An economic order quantity inventory model with time-varying demand and Weibull deterioration with shortages

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. Hence, in this paper, we derive the EOQ model for inventory of items that deteriorate at a Weibull-distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY to find the optimal reorder time. Further, we also find that the optimal procedure is independent from the form of the demand rate. Finally, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to generalize the EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.