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Facility Location with Price-Sensitive Demands: Private, Public, and Quasi-Public

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  • Donald Erlenkotter

    (University of California, Los Angeles)

Abstract

We formulate a general model for an uncapacitated facility location problem in which demands are related to the prices established at the various locations. Pricing decisions and location decisions are determined simultaneously in this model, in contrast to traditional location models that assume fixed demands and prices. We show that a transformation of the general model is equivalent to the fixed-demand location model of Efroymson and Ray, and thus may be solved by any of the exact or heuristic methods available for that model. Specifying either a private sector objective of maximizing profits or a public sector objective of maximizing net social benefits provides a particular case of the general model. A third plausible objective is the "quasi-public" one of maximizing net social benefits subject to a constraint that ensures sufficient revenues to cover costs. A Lagrangian relaxation of this constraint, which yields another case of the general model, is used to develop a solution procedure for the quasi-public objective. Details of the solution approach are given for quadratic revenue functions, and an example illustrates the procedure.

Suggested Citation

  • Donald Erlenkotter, 1977. "Facility Location with Price-Sensitive Demands: Private, Public, and Quasi-Public," Management Science, INFORMS, vol. 24(4), pages 378-386, December.
    • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:4:p:378-386
    DOI: 10.1287/mnsc.24.4.378
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    Cited by:

    1. Morton O’Kelly & Henrique Luna & Ricardo Camargo & Gilberto Miranda, 2015. "Hub Location Problems with Price Sensitive Demands," Networks and Spatial Economics, Springer, vol. 15(4), pages 917-945, December.
    2. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "Robust alternative fuel refueling station location problem with routing under decision-dependent flow uncertainty," European Journal of Operational Research, Elsevier, vol. 306(1), pages 173-188.
    3. G Leonardi, 1981. "A Unifying Framework for Public Facility Location Problems—Part 1: A Critical Overview and Some Unsolved Problems," Environment and Planning A, , vol. 13(8), pages 1001-1028, August.
    4. T L Friesz & T Miller & R L Tobin, 1988. "Algorithms for Spatially Competitive Network Facility-Location," Environment and Planning B, , vol. 15(2), pages 191-203, June.
    5. Meng, Qiang & Huang, Yikai & Cheu, Ruey Long, 2009. "Competitive facility location on decentralized supply chains," European Journal of Operational Research, Elsevier, vol. 196(2), pages 487-499, July.
    6. G Leonardi, 1981. "A Unifying Framework for Public Facility Location Problems—Part 2: Some New Models and Extensions," Environment and Planning A, , vol. 13(9), pages 1085-1108, September.
    7. V F Dökmeci, 1989. "Multiplant Location with Respect to Price-Elastic Demand," Environment and Planning A, , vol. 21(9), pages 1169-1178, September.
    8. Michael Johnson & David Turcotte & Felicia Sullivan, 2010. "What Foreclosed Homes Should a Municipality Purchase to Stabilize Vulnerable Neighborhoods?," Networks and Spatial Economics, Springer, vol. 10(3), pages 363-388, September.
    9. Zhang, Yue, 2015. "Designing a retail store network with strategic pricing in a competitive environment," International Journal of Production Economics, Elsevier, vol. 159(C), pages 265-273.
    10. V F Dökmeci, 1991. "Optimum Location of Hierarchical Production Units with Respect to Price-Elastic Demand," Environment and Planning A, , vol. 23(11), pages 1671-1678, November.
    11. Geunes, Joseph & Shen, Zuo-Jun Max & Emir, Akin, 2007. "Planning and approximation models for delivery route based services with price-sensitive demands," European Journal of Operational Research, Elsevier, vol. 183(1), pages 460-471, November.
    12. Dominique Peeters & Jacques Thisse & Isabelle Thomas, 1998. "Transportation networks and the location of human activities," ERSA conference papers ersa98p268, European Regional Science Association.

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