Uncertainty Quantification for a Middle East Water Supply System

Abstract

This paper introduces a framework for incorporating uncertainty in water supply system models that uses Bayesian statistics and mixed-integer programming. The output of the framework includes the most probable least cost solution, the probability of feasibility for a given solution, component probabilities for each decision, and a distribution of the optimal objective function value. The method is applied to the problem of developing a water supply system design for Israel, Jordan, and the Palestinian territories. The method allows decision makers to evaluate various alternatives for a water supply plan that incorporates uncertainties in future demand and costs. The design of a water supply plan is a concern with properties that are distinct from traditional approaches to the design of water distribution systems; namely, local engineering decisions concerning pipe diameters and water pressure are not explicitly modeled, but large-scale decisions concerning the construction of water conveyances (pipes, canals, and tunnels) and sources (desalination plants) are the focus in the model.