Inverse optimization of integer programming games for parameter estimation arising from competitive retail location selection

Tobias Crönert, Layla Martin, Stefan Minner and Christopher S. Tang

European Journal of Operational Research, 2024, vol. 312, issue 3, 938-953

Abstract: When determining store locations, competing retailers must take customers’ store choice into consideration. Customers predominantly select which store to visit based on price, accessibility, and convenience. Incumbent retailers can estimate the weight of these factors (customer attraction parameters) using granular historical data. Their location decision under full information and simultaneous competition translates into an integer programming game. Unlike incumbents, new entrants lack this detailed information; however, they can observe the resulting location structure of incumbents. Assuming the observed location structure is (near-)optimal for all incumbent retailers, a new entrant can use these observations to estimate customer attraction parameters. To facilitate this estimation, we propose an “inverse optimization approach” for integer programming games (IPGs), enabling a new entrant to identify parameters that lead to the observed equilibrium solutions. We solve this “inverse IPG” via decomposition by solving a master problem and a subproblem. The master problem identifies parameter combinations for which the observations represent (approximate) Nash equilibria compared with optimal solutions enumerated in the subproblem. This row-generation approach extends prior methods for inverse integer optimization to competitive settings with (approximate) equilibria.

Keywords: Integer programming; Choice estimation; Retail location; Inverse optimization (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221723005131
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:312:y:2024:i:3:p:938-953

DOI: 10.1016/j.ejor.2023.06.041

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu (repec@elsevier.com).