A Robust Stochastic Programming Model for the Well Location Problem: The Case of The Brazilian Northeast Region

Abstract

Slow-onset disasters, such as drought, are usually more destructive in the long term since they affect the productive capacity of a community, thereby preventing it from recovering using its resources. This requires the leaders and planners of drought areas to establish the best strategies for effective drought management. In this direction, the present work develops a robust stochastic programming approach for the problem of locating artesian wells for the relief of drought-affected populations under uncertainty. Our model considers different demand scenarios and proposes a novel perspective which considers both social and hydrogeological aspects for the location choice, aiming to maximize the affected area’s satisfaction through its prioritization using a composite drought risk index as well as to maximize the probability of success in water prospecting. We present a case study of our robust stochastic optimization approach for the Brazilian Semiarid Region using demand points from the database of Operação Carro-Pipa. Our findings show that a robust solution has a better expected value for the objective function considering all scenarios, so it can help decision makers to plan facility location and demand allocation under demand uncertainty, pointing out the best solution according to their degree of risk aversion.