Journal article
Distributionally robust facility location problem under decision-dependent stochastic demand
European journal of operational research, Vol.292(2), pp.548-561
07/16/2021
DOI: 10.1016/j.ejor.2020.11.002
Abstract
•We study distributionally robust facility location with a moment, decision-dependent ambiguity set.•We examine the case when means and variances of demand are piecewise linear functions of location solutions.•We derive exact mixed-integer linear programming reformulation as well as valid inequalities.•We conduct numerical studies to compare with decision-independent stochastic and distributionally robust approaches.•Our results show remarkable improvements in profit and quality of service using our approach.
While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. The results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by 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.
Details
- Title: Subtitle
- Distributionally robust facility location problem under decision-dependent stochastic demand
- Creators
- Beste Basciftci - University of Iowa, Business AnalyticsShabbir Ahmed - H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, USASiqian Shen - Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA
- Resource Type
- Journal article
- Publication Details
- European journal of operational research, Vol.292(2), pp.548-561
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.ejor.2020.11.002
- ISSN
- 0377-2217
- eISSN
- 1872-6860
- Grant note
- DOI: 10.13039/100000001, name: National Science Foundation
- Language
- English
- Date published
- 07/16/2021
- Academic Unit
- Business Analytics
- Record Identifier
- 9984119798702771
Metrics
18 Record Views