Developing a Mathematical Model for Competitive Facility Location with Multiple Commodities and Multiple Competitors

Document Type : Original Article


1 PhD student, Shahid Beheshti University.

2 Professor, Shahid Beheshti University.

3 Assistant Professor, Shahid Beheshti University.

4 Associate Professor, Shahid Beheshti University.


Facility location along with taking account the competition is a critical component of strategic planning. The location affects the competitiveness and market share of new entrants, in long-term. Because of the complications of location problems, most of the location models are faced whit many different limitations. In this paper a competitive facility location model with three competitors which produce two commodities is developed. The problem is modeled in the form of a location-price game. A bi-level model is developed to investigate the location and price. In location-pricing models, the location decision should come before the pricing game. From the second level and the use of Nash equilibrium, equilibrium will be obtained. In this paper, probabilistic costumer behavior with the help of exponential function is modeled. A metaheuristic based on tabu search is proposed to search the optimal location-price solution of the model. Findings show that changing the equilibrium price affect the profitability of new entry firms.


Main Subjects

  1. Aboolian, R., Oded, B., & Krass, D. (2021). Optimizing facility location and design. European Journal of Operational Research, 289(1), 31-43.
  2. Alimi, A., Kazemi, M., Pooya, A. & Naji Azimi, Z. (2018).Presenting a maximum capture model by calculating the interval facility number and taking into account the cost objective function. The Journal of Industrial management Perspective, 8(30), 71-83. (In Persian)
  3. Arbib, C., Pinar, M. C., & Tonelli, M. (2020). Competitive location and pricing on a line with metric transportation cost. European Journal of Operational Research, 28(1), 188-200.
  4. Ashtiani, M. (2016). Competitive location: a state-of-art review. International Journal of Industrial Engineering Computations, 7(1), 1-18.
  5. Bitaraf, A. (2021). The use of the tabu search methaheuristic to solve location problems: a review. Application of geography information system and remote sensing in planning, 12(1), 26-40. (In Persian)
  6. , Z. & Kochetov, Yu. (2012). A double VNS heuristic for the facility location and pricing problem. Electronic Notes in Discrete Mathematics, 39, 29–34.
  7. Diaz-Banez, J.M., Heredia, M., Pelegrin, B., Perez-Lantero, P. & Ventura, I. (2011). Finding all pure strategy Nash equilibria in a planar location game. European Journal of Operational Research, 214, 91–98.
  8. Drezner, T. (2014). A review of competitive facility location in the plane. Logestic research, 7, 102-114.
  9. Eiselt, H.A. & Marianov, V. (2011). Foundation of Location Analysis. Springer .Newyork
  10. Fernandez, J., Salhi, S. & G-Toth, B.(2014). Location equilibria for a continuous competitive facility location problem under delivered pricing.Computers & Opration Research,41(1):185-195
  11. Fischer, K. (2002). Sequential Discrete p-Facility Models for Competitive Location Planning. Annals of Operations Research, 111, 253–270.
  12. García, M.D., Pelegrín, B. & Fernández, P. (2011). Location Strategy for a Firm Under Competitive Delivered Prices. Ann Reg Sci, 47, 1–23.
  13. , P & Dias.,J.(2010(. A two-player competitive discrete location model with simultaneous decisions. European Journal of Operational Research, 207, 1419–1432.
  14. Hotelling, H. (1991).The Economics of Exhaustible Resoources. Bulletin of Mathematical Biology, 53, 281–312.
  15. Karakitsiou, A. (2015). Modeling Discrete Competitive Facility Location. Springer. 1st ed. Newyork.
  16. Laporte, G., Nickel, S. & da Gama, F. (2015). Location science. Springer International Publishing Switzerland.
  17. Lederer, P.J. & Thisse, J.F. (1990). Competitive Location on Networks under Delivered Priving. Operations Research Letters, 9, 147-153.
  18. Lu, X., Li, J. & Yang, F. (2010). Analyses of location-price game on network with stochastic customer behavior and its heuristic. J Syst Sci Complex, 23, 701–714.
  19. Maa, H., Lia, X., Guana, X., Zhaob, X. & Wangb, L. (2020). A single-facility competitive location problem in the plane based on customer choice rules. Journal of Data, Information and Management2(4), 323-336
  20. Mai, T. & Lodi, A. (2020). A multicut outer-approximation approach for competitive facility location under random utilities. European Journal of Operational Research, 284(3), 874-881.
  21. Makui, A., Sarajian, A. &Torkestani, S. (2014). Review on Facility location with game theory papers. Journal of industrial engineering research in production systems, 2(3), 1-19 (In Persian)
  22. Makui, A., Ghousi, R. & Asadi, Z.(2021). A Review of Competitive Facility location. Journal of industrial engineering research in production systems, 8(17), 227-273. (In Persian)
  23. Marvin, A., Jr., Sukran, N., Basheer M. (2006). An empirical comparison of Tabu Search, Simulated Annealing, and Genetic Algorithms for facilities location problems. J. Production Economics, 103, 742–754.
  24. Miliotis, P., Dimopoulou, M., & Giannikos, I. (2002). A hierarchical location model for locating bank branches in a competitive environment. International transactions in operational research, 9(5), 549-565.
  25. Mohaghar, A., & Ariaee, S. (2017).Location using GIS and Weighted Maximum covering model. The Journal of Industrial management Perspective, 26, 9-22. (In Persian)
  26. Plegrin, B., Dorta-Gonzales, P. & Hernandez, P. (2011). Finding location equilibria for competing firms under delivered pricing. Journal of the Operational Research Society, 62, 729 –741.
  27. Plegrin, M., & Plegrin, B. (2107). Nash equilibria in location games on a network. OR Spectrum, 39, 775-791.
  28. Qi, M., Xia, M., Zhang, Y., & Miao, L.(2017) Competitive Facility Location Problem with Foresight Considering Service Distance Limitations. Computers & Industrial Engineering, 112, 483-491.
  29. Raoufinia, M. Baradaran, V., & Sharjerdi, R. (2018). A dynamic game theory model for analyzing competition in the oligopoly markets. The Journal of Industrial management Perspective, 8(31), 63-94. (In Persian)
  30. Redondo, L., Fernandez, J.L., Garcia, J. & Ortigosa, P.M. (2008). Heuristics for the facility location and design (1|1)-centroid problem on the plane. Springer Science+Business Media, LLC.
  31. Rohaninejad, M., Navidi, H., Nouri, B. V., & Kamranrad, R. (2017). A new approach to cooperative competition in facility location problems: Mathematical formulations and an approximation algorithm. Computers and Operations Research, 83, 45-53.
  32. Serra, D., & ReVelle, C. (1999). Competitive Location and Pricing on Networks. Geographical Analysis, 31, 109–129.
  33. Shan, W., Yan, Q., Chao Chen, Mengjie Zhang, M., Yao, B., & Fu, X. (2019). Optimization of competitive facility location for chain stores. Annals of Operations research,273(1-2):187-205
  34. Zanjirani Farahani, R., & Hekmatfar, M. (2009). Facility Location Concepts, Models, Algorithms and Case Studies. Chapter, 12, 270-294.
  35. Zanjirani Farahani, , Asgri, N., Heidari, N., Hosseinnia, M. & Goh, M. (2014). Covering problems in facility location: A review. Computers & Industrial Engineering, 62, 368–407.