Artículos regulares

 

A Divide-and-Conquer Approach to Commercial Territory Design

 

Procedimiento divide y vencerás para el diseño de territorios comerciales

 

M. Angélica Salazar-Aguilar¹, J. Luis González-Velarde², and Roger Z. Ríos-Mercado³

 

¹ Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), HEC Montréal, Montréal, Canadá angelica.salazar@cirrelt.ca, Gonzalez.velarde@itesm.mx

² Center for Quality and Manufacturing, Tecnológico de Monterrey, México

³ Graduate Program in Systems Engineering, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, México, roger.rios@uanl.edu.mx

 

Article received on 09/02/2011;
accepted on 20/01/2012.

 

Abstract

A new heuristic procedure for a commercial territory design problem is introduced in this work. The proposed procedure is based on the divide-and-conquer paradigm and basically consists of a successive dichotomy process on a given large instance of the problem. During this process, a series of integer quadratic subproblems is solved. The obtained computational results have shown that the proposed heuristic is an attractive technique for obtaining locally optimal solutions for large instances which are intractable by using exact optimization methods.

Keywords: Territory design, heuristic optimization, integer quadratic programming, divide-and-conquer approach.

 

Resumen

En este trabajo se presenta un procedimiento heurístico para el diseño de territorios comerciales. El procedimiento propuesto, basado en el paradigma dividir-y-vencer, consiste básicamente en un proceso de dicotomías sucesivas a partir de una instancia dada. Durante este proceso se resuelven una serie de subproblemas de programación cuadrática entera. Los resultados computacionales muestran que la heurística propuesta es una técnica de solución atractiva que permite la obtención de soluciones óptimas locales para instancias grandes del problema, las cuales resultan intratables al intentar resolverlas a través de métodos exactos.

Palabras clave: Diseño territorial, optimización heurística, programación cuadrática entera, procedimiento divide y vencerás.

 

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Acknowledgements

The presentation of the paper was improved thanks to the comments by two anonymous referees. This work was supported by the Mexican National Council for Science and Technology under grants SEP-CONACYT 48499-Y and SEP-CONACYT 61903, Universidad Autónoma de Nuevo León under its Scientific and Technological Research Support, grant UANL-PAICYT CE012-09, and Tecnológico de Monterrey under research grant CAT128. The research of the first author has been funded by a doctoral fellowship from Universidad Autónoma de Nuevo León, grant NL-2006-C09-32652.

 

References

1. Bacao, F., Lobo, V., & Painho, M. (2005).Applying genetic algorithms to zone design. Soft Computing, 9(5), 341-348.         [ Links ]

2. Bertolazzi, P., Bianco, L., & Ricciardelli, S. (1977). A method for determining the optimal districting in urban emergency services. Computers & Operations Research, 4(1), 1-12.         [ Links ]

3. Blais, M., Lapierre, S. D., & Laporte, G. (2003). Solving a home-care districting problem in an urban setting. Journal of the Operational Research Society, 54(11), 1141-1147.         [ Links ]

4. Bong, C.W. & Wang, Y.C. (2004). A multiobjective hybrid metaheuristic approach for GIS-based spatial zone model. Journal of Mathematical Modelling and Algorithms, 3(3), 245-261.         [ Links ]

5. Bozkaya, B., Erkut, E., & Laporte, G. (2003). A tabu search heuristic and adaptive memory procedure for political districting. European Journal of Operational Research, 144(1), 12-26.         [ Links ]

6. Caballero-Hernández, S.I., Ríos-Mercado, R.Z., López, F., & Schaeffer, S.E. (2007). Empirical evaluation of a metaheuristic for commercial territory design with joint assignment constraints. In J.E. Fernandez, S. Noriega, A. Mital, S.E. Butt, T.K. Fredericks (Eds.), Proceedings of the 12th Annual International Conference on Industrial Engineering Theory, Applications, and Practice (IJIE), Cancun, México, 422-427.         [ Links ]

7. Chou, C.I., Chu, Y.L., & Li, S.P. (2007). Evolutionary strategy for political districting problem using genetic algorithm. Computational Science - ICCS 2007, Lecture Notes in Computer Science, 4490, 1163-1166.         [ Links ]

8. Drexl, A. & Haase, K. (1999). Fast approximation methods for sales force deployment. Management Science, 45(10), 1307-1323.         [ Links ]

9. Fleischmann, B. & Paraschis, J. N. (1988). Solving a large scale districting problem: A case report. Computers & Operations Research, 15(6), 521-533.         [ Links ]

10. Garfinkel, R.S. & Nemhauser, G.L. (1970). Optimal political districting by implicit enumeration techniques. Management Science, 16(8), B495-B508.         [ Links ]

11. Guo, J., Trinidad, G., & Smith, N. (2000). MOZART: A multi-objective zoning and aggregation tool. Proceedings of the Philippine Computing Science Congress (PCSC), Cebu City, Philippines, 197-201.         [ Links ]

12. Hess, S.W. & Samuels, S.A. (1971). Experiences with a sales districting model: Criteria and implementation. Management Science, 18(4), P41-P54.         [ Links ]

13. Hess, S.W., Weaver, J.B., Siegfeldt, H.J., Whelan, J.N., & Zitlau, P.A. (1965). Nonpartisan political redistricting by computer. Operations Research, 13(6), 998-1006.         [ Links ]

14. Hojati, M. (1996). Optimal political districting. Computers & Operations Research, 23(12), 1147-1161.         [ Links ]

15. Kalcsics, J., Nickel, S., & Schröder, M. (2005). Towards a unified territorial design approach -Applications, algorithms, and GIS integration. TOP, 13(1), 1-56.         [ Links ]

16. Marlin, P.G. (1981). Application of the transportation model to a large-scale districting problem. Computers & Operations Research, 8(2), 83-96.         [ Links ]

17. Mehrotra, A., Johnson, E.L., & Nemhauser, G.L. (1998). An optimization based heuristic for political districting. Management Science, 44(8), 1100-1114.         [ Links ]

18. Muyldermans, L., Cattrysse, D., Van Oudheusden, D., & Lotan, T. (2002). Districting for salt spreading operations. European Journal of Operational Research, 139(3), 521-532.         [ Links ]

19. Pezzella, F., Bonanno, R., & Nicoletti, B. (1981). A system approach to the optimal health-care districting. European Journal of Operational Research, 8(2), 139-146.         [ Links ]

20. Ricca, F. (2004). A multicriteria districting heuristic for the aggregation of zones and its use in computing origin-destination matrices. INFOR: Information Systems and Operational Research, 42(1), 61-77.         [ Links ]

21.Ricca, F. & Simeone, B. (2008). Local search algorithms for political districting. European Journal of Operational Research, 189(3), 1409-1426.         [ Links ]

22. Ríos-Mercado, R.Z. & Fernández, E. (2009). A reactive GRASP for a commercial territory design problem with multiple balancing requirements. Computers & Operations Research, 36(3), 755-776.         [ Links ]

23. Salazar-Aguilar, M.A., Ríos-Mercado, R.Z., & Cabrera-Ríos, M. (2011). New models for commercial territory design. Networks and Spatial Economics, 11(3), 487-507.         [ Links ]

24. Salazar-Aguilar, M.A. (2010). Models, Algorithms, and Heuristics for Multiobjective Commercial Territory Design. PhD thesis, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Nuevo León, México.         [ Links ]

25. Segura-Ramiro, J.A., Ríos-Mercado, R.Z., Álvarez-Socarrás, A.M., & de Alba, K. (2007). A location-allocation heuristic for a territory design problem in a beverage distribution firm. In J.E. Fernandez, S. Noriega, A. Mital, S.E. Butt, T.K. Fredericks (Eds.), Proceedings of the 12th Annual International Conference on Industrial Engineering Theory, Applications, and Practice (IJIE), Cancun, México, 428-434.         [ Links ]

26. Tavares-Pereira, F., Figueira, J.R., Mousseau, V., & Roy, B. (2007). Multiple criteria districting problems: The public transportaron network pricing system of the Paris región. Annals of Operations Research, 154(1), 69-92.         [ Links ]

27. Xu, R. & Wunsch, D., II (2005). Survey of clustering algorithms. IEEE Transactions on Neural Networks, 16(3), 645-678.         [ Links ]