A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities

This study focuses on the development of a modeling framework for multi-period stochastic capacitated multiple allocation hub location problems. We consider a planning horizon divided into several time periods. Uncertainty is assumed for the demands. The decisions to make concern the location of the hubs, their initial capacity, the capacity expansion of existing hubs and the transportation between origin-destination pairs. The goal is to minimize the total expected cost. For the situation in which uncertainty can be captured by a finite set of scenarios each occurring with some estimated probability we derive the extensive form of the deterministic equivalent. The resulting model is compact. However, it includes a set of binary variables that becomes too large for medium and large instances of the problem and thus hardly can it be tackled by a general optimization solver. For this reason, enhancements are proposed to the model making it possible to solve optimally instances that could not be solved using the initial model. This is confirmed by the computational tests performed using the well-known CAB data.