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Journal of Applied Mathematics
Volume 2013, Article ID 413206, 11 pages
Research Article

Effects of Lot-Sizing Integration and Learning Effect on Managing Imperfect Items in a Manufacturer-Retailer Chain

1Department of Industrial Management, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Da’an District, Taipei 106, Taiwan
2Department of Marketing & Distribution Management, National Pingtung Institute of Commerce, 51 Min-Sheng E. Road, Pingtung 90041, Taiwan

Received 13 August 2013; Revised 21 October 2013; Accepted 23 October 2013

Academic Editor: Frank Werner

Copyright © 2013 Yu-Chung Tsao et al. 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.


An optimal supply chain performance requires the execution of a precise set of actions, including coordination of the movement of materials, products, and information flows among suppliers, manufacturers, distributors, retailers, and customers. However, a supply chain usually involves several members who are primarily concerned with optimizing their own objectives. This self-serving focus often results in poor channel performance. The present study used the Nash game and the cooperation game in an imperfect production system to investigate the combined effects of lot-sizing integration, learning effect, and an imperfect production process on a manufacturer-retailer channel. This paper also developed a search procedure to solve the problem described, and the optimal properties and a numerical study were conducted to seek structural and quantitative insights into the relationship between the upstream and downstream entities of the supply chain. Numerical results indicated that the cooperation game policy created a higher cost reduction under a wide range of parameter settings.