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Commercial territory design planning with realignment and disjoint assignment requirements

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  • Ríos-Mercado, Roger Z.
  • López-Pérez, J. Fabián

Abstract

A territory design problem motivated by a bottled beverage distribution company is addressed. The problem consists of finding a partition of the entire set of city blocks into a given number of territories subject to several planning criteria. Each unit has three measurable activities associated to it, namely, number of customers, product demand, and workload. The plan must satisfy planning criteria such as territory compactness, territory balancing with respect to each of the block activity measures, and territory connectivity, meaning that there must exist a path between any pair of units in a territory totally contained in it. In addition, there are some disjoint assignment requirements establishing that some specified units must be assigned to different territories, and a similarity with existing plan requirement. An optimal design is one that minimizes a measure of territory dispersion and similarity with existing design. A mixed-integer linear programming model is presented. This model is unique in the commercial territory design literature as it incorporates the disjoint assignment requirements and similarity with existing plan. Previous methods developed for related commercial districting problems are not applicable. A solution procedure based on an iterative cut generation strategy within a branch-and-bound framework is proposed. The procedure aims at solving large-scale instances by incorporating several algorithmic strategies that helped reduce the problem size. These strategies are evaluated and tested on some real-world instances of 5000 and 10,000 basic units. The empirical results show the effectiveness of the proposed method and strategies in finding near optimal solutions to these very large instances at a reasonably small computational effort.

Suggested Citation

  • Ríos-Mercado, Roger Z. & López-Pérez, J. Fabián, 2013. "Commercial territory design planning with realignment and disjoint assignment requirements," Omega, Elsevier, vol. 41(3), pages 525-535.
    • Handle: RePEc:eee:jomega:v:41:y:2013:i:3:p:525-535
    DOI: 10.1016/j.omega.2012.08.002
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    References listed on IDEAS

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    1. María Salazar-Aguilar & Roger Ríos-Mercado & Mauricio Cabrera-Ríos, 2011. "New Models for Commercial Territory Design," Networks and Spatial Economics, Springer, vol. 11(3), pages 487-507, September.
    2. Andreas Drexl & Knut Haase, 1999. "Fast Approximation Methods for Sales Force Deployment," Management Science, INFORMS, vol. 45(10), pages 1307-1323, October.
    3. Ronen, David, 1983. "Sales territory alignment for sparse accounts," Omega, Elsevier, vol. 11(5), pages 501-505.
    4. Andris A. Zoltners & Prabhakant Sinha, 1983. "Sales Territory Alignment: A Review and Model," Management Science, INFORMS, vol. 29(11), pages 1237-1256, November.
    5. S. W. Hess & J. B. Weaver & H. J. Siegfeldt & J. N. Whelan & P. A. Zitlau, 1965. "Nonpartisan Political Redistricting by Computer," Operations Research, INFORMS, vol. 13(6), pages 998-1006, December.
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    1. Verónica Arredondo & Miguel Martínez-Panero & Teresa Peña & Federica Ricca, 2021. "Mathematical political districting taking care of minority groups," Annals of Operations Research, Springer, vol. 305(1), pages 375-402, October.

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