Distributionally robust facility location problem under decision-dependent stochastic demand
Abstract
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. Here, 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 customermore »
- Authors:
-
[3]
- Sabanci Univ., Istanbul (Turkey)
- Georgia Inst. of Technology, Atlanta, GA (United States).
- Univ. of Michigan, Ann Arbor, MI (United States)
- Publication Date:
- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- OSTI Identifier:
- 1735793
- Grant/Contract Number:
- SC0018018; CMMI-1727618; CCF-1709094; CMMI-1633196
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Journal of Operational Research
- Additional Journal Information:
- Journal Volume: 292; Journal Issue: 2; Journal ID: ISSN 0377-2217
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Uncertainty modeling; Facility location; Distributionally robust optimization; Decision-dependent uncertainty; Mixed-integer linear programming
Citation Formats
Basciftci, Beste, Ahmed, Shabbir, and Shen, Siqian. Distributionally robust facility location problem under decision-dependent stochastic demand. United States: N. p., 2020.
Web. doi:10.1016/j.ejor.2020.11.002.
Basciftci, Beste, Ahmed, Shabbir, & Shen, Siqian. Distributionally robust facility location problem under decision-dependent stochastic demand. United States. https://doi.org/10.1016/j.ejor.2020.11.002
Basciftci, Beste, Ahmed, Shabbir, and Shen, Siqian. Tue .
"Distributionally robust facility location problem under decision-dependent stochastic demand". United States. https://doi.org/10.1016/j.ejor.2020.11.002. https://www.osti.gov/servlets/purl/1735793.
@article{osti_1735793,
title = {Distributionally robust facility location problem under decision-dependent stochastic demand},
author = {Basciftci, Beste and Ahmed, Shabbir and Shen, Siqian},
abstractNote = {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. Here, 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.},
doi = {10.1016/j.ejor.2020.11.002},
journal = {European Journal of Operational Research},
number = 2,
volume = 292,
place = {United States},
year = {Tue Nov 10 00:00:00 EST 2020},
month = {Tue Nov 10 00:00:00 EST 2020}
}
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