Dynamic Facility Location Under Cumulative Customer Demand

Dynamic facility location problems aim at placing one or more valuable resources over a planning horizon to meet customer demand. The existing literature commonly assumes that customer demand quantities are defined independently for each time period. In many planning contexts, however, unmet demand carries over to future time periods. Unmet demand at some time periods may, therefore, affect decisions of subsequent time periods. This work studies a novel location problem, where the decision maker places facilities over time to capture cumulative customer demand. We propose two mixed-integer programming formulations for this problem, and we show that one of them has a tighter continuous relaxation and allows the representation of more general customer demand behavior. We characterize the computational complexity for this problem and analyze which problem characteristics result in NP hardness. We then propose an exact branch-and-Benders-cut method and show that this method is approximately five times faster, on average, than solving the tighter formulation directly in our computational experiments. Our results also quantify the benefit of accounting for cumulative customer demand within the optimization framework because the corresponding planning solutions perform much better than those obtained by ignoring cumulative demand or employing myopic heuristics. We also draw managerial insights on the quality of service perceived by customers when the provider places facilities under cumulative customer demand.

Funding: This work was supported by the Fonds de recherche du Québec [Grant FRQ-Institut de valorisation des données Research Chair], IVADO [Grant FRQ-IVADO Research Chair], and the Natural Sciences and Engineering Research Council of Canada [Grants 2017-05224 and 2024-04051]. Additionally, this work was funded by the Fonds de recherche du Québec - Nature et Technologie [Grant Doctoral Scholarship B2X-328911], and this research was enabled in part by support provided by Calcul Québec and the Digital Research Alliance of Canada.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2025.0104.