Cost function for a periodic reorder-point system with time dependent replenishment costs

A single-item inventory model with probabilistic demand is considered in this paper. The replenishment of items is cyclical and occurs every n-periods. The order for replenishment can be placed at the end of any period during the cycle. Replenishment costs (setup and unit costs) are stated as a function of time. The units ordered are set equal to an order quantity q. The general expression of this inventory system is formulated by developing the stationary distribution of the inventory position, units ordered and the probability of placing an order during any period. The expression is stated in terms of the reorder point and the order quantity and can be used to locate the optimal solution.