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A Case Study of Network Design for Middle East Water Distribution Virginia Commonwealth University VCU Scholars Compass Theses and Dissertations Graduate School 2010 A Case Study of Network Design for Middle East Water Distribution Rachel Bullene Virginia Commonwealth University Follow this and additional works at: https://scholarscompass.vcu.edu/etd Part of the Physical Sciences and Mathematics Commons © The Author Downloaded from https://scholarscompass.vcu.edu/etd/2260 This Thesis is brought to you for free and open access by the Graduate School at VCU Scholars Compass. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of VCU Scholars Compass. For more information, please contact [email protected]. A Case Study of Network Design for Middle East Water Distribution Submitted in partial fulfillment of the requirements for the degree of Master of Science in Operations Research at Virginia Commonwealth University by Rachel E. Bullene Thesis Director: James Paul Brooks, Assistant Professor, Department of Statistical Sciences and Operations Research Virginia Commonwealth University Richmond, Virginia May 28, 2010 Acknowledgements I would like to thank my advisors, Dr. J. Paul Brooks, Dr. Edward Boone, and Dr. Vijay Satyal for their instruction, support, and guidance. I have learned more than I ever thought possible in the last two years. In addition I would like to acknowledge all of the incredi- bly dedicated and talented faculty members in the Department of Statistical Sciences and Operations Research who helped me throughout my program. This thesis is dedicated to my parents, Mitch and Judy Bullene, and my sister Rebecca Bullene. Without their love and encouragement I never would have been able to to accom- plish this. i Contents List of Figures iv List of Tables vi Abstract vii Introduction 1 The Problem . 1 Background . 2 PotentialSolutions ................................... 4 Israel’s Desalination Master Plan . 5 Research Objectives . 5 Finding an Equitable Solution 6 Math Programming Model of the Middle East Water Distribution Network . 7 MiddleEastWaterDistributionNetwork . 8 Multiple Objectives in the Middle East Water Distribution Network . 11 FixedChargeNetworkFlowModel . 13 EquityModel...................................... 18 Results . 19 Incorporating Uncertainty in the Middle East Water Distribution Network 21 IncorporatingUncertaintyintoLinearPrograms . 22 Stochastic Programming . 23 Robust Optimization . 24 Simulation Optimization . 25 IncorporatingUncertaintyinNetworkModels . 25 Bayesian Mixed Integer Programming . 27 ModelingInputParameters .............................. 29 Modeling Demand . 30 Modeling Costs . 37 Results of Deterministic Model . 43 ii Results of Bayesian Mixed Integer Program . 44 Most Probable Solution . 44 Component Probabilities . 46 Conclusions . 47 Appendix 54 iii List of Figures 1Exampleofanetwork...............................8 2Existingwaterdistributionnetwork.Thismapbackgroundandtheback- ground of all maps in this document are courtesy of UNEP/DEWA/GRID- Europe (United Nations Environmental Program, 2010) . 9 3Potentialwaterdistributionnetwork.Existingnetworkelementsareblue, potential new network elements are green, and the proposed large water con- veyanceprojectsareshowninred.. 11 4Minimumcostsolutionwithunequalper-capitademand.Theexistingnet- work elements are blue, the network elements installed in this solution are green, and the Med-Dead Water Conveyance is shown in red. 15 5Minimumcostsolutionwithequalper-capitademand.Theexistingnetwork elements are blue, the network elements installed in this solution are green, and the Red-Dead Water Conveyance is shown in red. 17 6StepsintheBayesianMixedIntegerProgrammingprocess..........28 7PopulationforecastfromDLMmodelforIsrael(inblue)withupperand lower bounds of the 95% credible predictive interval (in red), and the Israeli government’s population projection for 2010, 2015, 2020, and 2025 (Xs) . 31 8PopulationforecastfromDLMmodelforthePalestinianTerritories(inblue) with upper and lower bounds of the 95% credible predictive interval (in red), and the United Nation’s population projection the West Bank and Gaza in 2010,2015,2020,and2025(Xs) . 32 9 Population forecast from DLM model for Jordan (in blue) with upper and lower bounds of the 95% credible predictive interval (in red), and the United Nation’s population projection for Jordan in 2010, 2015, 2020, and 2025 (Xs) 33 10 Histogram of Israeli population predictions from 2010 to 2025 . 34 11 Regression model plotted on a scatter plot of the unit cost data. 40 12 Solution to the deterministic model. The existing network elements are blue, the network elements installed in this solution are green, and the Med-Dead WaterConveyanceisshowninred. 44 13 Most probable solution from the BMIP. The existing network elements are blue, the network elements installed in this solution are green, and the Red- Dead Water Conveyance is shown in red. 45 iv 14 Histogram of the capacity needed on the connection between the Red-Dead desalinationplantandJerusalem . 48 15 Solution to the model where cost is capped at $1.7B . 54 16 Solution to the model where cost is capped at $1.6B . 55 17 Solution to the model where cost is capped at $1.5B . 56 18 Solution to the model where cost is capped at $1.4B . 57 19 Solution to the model where cost is capped at $1.3B . 58 20 Solution to the model where cost is capped at $1.2B . 59 v List of Tables 1Variables......................................13 2ModelParameters.................................14 3Solutionat$1.7B.................................20 4Solutionat$1.6B.................................20 5Solutionat$1.5B.................................20 6Solutionat$1.4B.................................21 7Solutionat$1.3B.................................21 8Solutionat$1.2B.................................21 9Desalinationplantexample............................37 10 Example with annualized capital costs . 38 11 Breakdown of annual desalination plant costs . 38 12 Probability that a desalination plant is included in the least cost solution . 46 13 Probability that a new arc is included in the least cost solution. 47 14 Population figures from World Bank . 60 15 Israeli Population by District . 61 vi Abstract The Middle Eastern region encompassing Israel, Jordan, and the Palestinian Territories (West Bank and Gaza) is an arid region with fast growing populations. Adequate and equitable access to water for all the people of the region is crucial to the future of Middle East peace. However, the current water distribution system not only fails to provide an adequate and equitable allocation of water, but also results adverse impacts on the environment. This project involves building a mathematical model to aid decision-makers in designing an optimal water distribution network. A new method for incorporating uncertainty in optimization that is based on Bayesian simulation of posterior predictive distributions is used to represent uncertainty in demands and costs. The output of the model is a most-probable least-cost modication to the existing water distribution infrastructure. Additionally, the model output includes the probability that a network component (new desalination plant, new pipe, new canal) is part of a least-cost installation. vii Chapter 1: Introduction The Problem Water scarcity is a world-wide problem that has implications for public health, food supply, ecosystem health, and political stability. The problem of water scarcity, if not addressed, will get worse in the future. Areas of the world that are currently facing water deficits may be further stressed as demand for water increases with population growth and a rising standard of living. Additionally, existing supplies of freshwater could be threatened by shifting weather patterns as a result of climate change. The Middle Eastern region encompassing Israel, Jordan, and the Palestinian Territories (West Bank and Gaza) is especially vulnerable to water stress as it is one of the most arid regions on earth and it has one of the fastest growing populations. Adequate and equitable access to water for all the people of the region is crucial to the future of Middle East peace. However, the current water supply and transmission system is failing to satisfy demand or provide an equitable allocation of water. Furthermore, the continued overexploitation of water resources has resulted in a decline in water quality and in adverse impacts on the environment. This project involves building an optimization model that allows decision makers to evaluate various alternatives for a Middle East water supply and transmission network plan 1 that takes that will satisfy the population’s forecasted demand in 2025 in a cost-effective, equitable manner. Background Israel derives one third of its fresh, natural water from Lake Kinneret (the Sea of Galilee) basin and the remainder from the streams and groundwater in the Mountain Aquifer and the Coastal Aquifer. Beginning in 1960s, Israel undertook an ambitions program to build the National Water Carrier (NWC) to transport water from the sources in the northern part of the country to the drier southern agricultural region. At its inception, 80% of the natural fresh water was supplied by the NWC went to agriculture, but the situation now is completely reversed, with urban areas receiving 80% of the water for drinking water and for domestic purposes. As the municipal demand for water grows with population growth and a rising standard of living, the allocations of fresh water to agriculture have decreased dramatically.
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