Water Supply and Demand Sensitivities of Linear Programming Solutions to a Water Allocation Problem

Author(s)
Konstantine P. Georgakakos

Abstract

This work formulates and implements a mathematical optimization program to assist water managers with water allocation and banking decisions to meet demands. Linear programming is used to formulate the constraints and objective function of the problem and tests of the developed program are performed with data from the Castaic Lake Water Agency (CLWA) in Southern California. The problem is formulated as a deterministic programming problem over a five year planning horizon with annual resolution. The program accepts annual water allocations from the State Water Project (SWP) in California. It then determines the least-cost feasible allocation of this water toward meeting annual demands in the five-year planning horizon. Local water sources, including water recycling, and water banking programs with their constraints and costs are considered to determine the optimal water allocation policy within the planning horizon. Although there is not enough information to fully account for the uncertainty in future allocations and demands as part of the decision problem solution for CLWA, uncertainty in the SWP allocation is considered in the tests, and sensitivity analyses is performed with respect to demand increases to derive inferences regarding the behavior of the median minimum-cost solutions and of the risk of failure to meet demand.

This work formulates and implements a mathematical optimization program to assist water managers with water allocation and banking decisions to meet demands. Linear programming is used to formulate the constraints and objective function of the problem and tests of the developed program are performed with data from the Castaic Lake Water Agency (CLWA) in Southern California. The problem is formulated as a deterministic programming problem over a five year planning horizon with annual resolution. The program accepts annual water allocations from the State Water Project (SWP) in California. It then determines the least-cost feasible allocation of this water toward meeting annual demands in the five-year planning horizon. Local water sources, including water recycling, and water banking programs with their constraints and costs are considered to determine the optimal water allocation policy within the planning horizon. Although there is not enough information to fully account for the uncertainty in future allocations and demands as part of the decision problem solution for CLWA, uncertainty in the SWP allocation is considered in the tests, and sensitivity analyses is performed with respect to demand increases to derive inferences regarding the behavior of the median minimum-cost solutions and of the risk of failure to meet demand.

Cite this paper

K. Georgakakos, "Water Supply and Demand Sensitivities of Linear Programming Solutions to a Water Allocation Problem,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1285-1297. doi: 10.4236/am.2012.330185.

K. Georgakakos, "Water Supply and Demand Sensitivities of Linear Programming Solutions to a Water Allocation Problem,"

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