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A Quadratic Knapsack Model for Optimizing the Media Mix of a Promotional Campaign

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Operations Research and Enterprise Systems (ICORES 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 509))

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Abstract

We consider the decision problem of a marketing manager who has to decide on the best selection of advertising media to be used in a promotional campaign. In this paper an optimization model is developed as part of the marketing management software solution MARMIND. It estimates the effect of each single medium and each pair of media from the evaluation data recorded for past campaigns. These evaluations are weighted by similarity measures which represent the distance between campaigns based on their attributes and goals. Furthermore, a memory effect is introduced to give lower weight to campaigns of the more distant past and higher weight to more recent campaign valuations. The resulting discrete optimization model is a Quadratic Knapsack Problem (QKP) which can be solved almost to optimality by a genetic algorithm. Then the given campaign budget is allocated to all selected advertising media based again on estimations from previous campaigns.

This research was supported by the Austrian Research Promotion Agency (FFG) under project “MARMIND media mix optimization”. Ulrich Pferschy and Joachim Schauer were supported by the Austrian Science Fund (FWF): [P 23829-N13].

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Notes

  1. 1.

    www.marmind.com/en.

  2. 2.

    www.uppernetwork.com.

References

  1. Färe, R., Grosskopf, S., Seldon, B., Tremblay, V.: Advertising efficiency and the choice of media mix: a case of beer. Int. J. Ind. Organ. 22, 503–522 (2004)

    Article  Google Scholar 

  2. Reynar, A., Phillips, J., Heumann, S.: New technologies drive CPG media mix optimization. J. Advertising Res. 50, 416–427 (2010)

    Article  Google Scholar 

  3. Balachandran, V., Gensch, D.: Solving the “marketing mix” problem using geometric programming. Manage. Sci. 21, 160–171 (1974)

    Article  MATH  Google Scholar 

  4. Sorato, A., Viscolani, B.: Using several advertising media in a homogeneous market. Optim. Lett. 5, 557–573 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  5. Nobibon, F., Leus, R., Spieksma, F.: Optimization models for targeted offers in direct marketing: exact and heuristic algorithms. Eur. J. Oper. Res. 210, 670–683 (2011)

    Article  MATH  Google Scholar 

  6. Sönke, A.: Optimizable and implementable aggregate response modeling for marketing decision support. Int. J. Res. Mark. 29, 111–122 (2012)

    Article  Google Scholar 

  7. Vakratsas, D., Ambler, T.: How advertising works: what do we really know? J. Mark. 63, 26–43 (1999)

    Article  Google Scholar 

  8. Pergelova, A., Prior, D., Rialp, J.: Assessing advertising efficiency: does the internet play a role? J. Advertising 39, 39–54 (2010)

    Article  Google Scholar 

  9. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  10. Pisinger, D.: The quadratic knapsack problem - a survey. Discrete Appl. Math. 155, 623–648 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Everitt, B., Landau, S., Leese, M., Stahl, D.: Cluster Analysis, 5th edn. Wiley, New York (2011)

    Book  MATH  Google Scholar 

  12. Guldemir, H., Sengur, A.: Comparison of clustering algorithms for analog modulation classification. Expert Syst. Appl. 30, 642–649 (2006)

    Article  Google Scholar 

  13. Tan, P.N., Steinbach, M., Kumar, V.: Introduction to Data Mining. Addison-Wesley, Boston (2006)

    Google Scholar 

  14. Sculley, D.: Rank aggregation for similar items. In: Proceedings of the 7th SIAM International Conference on Data Mining, pp. 587–592. SIAM (2007)

    Google Scholar 

  15. Kumar, R., Vassilvitskii, S.: Generalized distances between rankings. In: Proceedings of the 19th International World Wide Web Conference, pp. 571–580. ACM (2010)

    Google Scholar 

  16. Caprara, A., Pisinger, D., Toth, P.: Exact solution of the quadratic knapsack problem. INFORMS J. Comput. 11, 125–137 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Billionnet, A., Soutif, É.: An exact method based on lagrangian decomposition for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. 157, 565–575 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pisinger, D., Rasmussen, A., Sandvik, R.: Solution of large quadratic knapsack problems through aggressive reduction. INFORMS J. Comput. 19, 280–290 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pferschy, U., Schauer, J.: Approximating the quadratic knapsack problem on special graph classes. In: Kaklamanis, C., Pruhs, K. (eds.) WAOA 2013. LNCS, vol. 8447, pp. 61–72. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  20. Julstrom, B.: Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 607–614. ACM (2005)

    Google Scholar 

  21. Yang, Z., Wang, G., Chu, F.: An effective GRASP and tabu search for the 0–1 quadratic knapsack problem. Comput. Oper. Res. 40, 1176–1185 (2013)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Graz, Universitaetsstr. 15, 8010, Graz, Austria

    Ulrich Pferschy & Joachim Schauer

  2. UPPER Network GmbH, Seering 7/2, 8141, Unterpremstaetten, Austria

    Gerhild Maier

Authors
  1. Ulrich Pferschy
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  2. Joachim Schauer
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  3. Gerhild Maier
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Corresponding author

Correspondence to Ulrich Pferschy .

Editor information

Editors and Affiliations

  1. IMA, LISA, Angers, France

    Eric Pinson

  2. Polytechnic Institute of Setúbal, Setúbal, Portugal

    Fernando Valente

  3. Complutense University, Madrid, Spain

    Begoña Vitoriano

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Pferschy, U., Schauer, J., Maier, G. (2015). A Quadratic Knapsack Model for Optimizing the Media Mix of a Promotional Campaign. In: Pinson, E., Valente, F., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2014. Communications in Computer and Information Science, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-319-17509-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-17509-6_17

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