Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 513435, 20 pages
Research Article

Integrated Supply Chain Cooperative Inventory Model with Payment Period Being Dependent on Purchasing Price under Defective Rate Condition

1Department of Transportation Science, National Taiwan Ocean University, Keelung City 202, Taiwan
2Department of International Business, Kainan University, Taoyuan 338, Taiwan
3Department of Shipping and Transportation Management, National Taiwan Ocean University, Keelung City 202, Taiwan
4Graduate Institute of Industrial and Business Management, National Taipei University of Technology, No. 1, Sec. 3, Zhongxiao E. Road, Taipei City 106, Taiwan

Received 18 August 2014; Revised 7 November 2014; Accepted 18 November 2014

Academic Editor: Mu-Chen Chen

Copyright © 2015 Ming-Feng Yang 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.


In most commercial transactions, the buyer and vendor may usually agree to postpone payment deadline. During such delayed period, the buyer is entitled to keep the products without having to pay the sale price. However, the vendor usually hopes to receive full payment as soon as possible, especially when the transaction involves valuable items; yet, the buyer would offer a higher purchasing price in exchange of a longer postponement. Therefore, we assumed such permissible delayed period is dependent on the purchasing price. As for the manufacturing side, defective products are inevitable from time to time, and not all of those defective products can be repaired. Hence, we would like to add defective production and repair rate to our proposed model and discuss how these factors may affect profits. In addition, holding cost, ordering cost, and transportation cost will also be considered as we develop the integrated inventory model with price-dependent payment period under the possible condition of defective products. We would like to find the maximum of the joint expected total profit for our model and come up with a suitable inventory policy accordingly. In the end, we have also provided a numerical example to clearly illustrate possible solutions.