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Discrete Dynamics in Nature and Society - Volume 2016 2016, Article ID 7674027, 10 pages -

Research Article

College of Information System and Management, National University of Defense Technology, Changsha, Hunan, China

College of Humanities and Social Sciences, National University of Defense Technology, Changsha, Hunan, China

Received 20 July 2016; Accepted 25 September 2016

Academic Editor: Seenith Sivasundaram

Copyright © 2016 Jianmai Shi and Yiping Bao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.

Autor: Jianmai Shi and Yiping Bao



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