Annals of Operations Research

, Volume 167, Issue 1, pp 297–306 | Cite as

Efficient solution approaches for a discrete multi-facility competitive interaction model

  • Robert Aboolian
  • Oded Berman
  • Dmitry KrassEmail author


In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments show that the approximate approach (with small α) performs extremely well solving large scale problems while the exact approach performs very well for small to medium-sized problems.


Competitive facility location Spatial interaction models Nonseparable convex knapsack problem Approximation 


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  1. Aboolian, R. (2002). Competitive facility location and design problem. Ph.D. Thesis, University of Toronto, Toronto, Canada. Google Scholar
  2. Aboolian, R., Berman, O., & Krass, D. (2007). Competitive facility location model with concave demand. European Journal on Operational Research, 181, 598–619. CrossRefGoogle Scholar
  3. Achabal, D., Gorr, W. L., & Mahajan, V. (1982). MULTILOCC, a multiple store location decision model. Journal of Retailing, 58, 5–25. Google Scholar
  4. Bazaraa, M. S., & Shetty, C. M. (1979). Nonlinear programming: theory and algorithms. New York: Wiley. (pp. 454, 490, 491). Google Scholar
  5. Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (1993). Nonlinear programming, theory and algorithms, 2nd edn. New York: Wiley. Google Scholar
  6. Berman, O., & Krass, D. (1998). Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities. Location Science, 6, 41–65. CrossRefGoogle Scholar
  7. Bretthauer, K.M., & Shetty, B. (2002). The nonlinear knapsack problem—algorithms and applications. European Journal of Operational Research, 138, 459–472. CrossRefGoogle Scholar
  8. Caprara, A., Pisinger, D., & Toth, P. (1999). Exact solution of the quadratic knapsack problem. INFORMS Journal on Computing, 11, 125–137. CrossRefGoogle Scholar
  9. Davies, R. L., & Rogers, D. S. (1984). Store location and store assessment research. New York: Wiley. Google Scholar
  10. Drezner, T. (1994). Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. Journal of Retailing, 70(1), 49–64. CrossRefGoogle Scholar
  11. Drezner, T. (1995). Competitive facility location in the plane. In Z. Drezner (Ed.), Facility location (pp. 291–298). Berlin: Springer. Google Scholar
  12. Drezner, T., & Drezner, Z. (1997). Replacing discrete demand with continous demand in a competitive facility location problem. Naval Research Logistics, 44, 81–95. CrossRefGoogle Scholar
  13. Drezner, T., & Salhi, S. (2002). Solving the multiple competitive facilities location problem. European Journal of Operational Research, 142, 138–151. CrossRefGoogle Scholar
  14. Dussault, J. P., Ferland, J. A., & Lemaire, B. (1986). Convex quadratic programming with one constraint and bounded variables. Mathematical Programming, 36, 90–104. CrossRefGoogle Scholar
  15. Gallo, G., Hammer, P. L., & Simon, B. (1980). Quadratic knapsack problems. Mathematical Programming, 12, 132–149. Google Scholar
  16. Ghosh, A., & Craig, C. S. (1984). A location-allocation model for facility planning in a competitive environment. Geographical Analysis, 20, 39–51. Google Scholar
  17. Ghosh, A., & Craig, C. S. (1987). Location strategies for retail and service firms. Lexington: Lexington Books. Google Scholar
  18. Ghosh, A., & Craig, C. S. (1991). FRANSYS: a franchise location model. Journal of Retailing, 67, 212–234. Google Scholar
  19. Ghosh, A., McLafferty, S. L., & Craig, C. S. (1987). Multifacilty retail networks. In Z. Drezner (Ed.), Facility location (pp. 301–330). Berlin: Springer. Google Scholar
  20. Hillsman, E. L., & Rhoda, R. (1978). Errors in measuring distances from populations to service centers. Annals of Regional Science, 12, 74–88. CrossRefGoogle Scholar
  21. Huff, D. L. (1962). Determining of intra-urban trade areas. Real estate research program, UCLA. Google Scholar
  22. Huff, D. L. (1964). Defining and estimating a trade area. Journal of Marketing, 28, 34–38. CrossRefGoogle Scholar
  23. Huff, D. L. (1966). A programmed solution for approximating an optimum retail location. Land Economics, 42, 293–303. CrossRefGoogle Scholar
  24. Klastorin, T. D. (1990). On a discrete nonlinear nonseparable knapsack problem. Operations Research Letters, 9, 233–237. CrossRefGoogle Scholar
  25. Lea, A. C., & Menger, G. L. (1990). An overview of formal methods for retail site evaluation and sales forecasting. Part 2. Spatial interaction models. The Operational Geographer, 8, 17–23. Google Scholar
  26. Nakanishi, M., & Cooper, L. G. (1974). Parameter estimates for multiplicative competitive interaction models-least square approach. Journal of Marketing Research, 11, 303–311. CrossRefGoogle Scholar
  27. Plastria, F. (1992). GBSSS, the generalized big square small square method for planar single facility location. European Journal of Operations Research, 62, 163–174. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.College of Business AdministrationCalifornia State University San MarcosSan MarcosUSA
  2. 2.Rotman School of ManagementUniversity of TorontoTorontoCanada

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