Presenting a Maximum Capture Model by Calculating the Interval Facility Number and Taking into Account the Cost Objective Function

Document Type : Original Article


1 Ph.D student, Ferdowsi University of Mashhad.

2 Professor, Ferdowsi University of Mashhad.

3 Associate professor, Ferdowsi University of Mashhad.


The maximum capture problem seeks to find a suitable location for facilities in the network space and in a competitive condition. In this problem, the new company intends to enter the market with the aim of capturing more demand. In this study, the cost factor is considered to be a separate objective function and a bi-objective model is proposed. The number of facilities parameter is considered to be an interval and for its upper and lower bounds calculations two models are proposed. To obtain upper bound a model with the maximum capture objective and the maximum budget constraint and to obtain lower bound a model with the minimum cost objective and the minimum market share constraint. To solve the proposed model, a goal programming method is used. The steps of the research methodology and modelling are shown in a case study from Yazd city. The results show that if the weight of the objective functions is assumed to be equal and the investor neglect 7 % of the market share, 55% of initial investment could be saved.


1. Ahmadian, M. A. (2014). Modeling and solution of competitive location problem considering competitors reaction and pricing, Dissertation, science and Culture University (In Persian).
2. Benati, S. (1999). The maximum capture problem with heterogeneous customers. Computers and Operations Research, 26, 1351-1367
3. Benati, S., & Hansen, P., (2002). The maximum capture problem with random utilities: problem formulation and algorithms. European Journal of Operational Research, 143, 518-530.
4. Colombo, F., Cordone, R., & Lulli, G. (2016). The multimode covering location problem. Computers and operations research, 67, 25-33.
5. Eiselt, H. A., & Laporte, G. (1989). Competitive spatial models. European Journal of Operations Research, 39, 231-242.
6. Freire, A., S., Moreno, E., Yushimito, W., F. (2016). A branch-and-bound algorithm for the maximum capture problem with random utilities. European journal of operational research, in press.
7. Hosseini Nasab, H., & Izadpanahi, E. (2015). Using Fuzzy-Robust approach for Minimizing Transportation and Fuel Costs in Location Problem. Production and operations management, 11(2), 41-54 (In Persian).
8. Hua, G., Cheng, T. C. E., & Wang, S., (2011). The maximum capture per unit cost location problem. International Journal of Production Economics, 131, 568-574.
9. Kariznoei, A. (2013). Using AHP, Monte carlo simulation and PROMETHEE to prioritize cities and market selection. Dissertation, Ferdowsi university of Mashhad (In Persian).
10. Lotfalipour, Z. (2003). Bank branches location using AHP and Monte carlo simulation, Dissertation, Ferdowsi university of Mashhad (In Persian).
11. Mohaghar, A., & Ariaee, S. (2017). Location using GIS and weighted maximum covering model. Industrial management perspective, 26, 9-22 (In Persian).
12. ReVelle, C. (1986). The maximum capture or ‘‘Sphere of Influence’’ location problem: Hotelling revisited on a network. Journal of Regional Science 26 (2), 343-358.
13. ReVelle, C., & Serra, D. (1991). The maximum capture problem including relocation. INFOR, 29(2), 130-138.
14. Sari, Z. (2011). Mathematical models for competitive facility location model. Dissertation, Ferdowsi university of Mashhad (In Persian).
15. Serra, D., Marianov, V., & ReVelle, C. (1992). The hierarchical maximum capture problem. European Journal of Operations Research, 62(3), 58-69.
16. Serra, D., & Colomé, R. (2001). Maximum consumer choice and optimal locations models: Formulations and heuristics. Papers in Regional Science, 80, 439-464.
17. Shaikh, A., Salhi, S., & Ndiaye, M. (2012). Customer allocation in maximum capture problems. J Math Model Algor, 11, 281-293.
18. Shaikh, A., Salhi, S., & Ndiaye, M. (2015). New MAXCAP related problems: formulation and model solutions. Compiuters and industrial engineering, 85, 248-259.