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Multiproduct Multiperiod Newsvendor Problem with Dynamic Market Efforts

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  • Jianmai Shi
  • Yiping Bao

Abstract

We study a multiperiod multiproduct production planning problem where the production capacity and the marketing effort on demand are both considered. The accumulative impact of marketing effort on demand is captured by the Nerlove and Arrow (N‐A) advertising model. The problem is formulated as a discrete‐time, finite‐horizon dynamic optimization problem, which can be viewed as an extension to the classic newsvendor problem by integrating with the N‐A model. A Lagrangian relaxation based solution approach is developed to solve the problem, in which the subgradient algorithm is used to find an upper bound of the solution and a feasibility heuristic algorithm is proposed to search for a feasible lower bound. Twelve kinds of instances with different problem size involving up to 50 products and 15 planning periods are randomly generated and used to test the Lagrangian heuristic algorithm. Computational results show that the proposed approach can obtain near optimal solutions for all the instances in very short CPU time, which is less than 90 seconds even for the largest instance.

Suggested Citation

  • Jianmai Shi & Yiping Bao, 2016. "Multiproduct Multiperiod Newsvendor Problem with Dynamic Market Efforts," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7674027
    DOI: 10.1155/2016/7674027
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    References listed on IDEAS

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    1. Alain Bensoussan & Metin Çakanyıldırım & Suresh P. Sethi, 2007. "A Multiperiod Newsvendor Problem with Partially Observed Demand," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 322-344, May.
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