Solving the robust two-stage capacitated facility location problem with uncertain transportation costs

In this study, we start from a multi-source variant of the two-stage capacitated facility location problem (TSCFLP) and propose a robust optimization model of the problem that involves the uncertainty of transportation costs. Since large dimensions of the robust TSCFLP could not be solved to optimality, we design a memetic algorithm (MA), which represents a combination of an evolutionary algorithm (EA) and a modified simulated annealing heuristic (SA) that uses a short-term memory of undesirable moves from previous iterations. A set of computational experiments is conducted to examine the impact of different protection levels on the deviation of the objective function value. We also investigate the impact of variations of transportation costs that may occur on both transhipment stages on the total cost for a fixed protection level. The obtained results may help in identifying a sustainable and efficient strategy for designing a two stage capacitated transportation network with uncertain transportation costs, and may be applicable in the design and management of similar transportation networks.