrence) that includes real costs of the deployment of commodities and subsequent benefits to the individuals and the society. An estimation of the benefit would include the costs associated with not providing the item during the relief operation. For example, if vaccines are not provided to a population at risk, then one must consider the cost associated with an ulterior consequence such as an epidemic outbreak. To weigh either the benefits of peoples life changes, such as providing non-vital commodities, or the benefits of saving lives (providing primal commodities), the benefits should be translated into monetary values to apply quantitative techniques. Economic theory assumes that individual utility perception is exhibited by how trade products, services, and money. Therefore, when people trade goods and services, there is a utility equivalency between what is exchanged. Price willingness to pay (PWTP) and cost willingness to accept (CWTA) are two monetized values of an individuals utility assigned to the willingness to pay or accept compensations for these 22

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goods and services, or the deprivation of them. Consider that someone with a terminal illness who is going to undergo a medical treatment that he or she values at $10 million is WTP that amount as a trade-off for individual recovery. Similarly, the salary earned by an employee for performing a job is the CWTA as compensation for being deprived from the freedom to spend time in whatever he or she wants. The PWTP and the CWTA compensation are two measures of the utility conferred to goods and services in a trade-off transaction. Although the PWTP and the CWTA are not necessary equal [...] economists expect that the difference between them will be small in most cases (U.S. Environmental Protection Agency, 2000: p, 60). 3.5 Decision Trees Analysis A decision tree is a graphical diagram compound of branches and nodes. A branch is the path following a decision or an event. A node is the representation of the point where one or several branches will divide. A node can be a either a decision node, where the criteria of the decision maker comes into play, or an event node where the uncertainty of the different outcomes is represented by assigning every branch a probability number. In a decision tree, the user computes the expected value and makes a decision based on that value. The primary benefit of a decision tree diagram is that it provides a picture of the decision-making process, which helps the decision maker understand the possible variables and outcomes that are interacting in the expected value (Taylor, 1999). Another advantage is that the decision tree diagram provides a fully detailed view of the structure and the chronological sequence of the decision problem (Bielza & Shenoy, 23

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1999: p, 1553). Trigeorgis (1996) states that decision-tree analysis and simulation are practically useful in dealing with uncertainty and with the modeling of interdependent variables and decisions (p. 23). Doctor, Newton, & Pearson (2001) state that decision trees are relatively old technology in decision analysis terms (p. 83) but claim that decision tree models include a broad application in the literature and in the industry. They point out these other advantages of the decision-tree approach: They are easy to understand for the personnel involved in the decision-tree model and easy to solve Their construction can help the decision-maker understand the process and the variables involved in it They help with understanding the relationship between probabilities associated with the event nodes and the impact in the final outcome It is easy to incorporate variations in the inputs and facilitates the calculation of revised success probabilities Rational economic decision-making models assume perfect markets and perfect information; however, the real word decision makers have scarce information about hazards and market conditions that do not behave as models (Fuguitt & Wilcox, 1999; Mileti, 1999). Hence, decision tree analysis provides a useful tool to determine the uncertainties involved in the decision-making process of accepting or rejecting donations. The impact of providing the commodity for humanitarian relief should be transferred into a monetary value. For example, to define cost-effectiveness of a 24

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collective risk, a life-saving cost (LSC) must be assessed. The financial impact to the society of the loss of a person is an assessment of the LSC, or the amount that a life insurance company has to pay to the victims relatives. Nevertheless, the emotional LSC may be higher and varies across age-groups and individuals as well; LSC is estimated to be between $1 and $10 million (Beroggi, 1999: p, 162). Cost of human life differs across groups of individuals. For example, for air pollution policies, the Bush administration valued the life of someone over 70 at $2.3 million, and for someone younger at $3.7 million (Tierney, 2003). Also, the value of a life differs across levels of development; life in developing countries are worth less than in developed countries). 3.5.1 Decision Variables An action (a) of accepting or rejecting donations is warranted to solve the problem of how to either maximize profits or minimize costs. Any action is assigned a decision variable ( jj x ) with the value of the intensity of the action. In the action of the acceptance or rejection of donations, the intensity of the action must be a binary decision variable, either 0 or 1, 0 being the rejection and 1 being the acceptance of the donation. Therefore: {0,1} B where jjjjxaxa The actions of the decision are defined explicitly in terms of scenarios by the model. In the terms of Beroggi (1999), the uncertainty about the future state of the system is defined in partitions of the uncertainty space. Each partition of the uncertainty space 25

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has states, and the subsequent combination of the states define the scenarios that must be assessed during the decision-making process. The potential action is first determined by: The evaluation measure that describes the actions performance (acceptance or rejection) with respect to the evaluation criterion (maximize profits or minimize costs) The scenarios acceptance or rejection The use or non-use of the donation The purchasing of the commodity, having a later donation after the first refusal; and The decision-maker aptitude. 26

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CHAPTER 4 FORMULATION OF THE MODEL 4.1 Notations P(D): Probability of occurrence of the disaster P(ND): Probability of no occurrence of disaster P(U): Probability of use of the commodity P(NU): Probability of not using the commodity P(U|D): Probability of use of the commodity given the occurrence of disaster P(U|ND): Probability of use the commodity given the no occurrence of disaster P(NU|D): Probability of not using the commodity given the occurrence of disaster P(NU|ND): Probability of not using the commodity given no occurrence of disaster P(LD): Probability of having a later donation given the occurrence of the disaster P(NLD): Probability of not having a later donation given the occurrence of the disaster PWTP: Price Willing to Pay CWTA: Cost Willing to Accept SP: Sale Price HC: Holding cost : Ratio sale price to benefit. Therefore = SP/PWTP : Ratio holding cost to sale price. Therefore = HC/SP 27

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4.2 Equalities P(ND) = 1 P(D) P(NU|D) = 1 P(U|D) P(NU|ND): 1 P(U|ND) P(NLD): 1 P(LD) CWTA = PWTP 4.3 Building the Model All the information contained in the graph exhibited in Figure 1 was gathered and then incorporated into the decision tree model displayed in Figure 2. The decision tree model is suggested as a means of assessing the best criteria between accepting and rejecting a donation towards a contingent emergency situation that may trigger a disaster. The advantage of the decision tree is that it provides a picture of the variables included in the decision making process and the possible outcomes. The decision tree represents a sequence of events with their outcomes in a given situation. As the exact date of the occurrence and the magnitude of a possible natural disaster are often not known in advance, the historical data collected about previous disasters provide a means for evaluating the occurrence probability of a new disaster during the considered time period. The notation for the probability of disaster occurrence is P(D).Similarly, the disasters uncertainty is coupled with the uncertainty of the commoditys use that was previously accepted. A probabilistic number is then associated 28

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with the use of the commodity either given the disaster P(U|D) or given the fact of no occurrence of disaster P(U|ND). Node 4 and node 5 depict this situation in Figure 3. Do not use Time N ote: Every terminal situation framed by the rectangles, entails costs and benefits for the HRO. Purchase Use Ask for a Later Donation Do nothin g Donation Rejection Disaster Use Do not use Use Acce p tance Acce p tance Decision Rejection Decision Figure 1: Decisions and Events when Accepting or Rejecting Donations For situations in which the donation is rejected and the disaster occurs, the HRO would have to either go back to the previous donor asking again for the commodity that was rejected, find a new donor, or purchase the commodity in the marketplace. 29

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LegendUseDecision NodeDisasterEvent NodeTerminal ValueCannot UseAcceptUseNo disasterCannot UseDonation"Later" DonationUseDisasterBuy CommodityUseNo DonationRejectDo NothingNo Disaster 30 Figure 2: Graph of the Decision Tree Model 30

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LegendUseDecision NodeDisasterEvent NodeTerminal ValueCannot UseAcceptUseNo disasterCannot UseDonation"Later" DonationUseDisasterBuy CommodityUseNo DonationRejectDo NothingNo Disaster T 1 N ode 4 T 2 N ode 2 T 3 N o d e 5 T 4 N ode 1 31 T 5 N ode 6 N ode 7 T 6 N ode 3 T 7 T 8 Figure 3: Layout of the Decision Tree Diagram 31

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Such uncertainty is evaluated through a probability number assigned to the options of the disaster occurrence P(D) and the probability of having or not having a later donation P(LD) and P(NLD) from either the former donor or a new one. After the disaster has occurred and the peoples needs that arise because of the tragedy have been identified, the HRO will only accept or purchase what the organization considers will be used. Terminal nodes T-5 and T-6 in Figure 3 exhibit the certainty of using the commodity, once it is accepted or purchased in the market place, respectively. Once a disaster occurs and the need is properly assessed, the acceptance of the donation or the decision to buy the commodity is based upon demand of the item. Hence, there is no probability associated with the use of the commodity after the disaster occurrence. 4.4 Description of the Model The description of the model is as follows: The decision maker has the option to decide to accept the donation or to reject it (decision node 1 in Figure 3). If the donation is accepted, the decision maker is facing the scenario of the occurrence of the disaster (node 2) and the conditional subsequent use of the item that is accepted (node 4 and node 5) The conditional probability of either using of the commodity given the disaster or given no disaster is evaluated through the various probability numbers associated with the assorted branches of the event (node 4 and node 5). Each of the branches 32

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at the end of node 4 and node 5 (i. e., terminal node T 5 and T 6) entails an alternate gain or benefit that is monetized for evaluation purposes If the commodity donation is rejected, as is depicted in node 3, the decision maker has to face the uncertainty, as is the case when the commodity is accepted, of either occurrence or no occurrence of disaster If there is no disaster after rejecting the donation, then there is neither cost nor benefit associated with the decision, as is exhibited by node T-8. If a disaster occurs, there is a probability that a later donation will be obtained from either the former contributor whose donation was rejected before the occurrence of the disaster or from a new donor or donors. This situation is displayed by node 6. The example where there is no later donation triggers the decision node 7; the HRO may opt to either buy the commodity, in which case the organization guarantees that the item will be used or may decide to do nothing. As is the examples mentioned in previous scenarios, the rejection of the donation entails different cash flow at the end of the node 3 (i.e., terminal node T-5 through T-8). Figure 4 exhibits the various event and decision nodes and the cash flow associated with the different scenarios. 33

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34 Figure 4: Decision, Events, and Cash Flow for the Donation Process 34

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4.5 Assumptions To run the model, the SP and the HC are computed as a fraction of the PWTP as follows: The holding cost (HC) is a percentage of the sale price (SP) of the item as described by in the equation HC = *SP The sale price (SP) is a percentage of the PWTP, as described by in the equation SP = *PWTPThe CWTA is the negative value of the PWTP. Note that since the word cost means a negative value for the HRO; therefore, the CWTA in the cash flow diagrams (e.g., Figures 4 and 5, and Tables 2 and 3), though without negative sign is indeed a negative value. The model is run under the following general assumptions: The numbers of items of the donations is high The HRO is a considerable organization with national and international recognition Market price of the commodity is the sale price of the product at the market place The SP is the price of buying the commodity after and before the occurrence of the disaster. It is assumed that the SP is the same in both cases HC is the cost the holder of the inventory will incur during the time elapsed from the moment of the acceptance of the donation until the time that it will be distributed. It is expressed as a fraction of the sale price of the item by The PWTP is the monetary value of the HROs efforts. It is the organizations monetary estimation of providing relief to the people in need 35

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The cost CWTA is the monetary cost for the HRO in the case that the commodity would not be provided when the people need that item The validity of the decision tree diagram is for a specific timeframe defined by the decision-maker. It is within such a timeframe that the different probabilities and different assumptions have any validity. Nonetheless, the same model can be used when the timeframe had elapsed without the use of the donation, and a new assessment regarding keeping or disposing of the donation may be estimated. For example, if any further information or revised probability is available, the new data may be entered into the model and the new EMV should be re-assessed. Consequently, the decision tree model can be used for several time periods in which the new input data have to be reviewed and updated In the decision tree diagram, the scenarios will be the combinations of different states of the uncertainty space that is a combination of the probability events and decisions already mentioned 4.6 The Scenarios There are eight possible scenarios for every path of the decision tree diagram. Each branch goes from node 1 to one of the terminal nodes T1, T2, and T8, as illustrated in Figure 3. Therefore, with the following notation, the complete partitioning of the uncertainty space of the decision tree diagram is as follows: 36

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4.6.1 Notation for the Different Scenarios A: Acceptance Decision R: Rejection Decision D: Probability of Disaster ND: Probability of No Disaster U: Probability of Using the Commodity NU: Probability of Not Using the Commodity LD: Probability of Having a Later Donation NLD: Probability of Not Having a Later Donation B: Decision to Buy the Commodity NB: Decision to Not Buy the Commodity DN: Decision of Doing Nothing 4.6.2 Uncertainty Space of the Scenarios S = {A D U, A D NU, A ND U, A ND NU, R D LD U, R D NLD B U, R D NLD NB DN, R ND} The regions of the uncertainty space defined by the previous combinations are a collective exhaustive set of the uncertainty space. It accounts for the possible outcomes of the proposed model. The outcomes associated with each of the scenarios depend on the input values of the model. The costs and benefits of making a set of decisions are represented by a cash flow at the end of every branch, as is indicated at the end of any node exhibited in 37

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Figure 4, and incorporated into the decision tree in Figure 5. Cost variables of the decision tree model are holding cost, sale price of the commodity, and the cost that the organization may incur if the humanitarian assistance is not provided (i.e., CWTA). Similarly, the benefit is what the decision maker considers would be the payoff for assisting the people in need (i.e., PWTP). Tables 3 and 4 summarize the possible scenarios and their consequences. Table 3: Possible Scenarios and Consequences if the Donation is Accepted Accept Disaster Use Consequences X X X PWTPHC X X CWTA-HC X X PWTP-HC X HC Table 4: Possible Scenarios and Consequences if the Donation is Rejected Reject Disaster New Donation Buy commodity Use Consequences X X X X PWTP X X X X PWTP-SP X X CWTA X None Note: The X in cells means that the action takes place, conversely, the absent of the X symbol in the cell means that the action does not occur 38

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39 Figure 5: Layout of Probabilities and Cash Flow of the Decision Tree Diagram P(U/D)P(D)PWTPHCScenario 1$$$$$$P(NU/D)CWTA-HCScenario 2Accept Donation$$$$$$P(U/ND)P(ND)PWTP-HCScenario 3$$$$$$P(NU/ND)-HCScenario 4$$$Max(Accept Donation, Reject Donation)P(LD)UsePWTPScenario 5P(D)$$$$$$$$$Buy CommodityUseP(NLD)PWTP-SPScenario 6$$$Reject Donation$$$Do Nothing$$$CWTAScenario 7$$$LEGENDP(ND)Decision Node$0Scenario 8Event Nodes$$$Terminal Node Probabilities Decision Node Event Node Partial "Cash Terminal Values/Total "Cash Flow" of the branch Final Expected Monetary Value 39

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4.7 Simulation of the Different Scenarios To determine the impact of the variables that the model involves, a Monte Carlo simulation was run. The variable generated by the pseudorandom numbers is the PWTP. The EMV is calculated as the criterion for deciding which of the two decisions, accepting or rejecting the donation, should be selected. The random numbers are generated from a uniform distribution between zero dollars ($0) and a billion dollars ($1 x 10 9 ). Excel environment and Visual Basic Applications for Excel (VBA) code is chosen to run the simulation for two factors: the availability and the customizability). Excel environment is available and it is used in most business settings; one of its advantages includes the ease with which it can be modified to fit the users needs. The VBA for Excel code complements any limitation that should arise from any of the add-in functions that run by default with Excel Another advantage of the VBA for Excel code is that it may be run and invoked from any of the spreadsheets contained in the Excel workbook. 4.8 Generating the Random Numbers To run the Monte Carlo Simulation, a pseudorandom chart was populated through the use of the uniform probabilistic distribution function RAND from the built-in functions available in the Excel software. VBA for Excel code was used for populating the spreadsheet. The size of the pseudorandom table was 1,000,000 cells out of the 16,777,216 cells contained in each worksheet (65,536 rows by 256 columns). Appendix A exhibits the VBA code for generating the table. 40

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To run the different scenarios, the values of all variables are changed in incremental amounts of 0.10. For example, the probabilities (i.e., P(U|D), P(U|ND), P(LD|D), and P(D)) are incremented from 0.0 to 0.1, then from 0.1 to 0.2, and so forth, up to 1.0. The same method was followed with the SP and the HC whose values are expressed as percentages of the PWTP, as follows: = SP/PWTP = HC/SP 4.9 Assessing the Input Data to the Model 4.9.1 Probability of the Use of the Commodity The use of the commodity depends on the disaster. For example, the use of a large stock of sheets may depend on whether the disaster is from a cold wave or a hot wave. A method to obtain the probability of use of the donation P(U) is to look for the type of disaster that is expected to occur. Some of the factors that should be considered when assessing the probability of use and the need of the donation include the onset of the disaster, the vulnerability of the people along with the geographical location, and the historical data of the damage generated for the type of disaster under consideration. The Pan American Heath Organization (PAHO, 2000p. 36) states the following: Based on the experience of many humanitarian organizations around the world and the thousands of emergencies they have faced, it is now possible to determine which supplies are most likely to be needed. Additionally, the same organization claims that international standard 10 categories are recognized as commodities 41

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that are donated for humanitarian relief purposes. These categories include these items: Drugs Water and environmental sanitation Health Food and drink Shelter, housing, electricity, construction Logistics, administration Personal needs, education Human resources Agriculture and animal husbandry 10. Unclassified The various impacts due to the disaster occurrence result in different needs of the commodities retained by the humanitarian relief organization. The impacts are described as a function of the type of disaster. For example, the Pan American Health Organization (2001), exhibits the short term effects of major disasters, as displayed in Table 5. This table and the geographical location historic data of the expected disaster can be used to assess the probability of the need of the donation. For example, a donation of bottled water is critical in case of an earthquake, but minimal in case of progressive floods with long onset time. See effect Damage to water supply system in Table 5. In the same way, a vaccine for transmissible diseases is critical for disasters causing overcrowding situations and also on the impact suffered for 42

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Table 5: Short Term Effects of Major Disasters. Source: Pan American Health Organization (2001p. 8) the sanitary infrastructure. See the effect Greater Risk of transmissible diseases in Table 5. In the model, the occurrence of the disaster is incorporated as a probability and is related to the type of disaster. For example, hurricanes exhibit a high probability of occurring in the southeast United States than a disaster earthquake. Therefore, the use of the commodity depends on the occurrence of the disaster and depends on the type of disaster as well. 4.9.2 Probability of the Occurrence of the Disaster The probability of the disaster P(D) is the likelihood of the occurrence of a disaster. The impact generated for the various types of disasters has been tabulated from 43

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historical strikes of various events. The historical data is organized to forecast varied occurrence from selected disasters. Statistics applied to the occurrence of disaster and the levels of communication among the humanitarian relief organizations have increased the understanding of the probability of the occurrence of different disasters. The World Wide Web helped share the knowledge about hazards, risks, and statistical records about the historical occurrence of different disasters. Historical data from previous events contributed to understanding disasters trends, forecasting future occurrence, and estimating possible consequences. Governments, humanitarian relief organizations, and universities are collecting data and preparing maps to share geographical knowledge about historical occurrence of disaster. This information is updated with the new data available every time a disaster takes place. This information is organized and processed to obtain the probability of the occurrence of the different disasters. To illustrate, the United States Geological Survey (USGS) (U.S. Geological Survey, 2003), through its web site, offers the geographical distribution of major hazards in the United States Figure 6 exhibits the distribution of six major hazards: Earthquakes, volcanic, landslides, flooding, hurricanes, and tornadoes. 44

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Figure 6: Geographical Distribution of Major Hazards in the US (Source: United States Geological Survey) The information was obtained from historical occurrence of disasters. Each qualitative scale (e.g., highest, high, moderate) has either a probability of occurrence associated with it, or a recurrence interval of the hazard. According to the website, the period of observation is 1888 to 1988, and the number of hurricanes per 100 years is expected to pass within 75 nautical miles from the coast. For example, the highest risk area for hurricanes (red-line in the east coast of Florida), which reveals 60 hurricanes in 100 years, skim up the east coast. It means that the occurrence interval of a hurricane hitting the East Coast of Florida is 60 years and the probability of the occurrence per year is 0.06. However, this probability increases depending on the certainty that a hurricane is going to strike the peninsula. 45

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As an example for the hurricane case, meteorological services may estimate that the occurrence of a hurricane that is heading Florida in the following five days is 70 percent or 0.7. 4.9.3 Probability of Having a Later Donation The probability of having a later donation depends on the role played for the humanitarian relief organization and the relationship organization-stakeholders. For example, if the organization boasts an outstanding performance and enjoys high credibility with the commodity donor, he or she donor may be more willing to donate in the future even though the current donation was refused. A question that should be answered for every HRO is how bound is the relationship organization-donor? Can the relationship endure if there is rejection of a significant donation? The assessment of the probability of incurring a later donation should be calculated by each humanitarian relief organization according to their relationship with its donors. Some of the factors that influence the LD include: The countryvarious countries exhibit dissimilar donor profiles Level of wealth of the society Tax structure Type, magnitude and location of the disasterconsider that the donor could also be affected by the disaster and the inventory is spoiled Type of donor 46

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Donors intentionif the intention of the donor is not going to be honored, then the donations may have to be rejected Type of relationship with the donorprior donor rejection may affect future donations Type of donation 4.9.4 Eliciting of the Ratio Holding Cost-sale Price () is defined as the relationship between the SP and the HC. Therefore, = HC/SP. It means that is greater than one when the HC surpasses the SP, and conversely, is lesser than one when the SP surpasses the HC. For the same SP, the higher the HC the higher For the humanitarian relief organization, the higher the factor the less likely an organization may keep the inventory on handt he SP is less than the holding cost. In such cases, the best decision may be to wait until the disaster occurs, then buy the commodity rather than accept the donation subsequently at a high HC. 4.9.5 Eliciting of the Ratio Sale Price-benefit () is defined as the relationship between the SP and the monetized benefit as PWTP. Therefore, = SP/PWTP. It means that is greater than one when the SP surpasses the PWTP, and conversely, is lesser than one when the PWTP surpasses the SP. For the same expected benefit defined as the PWTP, the higher the SP the higher the 47

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For the humanitarian relief organization, the acceptance of the donation depends on the trade-off between the SP and the benefit. For example, with a high PWTP and a low SP, the acceptance of the donation may not define the best decision; the lower the SP the more an organization should wait until the occurrence of the disaster and then purchase the donation. Conversely, a high PWTP may make the decision of the acceptance as the best decision regardless the SP of the commodity. 4.10 Summary of the Model The tree diagram is proposed as a way to assess the best decision when accepting or rejecting donations for humanitarian relief purposes. The advantage of this method is that it incorporates the decisions and the probability of the events occurring in the decision making process. The decision tree model provides a broad picture of the entire process, which may help the personnel unfamiliar with the process to understand. It will enable personnel to determine various outcomes of the decision. To simplify and run the model some assumptions need to be made and are already explained in section 4.5. The path from the initial node of the model to the end of every branch defines a scenario that yields a different outcome. Every outcome has a monetized value associated with the decision and possible costs and/or benefits are depicted in a graph of cash flow For running the model, the roll-back method is used with the purpose of maximizing the Expected Monetary Value of each decision. A Monte Carlo simulation is 48

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run This will generate random numbers using Excel and obtain the possible outcomes depending on the different inputs used with the model. 49

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CHAPTER 5 THE MODEL 5.1 Assessment of the Best Decision The calculated Expected Monetary Value (EMV) is a means of deciding which of the two alternatives of accepting or rejecting the donation should be chosen. Expected value is computed by multiplying each decision outcome for each alternative (state of nature) by the probability of its occurrence. When the probabilities of occurrence can be assigned to the possible scenarios, the expected value serves as an essential tool employed as a decision criterion (Taylor, 1999). If the manager is risk averse, he or she may use the EMV criterion to determine the correct outcome (Von Winterfeldt & Edwards, 1986). In assessing whether to accept or reject the donation, the expected monetary value is considered. This suggests there is no special preference between a change of lower probabilities and the same higher probabilities change. As previously mentioned, the decision maker of the model proposed is risk averse. The expected lottery value, or the subjective preference for certain outcomes as used by assessing the EMV in the decision tree model is the lotterys certainty equivalent. This applies if a person is indifferent between the lottery and its certainty equivalent is considered risk neutral, and a person 50

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who prefers the lottery over the certainty equivalent is risk prone (Beroggi, 1999). Beroggi also states that when drawing the subjective preference of different values (outcomes) of the EMV, three alternative value graphs can be obtaineda convex value graph defines a decision maker who prefers increases of low outcomes instead of high outcomes by the same change of the Expected Value Thus, one has a risk averse decision maker. A concave value graph means that the decision maker prefers an increase of high outcomes more than one from an increase of low outcomes by the same change of the Expected Value, resulting in a prone decision maker. Finally, a linear value graph defines a decision maker who is indifferent between an increase of high and low outcomes by the same Expected Value. The expected value of a random variable x, denoted by E(x), is calculated by the following expression, where n is the number of values of the random variable x: niii)*P(xxE(x)1 In the proposed model, the best strategic decision is the one that maximizes the profits measured by the EMV. Revealed by the sensitivity analysis of the decision tree model, any change in the independent variable will affect the dependent variable, the EMV. The sensitivity analysis provides the HRO manager with an analytical tool that helps assess what should be the right decision and its further implications in view of changes in the model inputs. Furthermore, under the uncertainties mimicked by the Monte Carlo Simulation, the HRO may decide to act proactively by running the model and then asking potential donors to contribute with in-kind supplies. 51

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5.2 Sensitivity Analysis To perform a sensitivity analysis, the model was run changing both the P(U) and the P(D), and a matrix named Matrix of Expected Value was populated with the corresponding value on its cells. In the decision tree diagram, the selected branch, one for acceptance and zero for rejection, defines the one with the greatest EMV. The calculation process is done from right to left, rolling back toward node number one. In the Matrix of Expected Value, the P(D) were displayed on the rows of the matrixes while those on the columns displayed either the P(U|D), P(U|ND), or the P(LD). As an example, the case for the random numbers or benefits of PWTP=$147,003,533 is displayed in Table 6. The matrix of the EMV exhibits the expected value, addressing different probabilities, yet provides no information on the probable decision. Figure 7 reveals the EMV results when P(D) varies from 0.0 to 1.0 and P(U|D)=0.5, and the cases in which acceptance is beneficial are indicated by the arrows. The shift from accepting to rejecting the donation, or vice versa, illustrates the change in the branch of the decision tree. Figure 8 is a 3-D graph of the same random benefit, or PWTP, for those where both P(D) and P(U|D) vary from 0.0 to 1.0. 52

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Table 6: Matrix of Expected Monetary Value (EMV) P(U/D)###0.00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.073,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 0.1 51,451,236 54,391,307 57,331,378 60,271,448 63,211,519 66,151,590 69,091,660 72,031,731 74,971,802 77,911,872 80,851,943 0.2 29,400,707 35,280,848 41,160,989 47,041,130 52,921,272 58,801,413 64,681,554 70,561,696 76,441,837 82,321,978 88,202,120 0.3 44,101,060 44,101,060 44,101,060 44,101,060 44,101,060 51,451,236 60,271,448 69,091,660 77,911,872 86,732,084 95,552,296 0.4 58,801,413 58,801,413 58,801,413 58,801,413 58,801,413 58,801,413 58,801,413 67,621,625 79,381,908 91,142,190 102,902,473 P(D)0.5 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 73,501,766 80,851,943 95,552,296 110,252,649 0.6 88,202,120 88,202,120 88,202,120 88,202,120 88,202,120 88,202,120 88,202,120 88,202,120 88,202,120 99,962,402 117,602,826 0.7 102,902,473 102,902,473 102,902,473 102,902,473 102,902,473 102,902,473 102,902,473 102,902,473 102,902,473 104,372,508 124,953,003 0.8 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 117,602,826 132,303,179 0.9 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 132,303,179 139,653,356 1.0 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 147,003,533 Note: Values in Dollars 53 53

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EMV for Different Disater's Probabilities,with P(U/D)=0,5, HC=0, LD=0, SP=0PWTP, and PWTP=$147,003,533$0$20,000,000$40,000,000$60,000,000$80,000,000$100,000,000$120,000,000$140,000,000$160,000,0000.000.100.200.300.400.500.600.700.800.901.00P(D): Probability of DisasterEMV [Dollar] EMV A cceptance DecisionRejection DecisionPoint of Decision's Shift ` Figure 7: EMV of P(D) from 0.0 to 1.0 When P(U|D)=0.5 00.10.20.30.40.50.60.70.80.91 00.20.40.60.81 -50,000,000100,000,000150,000,000EMV [Dollar]P(U/D): Probability of Use Given the DisasterP(D): Probability of Disaster3-D Diagram of the EMV for Different Disater's Probabilities,with HC=0, LD=0, SP=0PWTP, and PWTP=$147,003,533 100,000,000 150,000,000 50,000,000 100,000,000 50,000,000 Figure 8: EMV for Different Probabilities of the Occurrence of Disaster 54

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In the 3-D graph, when the PWTP is changed and other values are unchanged, the shape of the graph remains the same although the scale of the EMV-axis does change. To illustrate this occurrence, in Figures 8 and 9, the shapes of 3-D graphs are the same, although the PWTP generated randomly for Figure 8 is $147,003,533 and the PWTP for Figure 9 is $903,915,574. Hence, the EMV is changing for every different input of the benefit, but the shape of the graph displayed does not change at all. The reason for this behavior is that finding the EMV is similar to finding the absolute value of a function that results in a convex function as can be noted in Figure 7. 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91 -1002003004005006007008009001,000EMV [Dollar]MillionsP(U/D): Probability of Use Given the DisasterP(D): Probability of Disaster3-D Diagram of the EMV for Different Disater's Probabilities,with HC=0, LD=0, SP=0PWTP, and PWTP=$903,915,574 100 100 200 200 300 300 400 400 500 500 600 600 700 700 800 800 900 900 1,000 Figure 9: EMV for P(D) vs P(U|D). Case of PWTP = $903,915,574 55

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The most cost-effective decision to accept/reject may shift from either of the two branches of the decision tree diagram; thus, an equivalent matrix of the matrix of EMV containing zeros and ones is developed. This Matrix of Strategic Decision (MSD) tracks the changes in the P(D), P(U), and P(LD) that produce a branch shift in the decision tree diagram when calculating the largest EMV. The number one (1) is the acceptance of the donation that results in the largest EMV. Conversely, the number zero (0) means the rejection of the donation as the decision that yields the largest EMV. Table 7 displays the MSD generated from the matrix of EMV resulted from Figure nine. Table 8 and Table 9 display the matrices of EMV and the strategic decision respectively, for a random number of PWTP of ten dollars. The matrix of strategic decision is the same as Table 7 with a different matrix of EMV. One of the findings from performing the simulation for each scenario is that the matrix of strategic decision remains unchanged for the same ratio sale price-benefit while the values of and the other probability cases remained unchanged. The matrix of strategic decision is defined as MED (i,j) = 1 or 0. In the model proposed, i is always P(D) and j is either P(U|D), P(U|ND), or P(LD). The matrix MED, is a square matrix of dimension 11, in which i and j changes from 0.0 to 1.0 with increments of 0.1. As the matrix remains unchanged, a column vector named Vector of Shift may capture the boundary of the changes that occurs in the matrix of strategic decision. Therefore, column vector can be defined as VS (i,j) 56

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Table 7: Matrix of Strategic Decision (MSD) UseP(U/D)00.000.100.200.300.400.500.600.700.800.901.000.00111111111110.10111111111110.20111111111110.30000001111110.4000000001111P(D)0.50000000001110.60000000000110.70000000000110.80000000000010.90000000000011.0000000000001 57 Note: Zero means rejection and one means acceptance of the donation 57

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Table 8: Matrix of Expected Monetary Value for Different Probabilities of P(D) and P(U|D). Case of PWTP=$10 P(U/D)5.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.05 5 5 5 5 5 5 5 5 5 5 0.1 4 4 4 4 4 5 5 5 5 5 6 0.2 2 2 3 3 4 4 4 5 5 6 6 0.3 3 3 3 3 3 4 4 5 5 6 7 0.4 4 4 4 4 4 4 4 5 5 6 7 0.5 5 5 5 5 5 5 5 5 6 7 8 0.6 6 6 6 6 6 6 6 6 6 7 8 0.7 7 7 7 7 7 7 7 7 7 7 9 0.8 8 8 8 8 8 8 8 8 8 8 9 0.9 9 9 9 9 9 9 9 9 9 9 10 1.0 10 10 10 10 10 10 10 10 10 10 10 Note: Values in dollars Table 9: Matrix of Strategic Decision for the PWTP=$10 58 P(U/D)00.000.100.200.300.400.500.600.700.800.901.000.00111111111110.10111111111110.20111111111110.30000001111110.40000000011110.50000000001110.60000000000110.70000000000110.80000000000010.90000000000011.0000000000001 58

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In the column vector VS (i,j) i = P(D) and j = 1, VS (i,j) is the value of the P(U|D), where the decision of donation acceptance will result in the largest EMV. To illustrate, the vector shift for the matrix exhibited in Table 8, or Table 9, is as follows: 0000.50.7VS =0.80.90.9111 Additionally, VS can be incorporated into a matrix shift of the decision, defined by MS (i,j) ,where i is the P(D) consecutive from 0.0 to 1.0, and j is the value of from 0.0 to 1.0 as well. Appendix B exhibits several MS for different scenarios. Therefore, the matrix of the strategic decision defines the threshold at which there is a change in the decision of either accepting or rejecting the donation. Figure 10 exhibits the threshold for accepting or rejecting the donation for the scenario P(D) vs. P(U|D) when =0, and when P(U|ND)=0.5, P(LD)=0, and HC=0SP. The exhibit of the values of from 0.0 to 1.0, with increments of 0.1, is the result of the matrix shift of the strategic decision. Figure 11 and Figure 12 display 2-D and 3-D charts of the decision shift from accepting to rejecting the donation or vice versa. 59

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P(D) vs P(U/D)Case P(U/ND)=0.5, P(LD)=0, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP Zone of Acceptance Zone of Rejection Figure 10: Threshold of P(D) vs. P(U|D) for Accepting or Rejecting the Donation when =0 P(D) vs P(U/D)Case P(U/ND)=0.5, P(LD)=0, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Zone of Acceptance Non Conclusive Z one Zone of Rejection Non Conclusive Zone Figure 11: Graph of Different Thresholds for P(D) vs. P(U|D) for from 0.0 to 1.0 60

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For the graph results of both P(D) vs. P(U|D) and P(D) vs. P(U|ND), exhibited in Appendix B,Figures 20 to Figure 33, the maximum EMV is obtained above the surface that depicts the shift of the decision. For the graph of P(D) vs.. P(LD), Figure 31 and Figure 32, the maximum EMV is located below the graph, which pinpoints the shift of the decision. Similarly, for both graphs of P(D) vs.. P(U|D) and P(D) vs. P(U|ND), below the surface indicate where rejecting donations will yield the highest EMV; whereas, for the graphs of P(D) vs. P(LD), above the surface determines where rejecting the donation will yield the highest EMV. Consequently, the charts obtained with the model proposed are very useful for sensitivity analysis of the various scenarios when accepting or rejecting the donations. 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91P(U/D)SP as a Function of PWPTP(D)P(D) vs P(U/D) and SP= 0.0WTP,.., 1.0WTPCase P(U/ND)=0.5, P(LD)=0, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 12: 3-D View of the Threshold of the Graph P(D) vs P(U|D) vs that Yields the Highest EMV 61

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Figure 13 summarizes the procedure model for calculating correct thresholds that determine the decision-making process for accepting/rejecting donations for humanitarian relief. Appendix B ( Figures 20 to 31) exhibits the graphs of P(D) vs. P(U|D) and P(D) vs. P(U|ND); and P(D) vs. P(LD) obtained after following the procedure indicated in Figure thirteen. 5.3 Deduction of the EMV The rationale towards finding a mathematical expression that simplifies the calculation through the decision tree diagram is from both Figures 3 and 5: Let EMV i be the Expected Monetary Value at node i. The maximum EMV at node 1 affects the decision to accept or reject the donation, therefore: EMV 1 = Max (EMV 2 EMV 3 ) 5.3.1 Expected Monetary Value for the Acceptance Decision Let CWTA = -PWTP for the case of vital or critical commodities as explained in the literature review section, therefore PWTP= CWTA (1) Moving back in the decision tree, from right to left as is indicated in Figure 3 and Figure 5, the EMV at node 4 is: EMV 4 = P (U|D) (PWTP HC) + [1 P (U|D)] [-PWTP HC] 62

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P(U|, Sensitivity Analysis End Locate Current Conditions and Verify Endorsement of Previous Results Obtain Charts for P(D) vs P(U|D) P(D) vs P(U|ND) P ( D ) vs P ( LD ) Obtain Matrix of Shift (MS) Obtain Matrix of Strategic Decision (MSD) Find Decision Through EMV (Eq. 6 & 7) Estimate P(D), P(U|D), ND), P(LD), Start Figure 13: Layout of the Model Proposed 63

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EMV 4 = PWTP P(U|D) HC P(U|D) PWTP HC + PWTP P(U|D) + HC* P(U|D) EMV 4 = 2PWTP P(U|D) PWTP HC (2) EMV at node 5 is: EMV 5 = P(U|ND)(PWTP HC) + [1 P(U|ND)] (HC)] EMV 5 = PWTP P(U|ND) HC P(U|ND) + HC P(U|ND) HC EMV 5 = PWTP P(U|ND) HC (3) From (2) and (3), EMV at node 2 is: EMV 2 = [2PWTP P(U|D) PWTP HC)] P(D) + [PWTP P(U|ND) HC] P(ND) EMV 2 = [2PWTP P(U|D) P(D)] [(PWTP P(D)] [HC P(D)] + [PWTP* P(U|ND) P(ND)] [HC P(ND)] Grouping the HC, EMV at node 2 results in: EMV 2 = [2PWTP P(U|D) P(D) (PWTP P(D) + ( PWTP* P(U|ND) P(ND)] HC [P(D) + P(ND)] Since P(D) + P(ND) = 1, therefore: EMV 2 = [2PWTP P(U|D) P(D)] [(PWTP P(D)] + [PWTP* P(U|ND) P(ND)] HC (4) Therefore, from Equation (4), the value of the acceptance decision is a function of PWTP, P(D), P(U|D), P(U|ND), and HC. 64

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5.3.2 Expected Monetary Value for the Rejection Decision EMV at node 7 is: EMV 7 = Max(PWTP SP, CWTA) From (1), the previous equation becomes EMV 7 = Max(PWTP SP, PWTP) If PWTP 0 and PWTP SP, therefore in all cases (PWTP SP) -PWTP EMV 7 = Max(PWTP SP, -PWTP) = PWTP SP EMV at node 6 is: EMV 6 = PWTP P(LD) + (PWTP SP) [1 P(LD)] EMV 6 = PWTP P(LD) + PWTP SP PWTP *P(LD) + SP* P(LD) EMV 6 = PWTP + SP P(LD) SP = PWTP + SP [P(LD) 1)] EMV at node 3 is as follows: EMV 3 = EMV 6 P (D) + 0 P(ND), then EMV 3 = EMV 6 P (D) EMV 3 = {PWTP + SP* P(LD) SP}P(D) (5) From Equation (5), the value of the rejection decision is a function of P(D), P(LD), SP, and PWTP. Although equations (4) and (5) exhibit the EMV of each decision as a function of the input variables, further simplification of those two equations is obtained using both the equivalences stated in the model and probabilistic principles for dependent events. Furthermore, if is defined as the ratio sale price-benefit (monetized benefit), and as the ratio holding cost-sale price, then the following results: 65

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= SP/PWTP (6) = HC/SP (7) For the case of dependent events we have: P(U.D) = P(U|D)* P(D), and (8) P(U.ND) = P(U|ND) P(ND) (9) P(U) = P(U D) + P(U. ND) (10) From Equation (8) and (9), Equation (4) becomes: EMV 2 = 2PWTP P(U.D) PWTP P(D) + PWTP* P(U.ND) HC From Equation (10), EMV 2 becomes: EMV 2 = PWTP P(U) + PWTP P(U.D) PWTP P(D) HC From (6) and (7), HC = PWTP, therefore EMV 2 = PWTP P(U) + PWTP P(U.D) PWTP P(D) PWTP Taking the common factor PWTP out of the expression:: EMV 2 = PWTP {P(U) + P(U.D) P(D) } (11) Note that P(U.D) = P(U|D)* P(D), and if it is replaced in (11), then EMV 2 = PWTP {P(U) + (P(U|D)* P(D)) P(D) } Taking P(D) as common factor EMV 2 = PWTP {P(U) + P(D) [P(U|D) 1] } (12) P(U|D) + P(NU|D) = 1, therefore, P(U|D) 1 = P(NU|D), and Equation (12) becomes: EMV 2 = PWTP {P(U) P(D) P(NU|D) } 66

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P(D) P(NU|D) = P(NU.D); therefore EMV 2 = PWTP {P(U) P(NU. D) } (13) Equation (13) is a reduction of equation (4) In Equation (5): EMV 3 = {PWTP + SP* P(LD) SP}P(D) = {PWTP + SP (P(LD) 1)}P(D) P(LD) + P(NLD) = 1; therefore, EMV 3 = {PWTP SP (P(NLD) }P(D). Replacing (7), this equation becomes: EMV 3 = {PWTP PWTP (P(NLD) }P(D), therefore, EMV3 = PWTP P(D){ 1(P(NLD) } (14) Whereas Equation (4) and Equation (5) display the EMV of the acceptance or rejection of the donation as a function of the variables of the graphs proposed in this thesis (i.e., P(D) vs. P(U|D), P(D) vs. P(U|ND), and P(D) vs. P(LD)), these equation can be reduced towards obtaining Equations (13) and Equation (14). 5.4 Discussion of the Model Equations (13) and (14) imply two important results. First, the introduction of the ratio sale price to benefit simplifies the mathematical expressions; second, the acceptance or rejection of the donation should be decided without the assessment of the benefit alone (i.e., PWTP) but with the ratio sale price to benefit and the other formula variables. This situation is one of the crucial reasons why term greatly affects the assessment of the best decision when accepting or rejecting a donation. The use of both 67

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terms and help to simplify the input variables considered for the assessment of the best decision of either accepting or rejecting the donation. The derivation of the mathematical expressions for the case in which P(D), P(U) and P(LD) are not dependent events, as was assumed so far, but independent events is as follows: Equations (8), Equation (9), and Equation (10) become: P(U.D) = P(U) P(D) (15) P(U.ND) = P(U) P(ND) (16) P(U) = 1 P(NU) (17) Therefore, Equation (11), becomes EMV 2 = PWTP {P(U) + P(U)P(D) P(D) } (18) Again with P(D) as a common factor EMV 2 = PWTP {P(U) + P(D) [P(U) 1] } (19) However, P(U) + P(NU) = 1; therefore, P(U) 1 = P(NU) and Equation (19) becomes: EMV 2 = PWTP {P(U) P(D) P(NU) } (20) Equation (20) is similar to Equation (13), the difference depends on the assumptions that the events are independent. For the case of the rejection, using Equations (8), Equation (9), and Equation (10), Equation (14) becomes: EMV3 = PWTP P(D){ 1(P(NLD) } (21) Equation (21) is equal to Equation (14). 68

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The mathematical expressions for the cases of dependent and independent events are the same although the results vary. The difference results because the probabilities are not conditional but marginal: P(D), P(U), and P(LD). Of course, the assessments of the input values are not the same. For example, the P(U) for the case in which the use is independent is not the same for the case in which the use of the commodity is dependent of the particular disaster. To illustrate, for the case of independent events, the likelihood of the use needs to be assessed as P(U); but, for the case of dependent events, the likelihood of the use needs to be assessed as two different values: P(U|D), and P(U|ND). Notwithstanding this difference, the procedure for running the model, as displayed in Figure 13, is the same. The displayed model provides counter intuitive results when limited conditions are considered. Asymptotic analysis of some of input parameters provides further understanding of this situation. Considering Equation (13) and Equation (14), and using Equation (6) and Equation (7), the following results: For the case of the rejection EMV 2 = PWTP {P(U) P(NU. D) HC/PWTP} (22) For the case of the acceptance EMV3 = PWTP P(D){ 1(SP/PWTP)*(P(NLD) } (23) Therefore, eliminating the common factor PWTP and finding the limit when PWTP tends to infinitethe probability of disaster=close to one results in the following: 69

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Lim EMV 2 = Lim {P(U) P(NU. D) HC_ } (24) PWTP PWTP PWTP And Lim EMV 3 = Lim P(D){ 1_ SP_ (P(NLD) } (25) PWTP PWTP PWTP Vital commodities, one of the assumptions, reveal a high PWTP; therefore, Equation (24) and Equation (25) becomes Lim EMV 2 = P(U) P(NU|D)* P(D) (26) PWTP Lim EMV 3 = P(D). (27) PWTP As probabilities are less or equal to one and greater or equal to zero, then the greater of two previous equations is Equation (27). Thus, the highest EMV for the case analyzed is the rejection instead of the acceptance. Therefore, the higher P(D), the higher is the EMV 3 As previously mentioned, this situation leads to a counter intuitive result. The drawback of the model can be summarize as follows: The best decision to make when there is a high disaster probability with a high donation of a vital commodity (the PWTP is extremely high) is to reject the donation. This results because the assumption exists that the commodity purchases can occur after the disaster. In such case, it is better to wait for the disaster and then the disaster event will pinpoint the real need of the item; this prevents incurring needless costs associated with holding the inventory stock. This makes the rejection decision more advantageous. 70

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This downside factor of the model is overcome by using utility theory instead of value theory. Even though utility theory is beyond the scope of this thesis, it is important to mention that the utility theory is an attempt to incorporate the subjective value given by the decision maker to a different set of outcomes that may result from the decision. Unlike the utility theory, the use of the value theory in the EMV assessment does not reflect the subjective preference of the decision maker. To illustrate, using the model proposed of value theory, an increase of 0.4 in the P(D) is valued the same for the decision maker regardless if the change in the probability of the disaster of 0.4 is from P(D)=0 to P(D)=0.4 or from P(D)=0.6 to P(D)=1.0; such an increase changes the input value of P(D) in the corresponding 40% as evidenced by the asymptotic analyses of Equations (26) and (27). This kind of decision maker is considered risk neutral because no matter what is the value of the probability neither the change of value of the probabilities, the criteria in selecting the right decision remains the same. Notwithstanding, this rationale fails when the utility theory comes into play and the subjective judgment of the decision maker is taken into account. To exemplify this situation, assume that the probability of a disaster occurrence is zero and the model suggests that the best decision is to reject the donation. Also assume that a change of the P(D) from 0.0 to 0.4 also makes a donation rejection the best decision. However, this might not hold true for an increase of a disaster probability from P(D)=0.6 to P(D)=1.0. In the former case, P(D)=0.4, the decision maker will be still willing to take the risk of not accepting the donation, but in the last case, P(D)=1.0, an intuitive decision may be to 71

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accept the donation due to the imminent occurrence of the disaster. In this case, the acceptance of the donations may be seen as most attractive and less risky than the rejection. When the decision maker is not prone to take the risk because of high values of the probability of disaster, then the decision maker will be shifting from risk neutral decision maker to risk averse decision maker. If the decision maker is going to modify the rejection criterion because of the imminence of the disaster occurrence, then the decision maker may hesitate to take the risk; hence, his or her criterion is not independent of the value of the P(D). When the decision maker assigns more value to a smaller change than to a larger one, the decision maker is risk averse (Beroggi, 1999, p. 129). An exception of the counter intuitive result is the case when SP is higher than the monetized benefit (PWTP). In such cases, as indicated by Equation (25), the EMV of the rejection may be less than zero and it may be the case when the acceptance yields the highest EMV, as indicated by the Equation (24). In practical terms, despite the other input values, when the sale price is considerably high and the HRO cannot afford to buy the commodity; then it could be more attractive for the HRO to accept the donation than to reject it. As was already mentioned, the introduction to the model of subjective utility theory is far beyond the aim of this thesis work. It suggests further research that may be approached by attempts to apply decision making under uncertainty, considering utility theory, for accepting or rejecting donations for humanitarian relief purposes 72

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CHAPTER 6 CASE STUDY 6.1 Introduction The purpose of this case study is to apply the model and verify its suitability to a real case situation. The best case scenario might be the situation in which the HRO is offered a commodity contribution, and the HRO has to decide whether to accept or reject the donation. The validity of the decision is assessed through the evaluation of the consequences of the particular decision. The disaster, response, and recovery phase from the tragedy occurred in the spring of 1997 to the summer of 1998 in Grand Forks, North Dakota. According to a study of the United States Geological Survey (USGS), the 1997 Red River flood, the main river that crosses North Forks in a north/south direction, is considered as one of the most significant floods in the United States during the 20 th century (Perry, 2000). A statistical study of various past floods creates a forecast of the occurrence of future floods. Additionally, the flood size and the magnitude is considered and then a probability of occurrence is associated with a recurrence interval. For example, a 100-year flood, or a 100-year recurrence interval, is one that will occur approximately once every century. Nonetheless, the probability of the flood occurrence remains at one percent each year. Generally speaking, the T-year annual maximum flood at a given site 73

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is defined as the stream flow that has a probability of 1/T of occurrence in any given year (Troutman & Karlinger, 2003). 6.2 The Situation During the preparation phase of the Grand Forks flood, a manager receives a phone call from an organization contributor stating that he wants to donate 180 pressure washers. To decide whether to accept the donation, the proposed model will be considered. Data: Event: Flood Region: East Grand Folks and Grand Folks Location: North Dakota Date of occurrence: Any time after 1997 Items to be accepted: Pressure washers Package: Pallets of six units Number of Pallets: 30 Price per pallet: $1,794 Price per Unit: $299 Market price of the pressure washers: $53,820 Warehousing costs: $12,558/year ($44.85 sq.ft/yr) Operational lifespan of the item: five years (information obtained from previous experiences of humanitarian relief organizations). 74

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Features: Small town Not able to locate and buy pressure washers in the local marketplace if the flood hits the zone After a flood, sanitation is a paramount concern Mold will trigger a health problem Dwelling infestation may create breathing problems Mold can lead to eventual death of those exposed If dwelling unit is infested, the property would be condemned and eventually demolished 6.2.1 Inputs to the Model SP = $53,820. This is the value of the donation in 1997 dollars. HC = $12,558. The cost of holding the donation. Ratio of Holding Cost/Sale price = HC/SP = 0.23. This value means that the holding cost in the time-framed considered is 0.23 the sale price of the whole amount of the item donated. Time frame to be considered: one year Probability of Disaster Analysis of the Maps from the Flood Insurance Rate Map (FIRM) indicates that the area along Red River is considered located within a 100-year flood recurrence interval. Figure 14 displays this map. For further information, Appendix D exhibits geographical distribution of six major hazards in the US. 75

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Figure 14: Flood Data Map for the Area along the Red River, Grand Forks, ND. Source: ISRI/FEMA Project Impact Hazard Map (Federal Emergency Management Agency, 2003) Calculated Probability of Disaster Recurrence interval 1/T is equal to 1/100, therefore the probability of the disaster is estimated to be P(D) = 0.01. Community eventually affected Should the 100-year recurrent flood occur, there exists the possibility that at least 2,000 people could be affected. Price of a Human Life From the review of the literature, the price of a human life estimated in the lower range at $2,400,000. 76

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Probability of Use The probability of using the pressure washers is very high, not only in the case of a disaster but also with no disaster. The director of the HRO organization estimates that the P(U|D) = 1.0, and the P(U|ND) = 0.30. Probability of Incurring a Future Donation The director of the organization estimates from previous experiences that the probability of having a future donation from the same donor is estimated at zero. Also, in case that the pressure washer will be needed, there will not be any possibility of procuring them from the local market. Therefore, P(LD) = 0. Estimation of the PWTP The PWTP is evaluated through the expression: PWTP = Cost of Human life is defined as the ratio that affects the price of human life and is dependent on the type of organization and the role that is expected for the organization in society. For example, for a church association, its stakeholders, beneficiaries, and sponsors may not expect the organization to be responsible for providing humanitarian assistance if a disaster strikes. Alternately, if an HRO has nationwide presence and is considered an HRO of high level, then its leading role after a disaster is expected to be not only immediate but also remarkable. The former case should entail a low value of whereas the latter case will entail a high value of 77

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To estimate the factor an interval scale of measurement was formulated that joins strategic factors according to the HRO mission. In the interval scale, its zero is arbitrarily established and the intervals are equals. For this case study, four strategic factors were defined to assess the price of human life for the humanitarian organization: Importance of the item toward achieving the organizations mission Deterioration of quality of life Position of the organization that must face the situation Usability of the donation The factors and the ranking assigned by the director of the HRO are displayed in Figure fifteen. The interval scale was used in accordance with the literature review as a decision support system for assessing the importance of the commodity considering various criteria. The method was formulated to weigh the resulting varied factors pertaining to the donation in accordance with the HRO Managers criterion. The manager of the HRO selected this parameter as the one that warranted appraisal and then he assigned the different quantitative values based on the qualitative scales for each of the considered parameters. 78

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Interval Scales of measurement Importance of the Item toward Achieving the Organizations Mission +--------+--------+--------+--------+--------+--------+--------+--------X--------+-------0 10 20 30 40 50 60 70 80 90 100 Never Seldom Sometimes Generally Always important important important Risk of Threat to the Quality of Life +--------+--------+--------+--------+--------+--------X--------+--------+--------+--------+ 0 10 20 30 40 50 60 70 80 90 100 No High consequences consequences (Outbreak cond.) Number of Organizations (Stakeholders) +--------+--------+--------+--------+--------+--------+--------+---X---+--------+--------+ 0 10 20 30 40 50 60 70 80 90 100 Should not Role One Should Assistance Face the unnoticeable among lead the champion problem many assistance (Unique) Usability +--------+--------+--------+--------+--------+--------+--------+--------X--------+--------+ 0 10 20 30 40 50 60 70 80 90 100 Never Seldom Sometimes Generally Always Figure 15: Strategic Factors for Evaluating the PWTP (Case Study) The geometric mean is used as a central tendency of the different ranking values. The geometric mean is a generalized method for finding relative number averages such as percentages, ratios, indexes and growth rates. It is useful for finding the averages when data fall in an ogive curve (e.g., growth curve) (Leedy & Ormrod, 2001). It is calculated 79

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by multiplying the different ratios and then obtaining the n th root of their product. In this case, n is the number of scores. Thus, the mathematical expression is as follows: GM = n xnxx))...(2)(1( Hence, the value obtained is the weight that the HRO would assign to the value of human life as follows: PWTP = Price of Human Life Number estimated of people impacted Therefore, the PWTP will be the following: PWTP = 0.77 $2,400,000 2,000 = $3,696,000,000 = SP/PWTP = 1.45 x 10 -5 0 The summary of the inputs to the model is displayed in Table 10. Table 10: Summary of the Inputs for Running the Model SP HC PWTP P(D) P(U|D) P(U|ND) P(LD) Time: $53,820 $12,558 $3,696,000,000 0.23 0 0.01 1.0 0.30 0 1 year 6.3 Results of Case Study Utilizing Equations (13) and (14) reveals a maximum EMV = $1,134,659,442; therefore, the decision should be to accept the donation, in which case the probabilistic payoff is expected to be the EMV. In the case of rejection, the EMV result is 36,959,462. To discover further information addressing changes in the various inputs, one should consult the sensitivity analysis proposed by the model. Following the proposed 80

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steps, one obtains the MSD for the cases P(D) vs. P(U|D), P(D) vs. P(U|ND), and P(D) vs. P(LD). These situations are displayed in Tables 11, 12 and 13, respectively. In addition, the VS can be obtained from the MSD and its values, and the current values for the case study can be incorporated into a chart, as it is displayed in Figures 16, 17, and 18. 81

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Table 11: Matrix of Strategic Decision P(D) vs. P(U|D) for the Case Study P(U/D)10.000.100.200.300.400.500.600.700.800.901.000.00111111111110.10111111111110.20000011111110.30000000011110.4000000000111P(D)0.50000000000110.60000000000110.70000000000010.80000000000010.90000000000011.0000000000001 Table 12: Matrix of Strategic Decision P(D) vs. P(U|ND) for the Case Study P(U/ND)10.000.100.200.300.400.500.600.700.800.901.000.00111111111110.10111111111110.20111111111110.30111111111110.4011111111111P(D)0.50111111111110.60111111111110.70111111111110.80111111111110.90111111111111.0011111111111 82 82

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Table 13: Matrix of Strategic Decision P(D) vs. P(LD) for the Case Study P(LD)11.000.900.800.700.600.500.400.300.200.100.000.00111111111110.10111111111110.20111111111110.30111111111110.4011111111111P(D)0.50111111111110.60111111111110.70111111111110.80111111111110.90111111111111.0011111111111 83 83

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VS (P(D),P(U|D)) = ; VS (P(D),P(U|ND)) = ;VS (P(D),P(LD)) = 11111111111 000.40.70.80.90.91111 11111111111 P(D) vs P(U/D)Case P(U/ND)=0.3, P(LD)=0, HC=0.23SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP Figure 16: Chart of P(D) vs. P(U|D) for the Case Study 84

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P(D) vs P(U/ND)Case P(LD)=0, P(U/D)=1, HC=0.23SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D) SP=0.0WTP Figure 17: Chart of the P(D) vs. P(U|ND) for the Case Study P(D) vs P(LD)Case P(U/D)= 1, P(U/ND)=0.3, HC=0.23SP 00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(LD) SP=0.0WTP Figure 18: Chart of the P(D) vs. P(U|LD) for the Case Study 85

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From the preceding graphs, the following conclusions result: Chart P(D) vs. P(U|D), Figure 16: The largest expected payoff is obtained when the donation is accepted. Any increase in the P(D) will mean no change in the current decision. When the disaster probability is equal to or greater than 0.7, the decision of acceptance yields the same EMV than the decision of rejection as revealed in Figure 16, Chart P(D) vs. P(U|D). Chart P(D) vs. P(U|ND), Figure 17 1. Considering the given values of , P(U|D), and P(LD), the decision should be to accept the donation despite any value of the P(D) and P(U|ND). Chart P(D) vs. P(LD), Figure 18: 1. Under the given values of , P(U|D), and P(U|ND) the decision that yields the highest monetary benefit is the acceptance, despite any value of P(D) or P(LD). In concluding this proposed study, the donation should have immediately been accepted, as evidenced from the chartsthe donation acceptance will yield the highest expected payoff (EMV). This decision in this case study was due to the high EMV compared with the sale price (i.e., ). Note: the actual decision made by the HRO director was acceptance of the donation. The Red River Flood in North Dakota and Minnesota, killed eight people and produced losses of about two billion dollars during the year 1997 and 1998. 86

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CHAPTER 7 HOW TO IMPLEMENT THIS METHODOLOGY IN HUMANITARIAN RELIEF ORGANIZATIONS The following steps will explain how to implement the methodology. This procedure was ordered from the research and subsequent results of this thesis. 7.1 Create an Influence Diagram The influence diagram graph helps identify the cause and effect relationship of the commodity acceptance or rejection through the donation process. It will allow the HRO to devise a business plan aimed at potential donors and obtain commodities for humanitarian relief purposes. An influence diagram of the decision of accepting/rejecting donations is displayed in Figure 19. The figure exhibits the different stakeholders and factors that influence the HRO along with the decision to accept or reject the donation. 7.1.1 Influence Diagram of the Decision of Accepting/Rejecting Donations An influence diagram that exhibits the different aspects of the complexity of the acceptance/rejection decision helps explain the process intricacies. The proposed diagram reveals the various inputs considered for the HRO in evaluating the feasibility of accepting or rejecting donations. It is not an exhaustive influence diagram and should be used as a guideline solely for analyzing possible needed inputs when considering donor 87

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acceptance/rejection. It may be altered depending on the HRO and the situational complexities that may exist. For methodological purposes, four different states of influence are defined: Governmental/External Influence Donors Influence Peoples influence Relief Organization Influence 7.1.2 Governmental/External Influence Government regulations and the countrys current tax structure are the macroeconomical conditions that affect the likelihood of donor contribution to the HRO. Government policies and tax deductible donations encourage contributor participation in humanitarian enterprises. Mass media and special interest groups also influence the decision of accepting or rejecting donations. Additionally, an HROs status compared to other HROs affects the decision of accepting or rejecting donations. For example, if the HRO is the only area relief organization, then the donor acceptance or rejection may be more critical. 7.1.3 Donors Influence Each country and subsequent culture exhibits a different attitude towards the donation and or the willingness to donate. The likelihood of a donation is not the same in a developing country where the basic needs are not covered than in a developed country where the basic needs are already satisfied and where the level of income is higher ((Diamantopoulos, 1993), (Danko & Stanley, 1986), and (Clotfelter, 1985)). 88

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Several attempts in different countries were made to assess the potential donor profiles. Schlegelmilch (1997) suggests that four variables, organized in decreasing order, are the most important discriminators between donors and no donors: (a) age, (b) the individuals perception of his or her own generosity, (c) previous experience in volunteering work, and (d) income. For a clearer understanding of the donors influence in the donations process the HRO should establish a donor profile list. It will devise a marketing strategy for fundraising and obtaining in-kind donations for humanitarian relief purposes, and to assess the willingness of the potential donor. Another fact that influences the willingness to donate is the donors intention. Usually, when the donor perceives that his or/her intention will be not honored the donor is less likely, if not totally discouraged, to donate. 7.1.4 Peoples influence The hazard levels influence the disaster type and intensity; this generates various risk levels that affect the peoples needs. Vulnerability and resilience, or the coping capacity levels (Mileti, 1999), influence peoples needs as well. Peoples needs also affect the deployment conditions and the acceptance or rejection of potential commodities. 7.1.5 Relief Organization Influence The organizations mission, vision, and objectives determine its existence and the activities in which the humanitarian relief organization will also be involved. It will also drive the acceptance or rejection of donation base, determining the commoditys use or non-use, depending on whether it will accomplish the organizations objectives. 89

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Government RegulationsPresent TaxStructureMass MediaSpecial InterestGroupsOther HROPerception of CharityEfficiencyPrevious ParticipationIn Volunteer WorkEconomicConditionsSocietyLevel of Wealth of the Society A lternativeOutcomeWillingnessto DonateDonor'sIntention Type ofOrganizationMission/Vision/Role of the HRO A cceptance/Rejectionof CommoditiesWarehousingConditions/CostsPossible Use inCase of DisasterPossible Usefor MitigationDeploymentConditionsSpecial Attributesof the ItemPeople's NeedsVulnerabilityResilienceFloodEarthquakeHurricanelandslideHeat WaveOthers..Disaster TypeHazardRisk DONOR'S INFLUENCE GOVERNMENTAL/EXTERNAL INFLUENCE RELIEF ORGANIZATION INFLUENCE PEOPLE'S INFLUENCE/DEMAND FROM PEOPLE 90 Figure 19: Influence Diagram of Accepting /Rejecting Donations 90

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Warehousing conditions, special care of the inventories, and costs associated with holding the commodities will influence the acceptance or rejection of the donations. In addition, especial attributes of the item, deployment conditions, and the odds of using the donation for mitigation purposes before and after the disaster will affect the acceptance or rejection of the items for humanitarian relief purposes. The governmental and external influence, the tax structure, the mass media, the pressure that could arise from special interest groups, and the existence or absence of other humanitarian relief organizations may all influence the decision of accepting donations. Acceptance or rejection of the commodities influenced by peoples needs will also influence the deployment conditions. The decision of accepting/rejecting donations will be also determined based on disaster type. The aforementioned causes and effects directly or indirectly will affect the decision making process. As was stated, these are not the only factors influencing the decision making process; the list of factors may be increased or simplified based on the humanitarian relief organization purpose. 7.2 Assess the Type of Disaster and its Probability of Occurrence Find the type of disaster and the probability of occurrence, P(D), associated with such event. For this purpose, the information that can be helpful is the information obtained from the following sources: Hazardous maps of the region Information from research centers, universities and government agencies that collect data, monitor and forecast natural events 91

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Use GIS (Geographical Information Systems) maps of vulnerabilities based on different events. Maps from the Insurance Rate Maps could provide some information regarding the vulnerability of some geographical regions 7.3 Assess the Possible Need of the Donation Evaluate the possible need of the commodities that can be used for humanitarian relief purposes and the probability of use, P(U), in case of a disaster. Usually, the international humanitarian relief organization may provide information regarding the commoditys use depending of the type of disaster. 7.4 Find the Costs Obtain costs associated with purchasing the commodities (SP). Also, obtain costs of holding the inventories on hand (HC); both are calculated as a function of time. Section 4.9.4 and 4.9.5 on page 47 depicts the eliciting of these costs. 7.5 Evaluate the Values of the PWTP Estimate, in accordance with the expected role of the humanitarian relief organization. Also, consider, the benefit provided by the commodity deployment and assigned dollar value to obtain the price willing to pay (PWTP) and the benefit of the relief provided to the people in need. For details see Section 3.3 and Section 3.4. on page 21 and 23 respectively. 92

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7.6 Review What may be of Interest to the Stakeholders and Assess the P(LD) Find potential donors and estimate the probability of obtaining a later donation P(LD). Evaluate the P(LD) if the decision to accept the donation is postponed after the occurrence of the disaster. 7.7 Estimate the Values of and and Obtain the Graphs Obtain the value of and and draw the graphs of P(U|D), P(U|ND), and P(LD) located on the ordinate, vs. the P(D) located on the abscissa. These graphs exhibit the sensitivity analysis when the different parameters of the model change. The procedure is explained in section 5.3. Figure 13 summarizes it on page sixty-four. The graphs may not be needed; thus, the decision maker is only interested in the expected monetary value (EMV). Therefore, despite the sensitivity analysis, Equations (13) and (14) can be employed (see page 67). A summary of the methodology for the implementation of the model for humanitarian relief purposes is as follows: Create an influence diagram to gather the complexity of the decision making process. Find the P(D). Evaluate the P(U) of the commodity in both cases given disaster and without the occurrence of the disaster. Obtain the cost of buying the commodity (SP) and the holding cost (HC) of keeping the inventory in stock. 93

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Estimate what may be the cost of providing the benefit (CWTA) and assess the monetized benefit of providing relief to the people in need (PWTP). Find potential donors and estimate the probability of having a later donation in the future P(LD). Obtain the value of and and draw the graphs of P(U|D), P(U|ND), and P(LD) if the sensitivity analysis is deemed to be needed. Locate P(U|D), P(U|ND), and P(LD) on the ordinate and P(D) on the abscissa. These graphs exhibit the sensitivity analysis of the different input of the model. Use Equations (13) and (14), located on page 67, for obtaining the values of the EMV in accordance with the different inputs that occur in the decision making process, and perform the sensitivity analysis preparing the graphs explained in section 5.3. The advantages of the preparation of the graphs as a function of the P(U), P(D), and P(LD) is that they help the HRO personnel in the decision making process. It clearly reveals the various parameters that should be considered when accepting or rejecting donations. The model proposed and the procedure explained is a mathematical approach of the decision making process and replaces the customary use of the subjective criterion when accepting or rejecting donation. 94

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CHAPTER 8 RESULTS, CONCLUSIONS, AND FURTHER RESEARCH 8.1 Summary of the Results The evaluating of the acceptance or rejection of the donations does not consider the expected benefit of the commodity alone (PWTP). The factor expresses the relationship between the sale-price (SP) of the item and the price willing to pay (PWTP). Some of the advantages of using the ratio of sale price to benefit for the decision making of the donation include the following reasons: It simplifies the calculation process The factor resembles the ratio cost-benefit, commonly used for cost analysis The factor simplifies the simulation process and allows the humanitarian relief organizations to create graphs, as the charts exhibited in Appendix B, to aid in the decision making process. Estimating is less prone to mistakes and is more robust than the estimation of the PWTP. Since the PWTP is part of the denominator of the ratio sale price to benefit (i.e., = SP/PWTP), therefore an error in the estimation of the PWTP, is less likely to impact the value of 95

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This research offers the decision maker the advantage of not having to estimate the PWTP alone, but to consider the relationship of the sale price to the benefit of the commodity Some of the results obtained after running the simulations for changes in the whole set of variables are as follows: One notices the robustness of the ratio and the value HC/PWTP as indicated by Equations (22) and (23) on page sixty-nine. An inaccurate assessment of the PWTP will greatly affect the EMV, whereas, an error in the estimation of will not influence the EMV to the same extent Another advantage is that the value of PWTP is common to Equations (13) and (14); therefore, the decision maker may disregard this value when comparing these two equations The matrix of strategic decision does not change when different values of PWTP are simulated, as long as the other input variables remained unchanged. Thus, with only one value of PWTP, it is possible to populate the matrix of strategic decision and the matrix of shift for the different values It is more crucial to assess the probability of the commodity use for both cases of occurrence or no disaster occurrence than the estimation of the probability of the disaster occurrence alone The holding cost is vital as the factor for cases when the donation would be accepted, as illustrated by Equation (22) 96

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The rejection of the donation does not consider the holding cost of the donation. Sometimes this situation makes the donation rejection worthwhile compared to acceptance. This remains valid especially when the holding cost is high, as evidenced by Equation (23) The graphs of P(D) vs. P(U/D) and P(NU/D) displayed in Figure 11, page 60, exhibit that when the disaster probability increases while the probability of use remains unchanged, the best decision is to reject the donation. This situation is caused by the weight of the disaster probability in Equation (13) compared to Equation (14) from page sixty-seven. The rejection of the donation when the disaster probability remains high may appear incorrect for a common sense decision maker, but it is the correct decision if he or she is expected to perform as a neutral decision maker. This situation means that because the decision maker is reluctant to reject the donation when the disaster is going to occur, the decision maker is risk averse. This situation was also addressed in Section 5.3 with asymptotic analysis of the factions display by Equations (13) and (14). 8.2 Conclusions This model exhibits the importance of considering the ratio of sale price to benefit for assessing the acceptance of donations. The holding cost is another variable of importance that should be considered in the assessment of accepting or rejecting the donation. The estimation of the likelihood of the disaster, the probability of use, and the probability of having a later donation are some of the variables that may be estimated 97

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before accepting donations. The estimation of the EMV indicates that when the P(D) increases, the right decision is not always the acceptance of the donation. The whole set of variables should be estimated before arriving at a decision of accepting or rejecting donations. Since HRO and nonprofit organizations in general are increasingly under public scrutiny, the use of the model proposed in this thesis may help to replace the sole subjective judgment of the managers when accepting or rejecting donations for humanitarian relief purposes. 8.3 Contribution The main advantage of the proposed decision tree analysis model is that it depicts a layout of the variables that should be considered for the acceptance or rejection of donations. It is easy to understand even for personnel not acquainted with the decision making process. The P(U/D) may include the deployment once the disaster strikes. The P(LD) may include the relationship of the HRO with the different stakeholders of its business purpose. This author believes that although most of the HRO are not-for-profit organizations, they have to be managed as business organizations if the HRO is going to remain in the marketplace in the long range. The literature review included in this research indicated that there was no analytical approach or policy for inventories used for humanitarian relief operations. Any attempt to propose methods to determine the validity of maintaining inventories for disaster relief should consider the uncertainty in the disaster occurrence and the 98

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probability of the inventory use. Additionally, one should consider the probability of having a later donation if the first donation was rejected. The main advantage of the method proposed for assessing the acceptance or rejection of donations, as any decision tree model, is that it encompasses the variables considered relevant in the decision making process. The proposed decision trees helps HRO upper level directors and managers to understand the process and the possible consequences associated with the decisions resulting from the different proposed scenarios. In the model, other variables can be incorporated based on the complexity level of the decision maker. The policy makers criterion, or the HRO directors judgment, is not replaced by the model. The model demonstrates a means of gathering the uncertainties that surround the acceptance or rejection of donations. Some of the advantages of using the model are as follows: The use of the model will help the HRO to lessen the possible suffering of the victims The selection of the right inventory may result in an increase of the efficiency of the organization. The right allocation of the ever-scarce humanitarian relief resources results in best serving the possible victims of disasters If the HRO can decrease the current inventory, the HRO can use the financial resources and the facility spaces for accomplishing its mission, vision, and objectives 99

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The use of an analytical tool can enhance the relationship HRO-Donors-Community. An objective rather than a subjective decision can easily be understood for the national and international community and for the potential donor as well Using this analytical tool may produce more accurate decisions and responsible reactions to the donation offerings for humanitarian relief purposes With this model, the HRO can decide scientifically to either accept or reject the donation 8.4 Scope for Future Research Further research should include the following: A thorough statistical analysis of the efficacy of the proposed approach for accepting or rejecting donations. This may include the evaluation of the inputs that intervene in the decision making process such as probability of disaster, probability of use given a disaster or no disaster, probability of having another donation in the future, and the HROs mission and its stakeholders strategic positions A study that determines which inventory control policies proposed in the literature may be suitable for modeling the inventory control problem in humanitarian relief operations. Results of this research may reveal more information about accepting /rejecting donations based on available inventory levels of frequently used humanitarian relief items 100

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A utility theory to cope with the counter intuitive output that appears in the results with high disaster probabilities. It may be a topic for further research with the inclusion of the utility theory and the subjective criteria of the decision maker can be considered as well. 101

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Dean, M. (2003, May 7). Third Sector in Need of Legal Aid. Guardian Unlimited Newspaper. Retrieved May, 2003, from http://society.guardian.co.uk Diamantopoulos, A., Schlegelmilch, B., Love, A. (1993). Giving to Charity: Determinants of Cash Donations Through Prompted Giving. Marketing Theory and Application, Volume 4. American Marketing Association. Chicago, 133-142. Disaster Management Center. (2003). Aim and Scope of Disaster Management. Retrieved August, 2003, from Web page of the University of Wisconsin Disaster Management Center http://dmc.engr.wisc.edu/courses/aimscope/AA02-01.html Doctor, R. N., Newton, D. P., & Pearson, A. (2001). Managing uncertainty in research and development. Technovation, 21(2), 79-90. Federal Emergency Management Agency. (2003). Project Impact Hazard Map. Retrieved August 18, 2003, from http://ks.water.usgs.gov Fiedrich, F., Gehbauer, F., & Rickers, U. (2000). Optimized resource allocation for emergency response after earthquake disasters. Safety Science, 35(1-3), 41-57. Fuguitt, D., & Wilcox, S. J. (1999). Cost-benefit analysis for public sector decision makers. Westport, Conn: Quorum Books. Gadd, L. (2003). The World Almanac and Book of Facts, 2003. New York, NY: World Almanac Education Group, Inc. Hansch, S., & Burkholder, B. (1996). When Chaos Reigns: Responding to Complex Emergencies. Harvard International Review, 18(4), 10-11. Hodgkinson, V. A., Weitzman, M. S., Noga, S. M., Gorski, H. A., & Kirsch, A. D. (1996). Giving and volunteering in the United States : Findings from a National Survey. Washington, D.C.: Independent Sector. Independent Sector. (2001). The New Nonprofit Almanac In Brief: Facts and Figures of the Independent Sector 2001. Waldorf, MD. International Federation of Red Cross and Red Crescent Societies. (1999). World disasters report 1999. Geneva, Switzerland. International Federation of Red Cross and Red Crescent Societies. (2000). World disasters report 2000. Geneva: International Federation of Red Cross and Red Crescent Societies. IRS. (2000). Charitable contributions. Publication 526. Washington, DC: Department of the Treasury. 103

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Journal of Prehospital and Disaster Medicine. (2002). Health Disaster Management Guidelines for Evaluation and Research in the 'Utstein-Style'. Retrieved April, 2003, from Journal's Web Page http://pdm.medicine.wisc.edu/vocab.htm Krupnick, A. (2002). The value of reducing risk of death: a policy perspective. Journal of Policy Analysis and Management, 21(2), 275-282. Leedy, P. D., & Ormrod, J. E. (2001). Practical Research: Planning and Design (7th ed.). New Jersey: Prentice Hall, Inc. Levin, H. M. (1983). Cost effectiveness: a primer (7 ed.). Newbury Park, CA: Sage Publication, Inc. McEntire, D. A. (2001). Triggering agents, vulnerabilities and disaster reduction: towards a holistic paradigm. Disaster Prevention and Management: An International Journal, 10(3), 189-196. Mileti, D. S. (1999). Disasters By Design : A Reassessment of Natural Hazards in the United States (Washington, DC. ed.). Washington, D.C.: Joseph Henry Press. Mrozek, J. R., & Taylor, L. O. (2002). What determines the value of life? a meta-analysis. Journal of Policy Analysis and Management, 21(2), 253-270. Nahmias, S. (2001). Production and operations analysis (4th ed.). Boston, Mass.: McGraw-Hill. National Institute of Building Sciences. (2003). Hazus, Multihazard Loss Estimation Methodology. Retrieved July, 18, 2003, from National Institute of Building Sciences web page http://www.nibs.org/hazusweb/ Orfinger, B. (2003). Donor DIRECT Program to Revolutionize Red Cross Disaster Fundraising. American Red Cross Press Conference. Retrieved June, 2003, from http://www.redcross.org PAHO. (1999). Humanitarian Assistance in Disaster Situations: A Guide for Effective Aid. Washington D.C.: Pan American Health Organization Regional Office of the World Heath Organization. PAHO. (2000). Logistics guide to Emergency Supply Management. Draft. Washington DC: Pan American Health Organization. Regional Office of the World Health Organization. Pan American Health Organization. (2001). Humanitarian Supply Management and Logistics in the Health Sector. Washington, D.C.: PAHO. 104

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Perry, C. A. (2000). Significant Floods in the United States During the 20th CenturyA Measure of Floods-: USGS, U.S. Geological Survey; U.S. Department of Interior. Rice, D. P. (1967). Estimating the cost of illness. American Journal of Public Health, 57, 424-440. Schelling, T. (1966, Sept. 15-16). The life you save may be your own. Paper presented at the at a conference of experts. In: Problems in public expenditure analysis., Washington, D.C. Schermerhorn, J. R. (2001). Management (6 ed.). New York: John Wiley & Sons, Inc. Schlegelmilch, B. B., Diamantopoulos, A., & Love, A. (1997). Characteristics Affecting Charitable Donations: Empirical Evidence from Britain. Journal of Marketing Practice: Applied Marketing Science, 3(1), pp. 14-28. Shaluf, I. M., Ahmadun, F. l.-r., & Said, A. M. (2003). A review of disaster and crisis. Disaster Prevention and Management: An International Journal, 12(1), 24-32. Taylor, B. W. (1999). Introduction to management science (6th ed.). New Jersey: Prentice-Hall, Inc. Tierney, J. (2003, May 18). Life: The Cost-Benefit Analysis. The New York Times, p. 14. Trigeorgis, L. (1996). Real options : managerial flexibility and strategy in resource allocation. Cambridge, Mass.: MIT Press. Troutman, B. M., & Karlinger, M. R. (2003). Regional Flood Probabilities. Water Resources Research, 39(4), 1095. U. S. Census Bureau. (2002). Statistical Abstract of the United States, Social Insurance and Human Services. Washington, D.C.: Bureau of Statistics, Treasury Department. U.S. Census Bureau. (2003). World Population Information. Retrieved May, 2003, from http://www.census.gov/ipc/www/world.html U.S. Department of Commerce. (2003). General economics indicators: Gross Domestic Product. Retrieved Feb, 2003, from http://www.stat-usa.gov/econtest.nsf U.S. Environmental Protection Agency. (1999). Benefits and Costs of the Clean Air Act, 1990 to 2010 (No. EPA 410-R-99-001). Washington, D.C.: Office of the Administrator. 105

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U.S. Environmental Protection Agency. (2000). Guidelines for preparing economic analyses (No. EPA 240-R-00-003). Washington, D.C.: Office of the Administrator. U.S. Geological Survey. (2003). Geographic Distribution of Major Hazards in the US. Retrieved September, 2003, from http://www.usgs.gov/themes/hazards.html United Nations. (2001). Population, Environment and Development: The Concise Report. New York: Department of Economic and Social Affairs. Population Division. United Nations. Von Winterfeldt, D., & Edwards, W. (1986). Decision analysis and behavioral research. Cambridge Cambridgeshire ; New York: Cambridge University Press. Waters, C. D. J. (1992). Inventory control and management. New York: John Wiley & Son. Worldwatch Institute. (2003). Quick Facts: Worldwatch Paper 158. Unnatural Disasters. Retrieved May, 2003, from http://www.worldwatch.org/pubs/paper/158facts.html 106

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APPENDICES 107

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APPENDIX A Visual Basic Codes for Generating the Random Numbers and the Charts A.1 VBA Code for Generating the Random Numbers Option Explicit Sub TableWithRandomNumbers() 'This sub creates the list of the random numbers Dim StartTime As Single, ElapsedTime As Single 'checking time of random generation StartTime = Timer Dim RandomList As String, i As Single, j As Integer Range("A1:IV65536").Name = "RandomList" 'Creating All the worksheet Randomize With Range("RandomList") For i = 1 To 65536 For j = 1 To 254 .Cells(i, j).Value = Int(Rnd 1000000000) + 1 Next j Next i ElapsedTime = Timer StartTime 'checking time of random generation MsgBox "This section took" & ElapsedTime & "seconds to run." End With End Sub A.2 VBA Code for Generating the MSD and the Charts Sub Macro10() '' Macro for display of the Tables Macro recorded 5/8/2003 by Francisco Ruiz. 108

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Appendix A (Continued) Keyboard Shortcut: Ctrl+Shift+K Sheets("SP=0WTP").Select Range("Y18:Y28").Select Selection.Copy Sheets("Sheet1").Select Range("C4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.1WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("D4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.2WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("E4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.3WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("F4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.4WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("G4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.5WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("H4").Select 109

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Appendix A (Continued) Selection.PasteSpecial Paste:=xlValues Sheets("SP=.6WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("I4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.7WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("J4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.8WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("K4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.9WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("L4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=1.0WTP").Select Range("Y18:Y28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("M4").Select Selection.PasteSpecial Paste:=xlValues 'SECOND Sheets("SP=0WTP").Select Range("AM18:AM28").Select Selection.Copy Sheets("Sheet1").Select Range("P4").Select 110

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Appendix A (Continued) Selection.PasteSpecial Paste:=xlValues Sheets("SP=.1WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("Q4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.2WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("R4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.3WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("S4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.4WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("T4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.5WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("U4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.6WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select 111

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Appendix A (Continued) Range("V4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.7WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("W4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.8WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("X4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.9WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("Y4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=1.0WTP").Select Range("AM18:AM28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("Z4").Select Selection.PasteSpecial Paste:=xlValues 'THIRD Sheets("SP=0WTP").Select Range("BA18:BA28").Select Selection.Copy Sheets("Sheet1").Select Range("AC4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.1WTP").Select Range("BA18:BA28").Select 112

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Appendix A (Continued) Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AD4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.2WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AE4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.3WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AF4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.4WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AG4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.5WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AH4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.6WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AI4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.7WTP").Select 113

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Appendix A (Continued) Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AJ4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.8WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AK4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=.9WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AL4").Select Selection.PasteSpecial Paste:=xlValues Sheets("SP=1.0WTP").Select Range("BA18:BA28").Select Application.CutCopyMode = False Selection.Copy Sheets("Sheet1").Select Range("AM4").Select Selection.PasteSpecial Paste:=xlValues End Sub 114

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Table 14: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 115 P(U/D)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910000000000000.1000000000000.2000000000000.30.50.40.40.30.30.20.20.10.1000.40.70.60.60.50.50.40.40.30.30.20.2P(D)0.50.80.70.70.60.60.50.50.40.40.30.30.60.90.80.80.70.70.60.60.50.50.40.40.70.90.90.80.80.70.70.60.60.50.50.40.810.90.90.80.80.70.70.60.60.50.50.9110.90.90.80.80.70.70.60.60.51110.90.90.80.80.70.70.60.60.5 APPENDIX B Different MS and Graphs for P(D) vs. P(U|D), P(D) vs. P(U|ND), and P ( D ) vs. P ( LD ) Cases When HC=0 115

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Appendix B (Continued) P(D) vs P(U/D)Case P(U/ND)=0.5, P(LD)=0, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 20: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91P(U/D)SP as a Function of PWPTP(D)P(D) vs P(U/D) and SPnd SP from 0.0WTP to 1.0WTPCase P(U/ND)=0.5, P(LD)=0, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 21: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0, and =0 116

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117 Table 15: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910000000000000.10.20.10.10.10.10.10.10.10.10.100.20.30.30.20.20.20.20.10.10.10.100.30.50.40.40.30.30.30.20.20.10.100.40.70.60.60.50.40.40.30.20.20.10P(D)0.510.90.80.70.60.50.40.30.20.100.611110.90.80.60.50.30.200.711111110.70.50.300.8111111110.80.400.91111111110.90111111111110 Appendix B (Continued) 117

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Appendix B (Continued) P(D) vs P(U/ND)Case P(LD)=0, P(U/D)=0.5, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/ND) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 22: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91P(U/ND)SP As a function of the WTPP(D)P(D) vs P(U/ND) and SP from 0.0WTP to 1.0WTPCase P(LD)=0, P(U/D)=0.5, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 23: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0, and =0 118

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Appendix B (Continued) Table 16: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 P(U/D)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WTP00.10.20.30.40.50.60.70.80.910000000000000.1000000000000.2000000000000.30.50.40.40.40.40.30.30.30.30.20.20.40.70.60.60.60.60.50.50.50.50.40.4P(D)0.50.80.80.70.70.70.70.60.60.60.60.50.60.90.90.80.80.80.80.70.70.70.70.60.70.90.90.90.90.80.80.80.80.70.70.70.8110.90.90.90.90.80.80.80.80.70.91110.90.90.90.90.80.80.80.8111110.90.90.90.90.80.80.8 119 119

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Appendix B (Continued) P(D) vs P(U/D)Case P(U/ND)=0.5, P(LD)=0.5, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 24: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 00.10.20.30.40.50.60.70.80.91 00.20.40.60.81 00.10.20.30.40.50.60.70.80.91P(U/D)SP as a Function fo the WPTP(D)P(D) vs P(U/D) and SP from 0.0WTP to 1.0WTPCase P(U/ND)=0.5, P(LD)=0.5, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 25: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=0.5, and =0 120

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Appendix B (Continued) Table 17: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0.5, and =0 P(U/ND)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910000000000000.10.20.20.10.10.10.10.10.10.10.10.10.20.30.30.30.30.20.20.20.20.20.20.20.30.50.50.40.40.40.40.30.30.30.30.30.40.70.70.60.60.60.50.50.50.40.40.4P(D)0.5110.90.90.80.80.70.70.60.60.50.6111111110.90.90.80.7111111111110.8111111111110.911111111111111111111111 121 121

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Appendix B (Continued) P(D) vs P(U/ND)Case P(LD)=0.5, P(U/D)=0.5, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/ND) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 26: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=0.5, and =0 00.10.20.30.40.50.60.70.80.91 00.20.40.60.81 00.10.20.30.40.50.60.70.80.91P(U/ND)SP As a function of the WTPP(D)P(D) vs P(U/ND) and SP from 0.0WTP to 1.0WTPCase P(LD)=0.5, P(U/D)=0.5, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 27: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=05, and =0 122

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Appendix B (Continued) Table 18: MS for P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=1.0, and =0 P(U/D)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910000000000000.1000000000000.2000000000000.30.50.50.50.50.50.50.50.50.50.50.50.40.70.70.70.70.70.70.70.70.70.70.7P(D)0.50.80.80.80.80.80.80.80.80.80.80.80.60.90.90.90.90.90.90.90.90.90.90.90.70.90.90.90.90.90.90.90.90.90.90.90.8111111111110.911111111111111111111111 123 123

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Appendix B (Continued) P(D) vs P(U/D)Case P(U/ND)=0.5, P(LD)=1.0, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/D) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 28: Graph of MS of P(D) vs. P(U|D) Given P(U|ND)=0.5, P(LD)=1.0, and =0 00.10.20.30.40.50.60.70.80.91 00.20.40.60.81 00.10.20.30.40.50.60.70.80.91P(U/D)SP as a Function fo the WPTP(D)P(D) vs P(U/D) and SP= 0.0WTP,.., 1.0WTPCase P(U/ND)=0.5, P(LD)=1.0, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 29: 3-D Graph of the P(D) vs. P(U|D) Given P(U|ND)=0.5,P(LD)=1.0, and =0 124

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Appendix B (Continued) Table 19: MS for P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=1.0, and =0 P(U/ND)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910000000000000.10.20.20.20.20.20.20.20.20.20.20.20.20.30.30.30.30.30.30.30.30.30.30.30.30.50.50.50.50.50.50.50.50.50.50.50.40.70.70.70.70.70.70.70.70.70.70.7P(D)0.5111111111110.6111111111110.7111111111110.8111111111110.911111111111111111111111 125 125

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Appendix B (Continued) P(D) vs P(U/ND)Case P(LD)=1.0, P(U/D)=0.5, HC=0SP00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(U/ND) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 30: Graph of MS of P(D) vs. P(U|ND) Given P(U|D)=0.5, P(LD)=1.0, and =0 00.10.20.30.40.50.60.70.80.91 00.20.40.60.81 00.10.20.30.40.50.60.70.80.91P(U/ND)SP As a function of the WTPP(D)P(D) vs P(U/ND) and SP from 0.0WTP to 1.0WTPCase P(LD)=1.0, P(U/D)=0.5, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 31: 3-D Graph of the P(D) vs. P(U|ND) Given P(U|D)=0.5,P(LD)=1.0, and =0 126

PAGE 140

127 Table 20: MS for P(D) vs. P(LD) Given P(U|D)=0.5, P(U|ND)=0.5, and =0 P(LD)SP=0.0W T SP=0.1W T SP=0.2W T SP=0.3W T SP=0.4W T SP=0.5W T SP=0.6W T SP=0.7W T SP=0.8W T SP=0.9W T SP=1WT P 00.10.20.30.40.50.60.70.80.910111111111110.1111111111110.2111111111110.3111111111110.40000.10.30.50.50.60.60.70.7P(U)0.50000000.10.20.30.40.50.6000000000.10.20.30.70000000000.10.20.800000000000.10.900000000000100000000000 Appendix B (Continued) 127

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Appendix B (Continued) P(D) vs P(LD)Case P(U/D)= 0.5, P(U/ND)=0.5, HC=0SP 00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.70.80.91P(D)P(LD) SP=0.0WTP SP=0.1WTP SP=0.2WTP SP=0.3WTP SP=0.4WTP SP=0.5WTP SP=0.6WTP SP=0.7WTP SP=0.8WTP SP=0.9WTP SP=1WTP Figure 32: Graph of MS of P(D) vs. P(LD) Given P(U|D)=0.5, P(U|ND)=0.5, and =0 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91 00.10.20.30.40.50.60.70.80.91P(LD)SP As a function of the WTPP(D)P(D) vs P(LD) and SP from 0.0WTP to 1.0WTPCase P(U/D)= 0.5, P(U/ND)=0.5, HC=0SP 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1 Figure 33: 3-D Graph of the P(D) vs. P(LD) Given P(U|D)=0.5 P(U|ND)=0.5, and =0 128


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Ruiz-Brand, Francisco Javier.
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A decision support tool for accepting or rejecting donations in humanitarian relief organizations
h [electronic resource] /
by Francisco Javier Ruiz-Brand.
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[Tampa, Fla.] :
University of South Florida,
2004.
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Thesis (M.S.E.M.)--University of South Florida, 2004.
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Includes bibliographical references.
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Text (Electronic thesis) in PDF format.
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System requirements: World Wide Web browser and PDF reader.
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ABSTRACT: With the increase in the occurrence of disasters (natural and man-made) that leave people injured, handicapped or dead, the disaster management theory is gaining more importance. As a consequence, human assistance and disaster relief organizations are managing increasingly more inventories anticipated to help people in need. Donations are the common means used by humanitarian relief organizations for procuring commodities to support some of their programs. Previous experiences have indicated that donations become a burden instead of offering relief when they do not match actual victims' needs. Accepting or rejecting donations is a key issue that can produce not only economic losses but loss of lives as well. The objective of this thesis is to provide a means of assessing acceptance or rejection decisions using decision tree analysis theory and utility theory. The proposed model considers the inputs that a decision-maker may face when accepting or rejecting a donation. Such inputs include these categories: the probability of the occurrence of disaster, the need for and further use of a commodity, the unit price and holding cost of the item, the benefit provided by the donation, and the probability of having subsequent donations when the initial donation is initially rejected. Various scenarios are simulated in Excel® environment through the Monte Carlo process. This will assess the varied impacts from the alternative inputs in the decision making process; a sensitivity analysis will evaluate the effects of various decisions. The results obtained from the simulation of the diverse scenarios indicate that the decision of accepting or rejecting donations is driven more by the possibility of the use of the commodity than by the probability of occurrence of the disaster. The findings from the model also indicate that the decision of accepting or rejecting is more sensitive to the relationship of sale price to benefit deployment of the commodity than to sale price alone. The simulation of the expected monetary benefit of the relief provided results in the development of graphs that can affect the decision making process when accepting or rejecting donations.
590
Adviser: Ali Yalcin.
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disaster management.
decision making.
disaster relief.
humanitarian assistance.
decision under uncertainty.
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Dissertations, Academic
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x Engineering Management
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t USF Electronic Theses and Dissertations.
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