Robust Stochastic Models for Profit-Maximizing Hub Location Problems

Abstract

This paper introduces robust stochastic models for profit -maximizing capacitated hub location problems in which two different types of uncertainty, including stochastic demand and uncertain revenue, are simultaneously incorporated into the problem. First, a two-stage stochastic program is presented in which demand and revenue are jointly stochastic. Next, robust stochastic models are developed to better model uncertainty in the revenue while keeping the demand stochastic. Two particular cases are studied based on the dependency between demand and revenue. In the first case, a robust stochastic model with a min-max regret objective is developed assuming a finite set of scenarios that describes uncertainty associated with the revenue under a revenue-elastic demand setting. For the case when demand and revenue are independent, robust stochastic models with a max-min criterion and a min-max regret objective are formulated considering both interval uncertainty and discrete scenarios, respectively. It is proved that the robust stochastic version with max-min criterion can be viewed as a special case of the min-max regret stochastic model. Exact algorithms based on Benders decomposition coupled with a sample average approximation scheme are proposed. Exploiting the repetitive nature of sample average approximation, generic acceleration methodologies are developed to enhance the performance of the algorithms enabling them to solve large-scale intractable instances. Extensive computational experiments are performed to consider the efficiency of the proposed algorithms and also to analyze the effects of uncertainty under different settings. The qualities of the solutions obtained from different modeling approaches are compared under various parameter settings. Computational results justify the need to solve robust stochastic models to embed uncertainty in decision making to design resilient hub networks.