Multiperiod transshipment location–allocation problem with flow synchronization under stochastic handling operations

The Transshipment Location-Allocation Problem consists of locating transshipment facilities (e.g., inter-modal hubs) of a transportation network and allocating freight flows trough them, from several origins to several destinations, to satisfy demand and supply constraints. The objective is to maximize the total net transportation utility given by the total shipping utility minus the total cost to locate the facilities. Moreover, flow synchronization at the facilities must also be ensured. Unfortunately, the flow synchronization depends on a broad set of unknown events, which could cause both unexpected reductions of the facility capacity and uncertain utility of handling operations. In this paper, we first want to evaluate how uncertainty on facility capacity and handling operations utility affects the Transshipment Location-Allocation Problem in terms of complexity, net gain, and optimal solutions. Moreover, we extend the problem from a single to a multi-period setting to have a wider view of future scenarios realizations and consequently synchronize the flows by using different facilities on different periods. We propose a two-stage Stochastic Programming formulation with recourse and analyze, over a ground set of instances, some well-known economic indicators to derive managerial insights on the importance of addressing uncertainty for the problem. Finally, given the computational burden of solving the deterministic equivalent problem, we propose several heuristics based on Progressive Hedging and test their performance.