Dynamic facility location problem with modular capacity adjustments under uncertainty

We address a stochastic multi-period facility location problem with two customer segments, each having distinct service requirements. While customers in one segment receive preferred service, customers in the other segment accept delayed deliveries as long as lateness does not exceed a pre-specified threshold. In this case, late shipments incur additional tardiness penalty costs. The objective is to define a schedule for facility deployment and capacity scalability that satisfies all customer demands at minimum cost. Facilities can have their capacities adjusted over the planning horizon through incrementally increasing or reducing the number of modular units they hold. These two features, capacity expansion and capacity contraction, can help substantially improve the flexibility in responding to demand changes. Future customer demands are assumed to be unknown. We propose two different frameworks for the capacity scalability decisions and present a two-stage stochastic model for each one of them. When demand uncertainty is captured by a finite set of scenarios, each of which having some known probability of occurrence, we develop the extensive forms of the associated stochastic programs. Additional inequalities are derived to enhance the original formulations. An extensive computational study with randomly generated instances that are solved with a generalpurpose optimization solver demonstrate the usefulness of the proposed enhancements. Specifically, a considerably larger number of instances can be solved to optimality in much shorter computing times. Useful insights are also provided on the impact of the two different frameworks for planning capacity adjustments on the network configuration and total cost.