A computational comparison of formulations for a multi-period facility location problem with modular capacity adjustments and flexible demand fulfillment

We consider a multi-period facility location problem that takes into account changing trends in customer demands and costs. To this end, new facilities can be established at pre-specified potential locations and initially existing facilities can be closed over a planning horizon. Furthermore, facilities operate with modular capacities that can be expanded or contracted over multiple periods. A distinctive feature of our problem is that two customer segments are considered with different sensitivity to delivery lead times. Customers in the first segment require timely demand satisfaction, whereas customers in the second segment tolerate late deliveries. A tardiness penalty cost is incurred to each unit of demand that is satisfied with delay. We propose two alternative mixed-integer linear formulations to redesign the facility network over the time horizon at minimum cost. Additional inequalities are developed to enhance the original formulations. A computational study is performed with randomly generated instances and using a general-purpose solver. Useful insights are derived from analyzing the impact of several parameters on network redesign decisions and on the overall cost, such as different demand patterns and varying values for the maximum delivery delay tolerated by individual customers.