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Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

Beste Basciftci (beste.basciftci***at***gatech.edu)
Shabbir Ahmed (shabbir.ahmed***at***isye.gatech.edu)
Siqian Shen (siqian***at***umich.edu)

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 mixedinteger 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.

Keywords: Facilities planning and design; Distributionally robust optimization; Decision dependent uncertainty; Integer programming

Category 1: Robust Optimization

Category 2: Applications -- OR and Management Sciences (Supply Chain Management )


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Entry Submitted: 12/11/2019
Entry Accepted: 12/11/2019
Entry Last Modified: 01/07/2020

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