Dynamic-demand capacitated facility location problems with and without relocation

We consider two multi-period dynamic-demand capacitated location problems. In the first problem, the facilities are allowed to be relocated in each period, whereas in the second they are kept at a fixed location determined at the beginning of the planning horizon. We provide Lagrangian Relaxation and Benders Decomposition algorithms, including an epsilon-optimal BD algorithm, for the solution for the first model and a Benders Decomposition algorithm for the second. For detailed analysis, we generate a wide variety of instances to test the performance of the algorithms by taking into account varying number of customer locations and time periods in the planning horizon as well as fixed cost structures and facility capacities. We observe that the efficiency of the solution algorithms depends on the input data structure, specifically the cost structures, the facility capacities (which, in turn, dictate the expected number of open facilities), and the variation in the total customer demand from period to period.