An Improved Stochastic Optimization Model for Water Supply Pumping Systems in Urban Networks

This study investigates a pump scheduling problem for the collection, transfer and storage of water in water supply systems in urban networks. The objective of this study is to determine a method to minimize the electricity costs associated with pumping operations. To address the dynamic and random nature of water demand, we propose a two-stage stochastic programming model with recourse, where the random variables are represented by a finite, discrete set of realizations or scenarios. The developed mathematical model is an extension of a previously developed deterministic model in the literature and reflects the basic assumption that a fixed cost could be incurred by the activating/deactivating activities of the hydraulic pumps. To control the possible violations of the water demand constraints for different scenarios, we also analyze a robustness technique in an attempt to obtain “almost feasible” solutions. In addition, we adopt the so-called Mean Absolute Deviation criterion, which is a risk-aversion criterion, to obtain second-stage costs that are less dependent on the realizations of the scenarios. The scenarios were generated using a Monte Carlo simulation procedure that may use any probability distribution to produce empirical probabilities of the random variables. Because the proposed pump scheduling problem with fixed cost is a two-stage stochastic mixed 0−1 program, we developed an efficient hybrid heuristic to obtain acceptable solutions for practical scenarios with a reasonable computational time. The overall results evidence the stability of the scenario generation method, the sensitivity of the solution based on the key parameters of the mathematical model, and the efficiency of the heuristic in solving large scenarios. Finally, we show that it is possible to conserve resources by solving the stochastic programming model rather than adopting simpler approaches based on the expected value.



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