Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

TL;DR

This paper introduces a novel distributionally robust facility location model that accounts for decision-dependent demand, providing improved profit and service quality over traditional models through exact reformulation and computational enhancements.

Contribution

It develops a decision-dependent distributionally robust optimization model with an exact MILP reformulation and valid inequalities, addressing demand dependence on location decisions.

Findings

Superior profit and service quality compared to existing models

Significant computational speed-ups due to formulation enhancements

Effective handling of decision-dependent demand in facility location

Abstract

Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information of stochastic demand as a piecewise linear function of facility-location decisions. Then, we propose a decision-dependent distributionally robust optimization model, and develop its exact mixed-integer linear programming reformulation. We further derive valid inequalities to strengthen the formulation. We conduct an extensive computational study, in which we compare our model with the existing (decision-independent) stochastic and robust models. Our results demonstrate superior performance of the proposed approach with remarkable improvement in profit and quality of service by extensively testing problem characteristics, in addition to computational speed-ups due to the formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.