Dynamic Facility Location under Cumulative Customer Demand

TL;DR

This paper introduces a new dynamic facility location model that accounts for cumulative customer demand over time, providing more accurate planning solutions and demonstrating significant computational and service quality improvements.

Contribution

It develops two mixed-integer programming formulations for cumulative demand, analyzes their complexity, and proposes an efficient exact solution method with practical benefits.

Findings

The proposed method is five times faster than direct solving of the tighter formulation.

Accounting for cumulative demand improves planning solution quality.

Ignoring cumulative demand leads to suboptimal service levels.

Abstract

Dynamic facility location problems aim at placing one or more valuable resources over a planning horizon to meet customer demand. 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 show that one of them has a tighter continuous relaxation and allows the representation of more general customer demand behaviour. 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, since 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.