Inventory replenishment policy with time-varying demand and shortages considering time-varying costs

In this paper, a generalized EOQ model is developed with time-varying demand and shortages considering time-varying costs. The solution procedure is shown for determining the optimal replenishment policy over a finite time horizon during which the replenishment periods are assumed to be constant. The existence and uniqueness of the optimal replenishment policy are presented. The procedure is illustrated with two special cases of linear and non-linear demands and costs. Two numerical examples are also given.