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Locating Discretionary Service Facilities, II: Maximizing Market Size, Minimizing Inconvenience

Author

Listed:
  • Oded Berman

    (University of Toronto, Toronto, Ontario, Canada)

  • Dimitris Bertsimas

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Richard C. Larson

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Discretionary service facilities are providers of products and/or services that are purchased by customers who are traveling on otherwise preplanned trips such as the daily commute. Optimum location of such facilities requires them to be at or near points in the transportation network having sizable flows of different potential customers. N. Fouska (Fouska, N. 1988. Optimal Location of Discretionary Service Facilities. MS Thesis, Operations Research Center, MIT, Cambridge, Mass.) and O. Berman, R. Larson and N. Fouska (BLF [Berman, O., R. C. Larson, N. Fouska. 1992. Optimal location of discretionary service facilities. Trans. Sci. 26 (3) 201–211.]) formulate a first version of this problem, assuming that customers would make no deviations, no matter how small, from the preplanned route to visit a discretionary service facility. Here the model is generalized in a number of directions, all sharing the property that the customer may deviate from the preplanned route to visit a discretionary service facility. Three different generalizations are offered, two of which can be solved approximately by greedy heuristics and the third by any approximate or exact method used to solve the p -median problem. We show for those formulations yielding to a greedy heuristic approximate solution, including the formulation in BLF, that the problems are examples of optimizing submodular functions for which the G. Nemhauser, L. Wolsey and M. Fisher (Nemhauser, G. L., L. A. Wolsey, M. L. Fisher. 1978. An analysis of approximations for maximizing sub-modular set functions, I. Math. Prog. 14 265–294.) bound on the performance of a greedy algorithm holds. In particular, the greedy solution is always within 37% of optimal, and for one of the formulations we prove that the bound is tight.

Suggested Citation

  • Oded Berman & Dimitris Bertsimas & Richard C. Larson, 1995. "Locating Discretionary Service Facilities, II: Maximizing Market Size, Minimizing Inconvenience," Operations Research, INFORMS, vol. 43(4), pages 623-632, August.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:4:p:623-632
    DOI: 10.1287/opre.43.4.623
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    Cited by:

    1. Wu, Shanhua & Yang, Zhongzhen, 2018. "Locating manufacturing industries by flow-capturing location model – Case of Chinese steel industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 112(C), pages 1-11.
    2. Yang, Woosuk, 2018. "A user-choice model for locating congested fast charging stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 189-213.
    3. Capar, Ismail & Kuby, Michael & Leon, V. Jorge & Tsai, Yu-Jiun, 2013. "An arc cover–path-cover formulation and strategic analysis of alternative-fuel station locations," European Journal of Operational Research, Elsevier, vol. 227(1), pages 142-151.
    4. Tanaka, Ken-ichi & Furuta, Takehiro & Toriumi, Shigeki, 2019. "Railway flow interception location model: Model development and case study of Tokyo metropolitan railway network," Operations Research Perspectives, Elsevier, vol. 6(C).
    5. Guo, Fang & Yang, Jun & Lu, Jianyi, 2018. "The battery charging station location problem: Impact of users’ range anxiety and distance convenience," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 1-18.
    6. Li, Xiaopeng & Ma, Jiaqi & Cui, Jianxun & Ghiasi, Amir & Zhou, Fang, 2016. "Design framework of large-scale one-way electric vehicle sharing systems: A continuum approximation model," Transportation Research Part B: Methodological, Elsevier, vol. 88(C), pages 21-45.
    7. Acar, Müge & Kaya, Onur, 2019. "A healthcare network design model with mobile hospitals for disaster preparedness: A case study for Istanbul earthquake," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 273-292.
    8. Bogyrbayeva, Aigerim & Kwon, Changhyun, 2021. "Pessimistic evasive flow capturing problems," European Journal of Operational Research, Elsevier, vol. 293(1), pages 133-148.
    9. Marković, Nikola & Ryzhov, Ilya O. & Schonfeld, Paul, 2017. "Evasive flow capture: A multi-period stochastic facility location problem with independent demand," European Journal of Operational Research, Elsevier, vol. 257(2), pages 687-703.
    10. Lin, Cheng-Chang & Lin, Chuan-Chih, 2018. "The p-center flow-refueling facility location problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 124-142.
    11. Wu, Tai-Hsi & Lin, Jen-Nan, 2003. "Solving the competitive discretionary service facility location problem," European Journal of Operational Research, Elsevier, vol. 144(2), pages 366-378, January.
    12. Barros, Lilian & Riley, Michael, 2001. "A combinatorial approach to level of repair analysis," European Journal of Operational Research, Elsevier, vol. 129(2), pages 242-251, March.
    13. Yongxi Huang & Shengyin Li & Zhen Qian, 2015. "Optimal Deployment of Alternative Fueling Stations on Transportation Networks Considering Deviation Paths," Networks and Spatial Economics, Springer, vol. 15(1), pages 183-204, March.
    14. Weiping Zeng & Ignacio Castillo & M. Hodgson, 2010. "A Generalized Model for Locating Facilities on a Network with Flow-Based Demand," Networks and Spatial Economics, Springer, vol. 10(4), pages 579-611, December.
    15. Taymaz, S. & Iyigun, C. & Bayindir, Z.P. & Dellaert, N.P., 2020. "A healthcare facility location problem for a multi-disease, multi-service environment under risk aversion," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    16. Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2013. "Infrastructure Planning for Electric Vehicles with Battery Swapping," Management Science, INFORMS, vol. 59(7), pages 1557-1575, July.
    17. Miyagawa, Masashi, 2010. "Distributions of rectilinear deviation distance to visit a facility," European Journal of Operational Research, Elsevier, vol. 205(1), pages 106-112, August.
    18. Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    19. Li, Shengyin & Huang, Yongxi, 2014. "Heuristic approaches for the flow-based set covering problem with deviation paths," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 144-158.
    20. Tong, Daoqin & Ren, Fang & Mack, James, 2012. "Locating farmers’ markets with an incorporation of spatio-temporal variation," Socio-Economic Planning Sciences, Elsevier, vol. 46(2), pages 149-156.
    21. Timothy C. Matisziw, 2019. "Maximizing Expected Coverage of Flow and Opportunity for Diversion in Networked Systems," Networks and Spatial Economics, Springer, vol. 19(1), pages 199-218, March.

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