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

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.