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Fast Approximation Methods for Sales Force Deployment

  • Andreas Drexl

    (Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24118 Kiel, Germany)

  • Knut Haase

    (Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24118 Kiel, Germany)

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    Sales force deployment involves the simultaneous resolution of four interrelated subproblems: sales force sizing, salesman location, sales territory alignment, and sales resource allocation. The first subproblem deals with selecting the appropriate number of salesman. The salesman location aspect of the problem involves determining the location of each salesman in one sales coverage unit. Sales territory alignment may be viewed as the problem of grouping sales coverage units into larger geographic clusters called sales territories. Sales resource allocation refers to the problem of allocating scarce salesman time to the aligned sales coverage units. All four subproblems have to be resolved in order to maximize profit of the selling organization. In this paper a novel nonlinear mixed-integer programming model is formulated which covers all four subproblems simultaneously. For the solution of the model we present approximation methods capable of solving large-scale, real-world instances. The methods, which provide lower bounds for the optimal objective function value, are benchmarked against upper bounds. On average the solution gap, i.e., the difference between upper and lower bounds, is about 3%. Furthermore, we show how the methods can be used to analyze various problem settings of practical relevance. Finally, an application in the beverage industry is presented.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 10 (October)
    Pages: 1307-1323

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:10:p:1307-1323
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    1. Andris A. Zoltners & Prabhakant Sinha, 1983. "Sales Territory Alignment: A Review and Model," Management Science, INFORMS, vol. 29(11), pages 1237-1256, November.
    2. Andris A. Zoltners & Prabhakant Sinha & Philip S. C. Chong, 1979. "An Optimal Algorithm for Sales Representative Time Management," Management Science, INFORMS, vol. 25(12), pages 1197-1207, December.
    3. Charles A. Beswick, 1977. "Allocating Selling Effort Via Dynamic Programming," Management Science, INFORMS, vol. 23(7), pages 667-678, March.
    4. Andris A. Zoltners & Prabhakant Sinha, 1980. "Integer Programming Models for Sales Resource Allocation," Management Science, INFORMS, vol. 26(3), pages 242-260, March.
    5. Roy J. Shanker & Ronald E. Turner & Andris A. Zoltners, 1975. "Sales Territory Design: An Integrated Approach," Management Science, INFORMS, vol. 22(3), pages 309-320, November.
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