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Fast Approximation Methods for Sales Force Deployment

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Andreas Drexl & Knut Haase, 1999. "Fast Approximation Methods for Sales Force Deployment," Management Science, INFORMS, vol. 45(10), pages 1307-1323, October.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:10:p:1307-1323
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    File URL: http://dx.doi.org/10.1287/mnsc.45.10.1307
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    References listed on IDEAS

    as
    1. Charles A. Beswick, 1977. "Allocating Selling Effort Via Dynamic Programming," Management Science, INFORMS, vol. 23(7), pages 667-678, March.
    2. 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.
    3. Andris A. Zoltners & Prabhakant Sinha, 1983. "Sales Territory Alignment: A Review and Model," Management Science, INFORMS, vol. 29(11), pages 1237-1256, November.
    4. Skiera, Bernd & Albers, Sönke, 1993. "COSTA: ein Entscheidungs-Unterstützungs-System zur deckungsbeitragsmaximalen Einteilung von Verkaufsgebieten," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 324, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. 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.
    6. Andris A. Zoltners & Prabhakant Sinha, 1980. "Integer Programming Models for Sales Resource Allocation," Management Science, INFORMS, vol. 26(3), pages 242-260, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Camacho-Collados, M. & Liberatore, F. & Angulo, J.M., 2015. "A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector," European Journal of Operational Research, Elsevier, vol. 246(2), pages 674-684.
    2. Sprecher, Arno, 1999. "Sales force deployment by genetic concepts," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 514, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Bard, Jonathan F. & Jarrah, Ahmad I., 2013. "Integrating commercial and residential pickup and delivery networks: A case study," Omega, Elsevier, vol. 41(4), pages 706-720.
    4. 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.
    5. Haase, Knut, 1999. "Sales force deployment by mathematical programming," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 508, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Bard, Jonathan F. & Jarrah, Ahmad I. & Zan, Jing, 2010. "Validating vehicle routing zone construction using Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 206(1), pages 73-85, October.
    7. repec:spr:topjnl:v:25:y:2017:i:3:d:10.1007_s11750-017-0456-1 is not listed on IDEAS
    8. Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre (Ed.), 2000. "Jahresbericht 1999," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 522, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    9. repec:spr:coopap:v:69:y:2018:i:1:d:10.1007_s10589-017-9936-3 is not listed on IDEAS
    10. Mourão, Maria Cândida & Nunes, Ana Catarina & Prins, Christian, 2009. "Heuristic methods for the sectoring arc routing problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 856-868, August.
    11. Haugland, Dag & Ho, Sin C. & Laporte, Gilbert, 2007. "Designing delivery districts for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 180(3), pages 997-1010, August.
    12. Haase, Knut & Müller, Sven, 2014. "Upper and lower bounds for the sales force deployment problem with explicit contiguity constraints," European Journal of Operational Research, Elsevier, vol. 237(2), pages 677-689.
    13. repec:pal:jorsoc:v:54:y:2003:i:11:d:10.1057_palgrave.jors.2601625 is not listed on IDEAS
    14. 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.

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