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Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms


  • Paul Berglund
  • Changhyun Kwon



We study a discrete facility location problem on a network, where the locating firm acts as the leader and other competitors as the followers in a Stackelberg-Cournot-Nash game. To maximize expected profits the locating firm must solve a mixed-integer problem with equilibrium constraints. Finding an optimal solution is hard for large problems, and full-enumeration approaches have been proposed in the literature for similar problem instances. We present a heuristic solution procedure based on simulated annealing. Computational results are reported. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Paul Berglund & Changhyun Kwon, 2014. "Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms," Networks and Spatial Economics, Springer, vol. 14(1), pages 117-132, March.
  • Handle: RePEc:kap:netspa:v:14:y:2014:i:1:p:117-132
    DOI: 10.1007/s11067-013-9217-3

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    References listed on IDEAS

    1. Drezner, Tammy & Drezner, Zvi & Salhi, Said, 2002. "Solving the multiple competitive facilities location problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 138-151, October.
    2. F. Parvaresh & S. Hashemi Golpayegany & S. Moattar Husseini & B. Karimi, 2013. "Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing," Networks and Spatial Economics, Springer, vol. 13(4), pages 445-470, December.
    3. Konur, Dinçer & Geunes, Joseph, 2012. "Competitive multi-facility location games with non-identical firms and convex traffic congestion costs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 373-385.
    4. Paul Berglund & Changhyun Kwon, 2014. "Robust Facility Location Problem for Hazardous Waste Transportation," Networks and Spatial Economics, Springer, vol. 14(1), pages 91-116, March.
    5. Frank Plastria & Lieselot Vanhaverbeke, 2007. "Aggregation without Loss of Optimality in Competitive Location Models," Networks and Spatial Economics, Springer, vol. 7(1), pages 3-18, March.
    6. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    7. Arostegui, Marvin Jr. & Kadipasaoglu, Sukran N. & Khumawala, Basheer M., 2006. "An empirical comparison of Tabu Search, Simulated Annealing, and Genetic Algorithms for facilities location problems," International Journal of Production Economics, Elsevier, vol. 103(2), pages 742-754, October.
    8. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Tan Miller & Terry Friesz & Roger Tobin & Changhyun Kwon, 2007. "Reaction Function Based Dynamic Location Modeling in Stackelberg–Nash–Cournot Competition," Networks and Spatial Economics, Springer, vol. 7(1), pages 77-97, March.
    10. Mehrdad Shahabi & Shirin Akbarinasaji & Avinash Unnikrishnan & Rachel James, 2013. "Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs," Networks and Spatial Economics, Springer, vol. 13(4), pages 497-514, December.
    11. Friesz, Terry L. & Rigdon, Matthew A. & Mookherjee, Reetabrata, 2006. "Differential variational inequalities and shipper dynamic oligopolistic network competition," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 480-503, July.
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