Abstract
In this work, a series of novel formulations for a commercial territory design problem motivated by a real-world case are proposed. The problem consists on determining a partition of a set of units located in a territory that meets multiple criteria such as compactness, connectivity, and balance in terms of customers and product demand. Thus far, different versions of this problem have been approached with heuristics due to its NP-completeness. The proposed formulations are integer quadratic programming models that involve a smaller number of variables than heretofore required. These models have also enabled the development of an exact solution framework, the first ever derived for this problem, that is based on branch and bound and a cut generation strategy. The proposed method is empirically evaluated using several instances of the new quadratic models as well as of the existing linear models. The results show that the quadratic models allow solving larger instances than the linear counterparts. The former were also observed to require fewer iterations of the exact method to converge. Based on these results the combination of the quadratic formulation and the exact method are recommended to approach problem instances associated with medium-sized cities.
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Acknowledgements
This work was supported by the Mexican National Council for Science and Technology, grant SEP-CONACYT 48499-Y, and Universidad Autónoma de Nuevo León under its Scientific and Technological Research Support Program, grants UANL-PAICYT CA1478-07 and CE012-09. The research of the first author was funded by a doctoral fellowship from Universidad Autónoma de Nuevo León, grant NL-2006-C09-32652. The authors would like to thank three anonymous referees for their comments and suggestions which have significantly improved this paper.
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Salazar-Aguilar, M.A., Ríos-Mercado, R.Z. & Cabrera-Ríos, M. New Models for Commercial Territory Design. Netw Spat Econ 11, 487–507 (2011). https://doi.org/10.1007/s11067-010-9151-6
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DOI: https://doi.org/10.1007/s11067-010-9151-6