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The newsvendor problem with advertising: an overview with extensions

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Abstract

The effect of advertising on sales has been the subject of recent studies as an important aspect in many demand-based problems. Herein, we deal with the newsvendor problem, due to its simple structure, as a suitable tool for illustrating how facets of marketing may affect decision-making concerning operational problems. In the setting presented, the newsvendor is faced with advertising-sensitive stochastic demand, where a demand-related random element comprises an advertising decision of the multiplicative or additive form. We assume that a suitable advertising strategy results in increased sales. Two advertising response functions are considered, these being concave downward and S-shaped. We review and extend the existing results relating to the newsvendor problem with marketing effects, which mostly pertain to the concave function. These are generalized by defining the S-shaped function, and some original insights into the effect of advertising are given. We establish that the optimal advertising expenditure for the multiplicative case is always less than or equal to the optimal amount in the equivalent deterministic model while it is always equal in the additive case. We finally illustrate the results that are obtained by providing numerical examples involving various advertising response functions, as well as management-related interpretations.

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Acknowledgments

The authors wish to thank two anonymous referees for their very helpful comments and suggestions. This work was supported by the European Regional Development Fund under the project CEBIA-Tech Instrumentation No. CZ.1.05/2.1.00/19.0376. The study was also supported by a specific research project entitled “Modern Methods of Applied Mathematics for the Use in Technical Sciences”, no. FSI-S-14-2290, id. code 25053; in addition to NETME CENTRE PLUS (LO1202), which was created with financial support from the Ministry of Education, Youth and Sports under National Sustainability Programme I. Gratitude is also expressed to the Programme EEA and Norway Grants for funding via the EEA Scholarship Programme: Bilateral Scholarship Programme, for a student mobility grant, and for grant on Institutional cooperation projects nr. NF-CZ07-ICP-4-345-2016.

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Authors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05, Zlín, Czech Republic

    Dušan Hrabec

  2. Molde University College - Specialized University in Logistics, Britvegen 2, 6402, Molde, Norway

    Kjetil K. Haugen

  3. Faculty of Mechanical Engineering, Institute of Mathematics, Brno University of Technology, Technická 2896/2, 616 69, Brno, Czech Republic

    Dušan Hrabec & Pavel Popela

Authors
  1. Dušan Hrabec
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  2. Kjetil K. Haugen
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  3. Pavel Popela
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Correspondence to Dušan Hrabec.

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Hrabec, D., Haugen, K.K. & Popela, P. The newsvendor problem with advertising: an overview with extensions. Rev Manag Sci 11, 767–787 (2017). https://doi.org/10.1007/s11846-016-0204-1

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