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Store location with multipurpose shopping trips and a new random utility customers’ choice model

Author

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  • Méndez-Vogel, Gonzalo
  • Marianov, Vladimir
  • Lüer-Villagra, Armin
  • Eiselt, H.A.

Abstract

This paper addresses retail store location in a duopoly. One firm, the so-called leader, has already located several stores, while a second firm, the follower that offers a different product, considers locating its stores in the same area. Both products have some degree of complementarity. Marianov et al. (2018) studied this problem considering a customer decision rule that is binary (winner-take-all) and deterministic (there are no uncertainties related to customers’ behavior). In that work, they concluded that multipurpose shopping has a strong influence on optimal store location. This paper extends that work by introducing random utility customer choice rules based on the Multinomial Logit model. Along these lines, we propose the new Partially Binary Logit rule, applicable to the case in which all stores of a firm have identical attributes, except for their location. In this case, a customer always chooses the least cost trip store of the firm to purchase its product. We propose one nonlinear and three linear formulations for the follower location problem, and a Branch and Cut method for one of them. Two of the formulations have a good performance for instances of up to at least 200 nodes. We compare the binary, Multinomial Logit, and Partially Binary Logit rules by analyzing the captured markets and location patterns for a large set of randomly generated 100-node instances.

Suggested Citation

  • Méndez-Vogel, Gonzalo & Marianov, Vladimir & Lüer-Villagra, Armin & Eiselt, H.A., 2023. "Store location with multipurpose shopping trips and a new random utility customers’ choice model," European Journal of Operational Research, Elsevier, vol. 305(2), pages 708-721.
    • Handle: RePEc:eee:ejores:v:305:y:2023:i:2:p:708-721
    DOI: 10.1016/j.ejor.2022.06.008
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    References listed on IDEAS

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    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 27-49.
    2. Lin, Yun Hui & Tian, Qingyun, 2021. "Branch-and-cut approach based on generalized benders decomposition for facility location with limited choice rule," European Journal of Operational Research, Elsevier, vol. 293(1), pages 109-119.
    3. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2021. "Optimizing facility location and design," European Journal of Operational Research, Elsevier, vol. 289(1), pages 31-43.
    4. Thill, Jean-Claude, 1992. "Spatial Duopolistic Competition with Multipurpose and Multistop Shopping," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 26(3), pages 287-304, September.
    5. Sedghi, Nafiseh & Shavandi, Hassan & Abouee-Mehrizi, Hossein, 2017. "Joint pricing and location decisions in a heterogeneous market," European Journal of Operational Research, Elsevier, vol. 261(1), pages 234-246.
    6. Rafael Suárez‐Vega & Dolores R. Santos‐Peñate & Pablo Dorta‐González, 2004. "Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem," Journal of Regional Science, Wiley Blackwell, vol. 44(3), pages 569-588, August.
    7. Kristoffersson, Ida & Daly, Andrew & Algers, Staffan, 2018. "Modelling the attraction of travel to shopping destinations in large-scale modelling," Transport Policy, Elsevier, vol. 68(C), pages 52-62.
    8. Eaton, B Curtis & Lipsey, Richard G, 1982. "An Economic Theory of Central Places," Economic Journal, Royal Economic Society, vol. 92(365), pages 56-72, March.
    9. Marianov, Vladimir & Eiselt, H.A. & Lüer-Villagra, Armin, 2018. "Effects of multipurpose shopping trips on retail store location in a duopoly," European Journal of Operational Research, Elsevier, vol. 269(2), pages 782-792.
    10. Li, Ran & Tong, Daoqin, 2017. "Incorporating activity space and trip chaining into facility siting for accessibility maximization," Socio-Economic Planning Sciences, Elsevier, vol. 60(C), pages 1-14.
    11. Subhash C. Narula & Mitchell Harwitz & Barry Lentnek, 1983. "Where Shall We Shop Today? A Theory Of Multiple‐Stop, Multiple‐Purpose Shopping Trips," Papers in Regional Science, Wiley Blackwell, vol. 53(1), pages 159-173, January.
    12. Yao, Rui & Bekhor, Shlomo, 2022. "A variational autoencoder approach for choice set generation and implicit perception of alternatives in choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 273-294.
    13. Freire, Alexandre S. & Moreno, Eduardo & Yushimito, Wilfredo F., 2016. "A branch-and-bound algorithm for the maximum capture problem with random utilities," European Journal of Operational Research, Elsevier, vol. 252(1), pages 204-212.
    14. Brandão, António & Correia-da-Silva, João & Pinho, Joana, 2014. "Spatial competition between shopping centers," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 234-250.
    15. Lüer-Villagra, Armin & Marianov, Vladimir & Eiselt, H.A. & Méndez-Vogel, Gonzalo, 2022. "The leader multipurpose shopping location problem," European Journal of Operational Research, Elsevier, vol. 302(2), pages 470-481.
    16. Mai, Tien & Lodi, Andrea, 2020. "A multicut outer-approximation approach for competitive facility location under random utilities," European Journal of Operational Research, Elsevier, vol. 284(3), pages 874-881.
    17. Jagpal, Sharan, 2008. "Fusion for Profit: How Marketing and Finance Can Work Together to Create Value," OUP Catalogue, Oxford University Press, number 9780195371055, Decembrie.
    18. Aros-Vera, Felipe & Marianov, Vladimir & Mitchell, John E., 2013. "p-Hub approach for the optimal park-and-ride facility location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 277-285.
    19. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    20. Vladimir Marianov & H. A. Eiselt, 2016. "On agglomeration in competitive location models," Annals of Operations Research, Springer, vol. 246(1), pages 31-55, November.
    21. Vladimir Marianov & H. A. Eiselt & Armin Lüer-Villagra, 2020. "The Follower Competitive Location Problem with Comparison-Shopping," Networks and Spatial Economics, Springer, vol. 20(2), pages 367-393, June.
    22. Oded Berman & Rongbing Huang, 2007. "The Minisum Multipurpose Trip Location Problem on Networks," Transportation Science, INFORMS, vol. 41(4), pages 500-515, November.
    23. Ljubić, Ivana & Moreno, Eduardo, 2018. "Outer approximation and submodular cuts for maximum capture facility location problems with random utilities," European Journal of Operational Research, Elsevier, vol. 266(1), pages 46-56.
    24. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    25. Wuyang Yu, 2020. "Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, January.
    26. Haase, Knut & Müller, Sven, 2014. "A comparison of linear reformulations for multinomial logit choice probabilities in facility location models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 689-691.
    27. Eaton, B Curtis & Lipsey, Richard G, 1979. "The Theory of Market Pre-emption: The Persistence of Excess Capacity and Monopoly in Growing Spatial Markets," Economica, London School of Economics and Political Science, vol. 46(182), pages 149-158, May.
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