American Institute of Mathematical Sciences

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April  2010, 6(2): 425-433. doi: 10.3934/jimo.2010.6.425

On the optimal replenishment in a finite planning horizon with learning effect of setup costs

Ta-Wei Hung 1, and  Ping-Ting Chen 2,

1. 

Department of Information Technology and Management, Shih Chien University, Taipei, Taiwan
2. 

Department of Accounting, Tamkang University, Taipei, Taiwan

Received  August 2009 Revised  January 2010 Published  March 2010

The traditional economic order quantity (EOQ) and/or economic production quantity (EPQ) have been extensively examined and continually modified so as to accommodate specific business needs and market environments. In this paper, the learning effect of setup costs is incorporated into an inventory replenishment system where the demand is assumed to be deterministically constant in a finite planning horizon. The inventory replenishment system with learning considerations of setup costs is formulated as a mixed-integer cost minimization problem in which the number of replenishments and the replenishment time points in the planning horizon are regarded as decision variables. We first show that the time interval between any two successive replenishments should be equal. Then, the conditions of the optimal solution for the proposed problem are derived. Finally, numerical examples are provided to illustrate the features of the proposed problem.
Keywords: inventory control, replenishment policy., EOQ.
Mathematics Subject Classification: Primary: 90B05, 90C11, 90C90; Secondary: 90C4.
Citation: Ta-Wei Hung, Ping-Ting Chen. On the optimal replenishment in a finite planning horizon with learning effect of setup costs. Journal of Industrial & Management Optimization, 2010, 6 (2) : 425-433. doi: 10.3934/jimo.2010.6.425
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