Abstract
We address a multi-period facility location problem with two customer segments 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. 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 planning capacity decisions and present a two-stage stochastic model for each one of them. While in the first model decisions related to capacity scalability are modeled as first-stage decisions, in the second model, capacity adjustments are deferred to the second stage. We develop the extensive forms of the associated stochastic programs for the case of demand uncertainty being captured by a finite set of scenarios. Additional inequalities are proposed to enhance the original formulations. An extensive computational study with randomly generated instances shows that the proposed enhancements are very useful. Specifically, 97.5% of the instances can be solved to optimality in much shorter computing times. Important insights are also provided into the impact of the two different frameworks for planning capacity adjustments on the facility network configuration and its total cost.
Highlights
Location analysis provides a framework for simultaneously finding sites for facilities and assigning spatially distributed demand points to these facilities to optimize some measurable criterion
A natural approach to the decision-making process is to develop a two-stage stochastic programming model, where the facility location and capacity planning decisions are made in the first stage, and the remaining processing and distribution decisions are deferred to the second stage
We have studied a novel multi-period facility location and capacity planning problem under uncertainty taking into account the sensitivity of each individual customer to delivery lead times
Summary
Location analysis provides a framework for simultaneously finding sites for facilities and assigning spatially distributed demand points to these facilities to optimize some measurable criterion (e.g., cost, profit). To the best of the authors’ knowledge, our work is the first attempt to understand the additional complexity that arises from incorporating stochasticity into the underlying difficult-to-solve deterministic facility location and capacity scalability problem in a multi-period setting For this reason, we focus on demand uncertainty and defer the consideration of additional uncertain parameters. Given that demand uncertainty is captured by a finite set of scenarios with known probabilities, we follow a scenario-based approach and formulate two-stage stochastic programs for two different strategies regarding capacity sizing. In both models, the first-stage problem determines the opening schedule for facilities and their initial capacities over the entire planning horizon before uncertainty about demand is revealed.
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