A note on a replenishment policy for an inventory model with linear trend in demand and shortages

The present paper deals with an alternative approach for finding the optimal number of replenishments and optimal replenishment times for a finite-horizon inventory problem with linearly increasing demand allowing shortages which are fully backlogged. The method is developed by assuming that successive replenishment cycle lengths are in arithmetic progression. The corresponding results in the absence of shortage are also derived and finally some numerical examples are presented and compared with the existing methods to test the accuracy and effectiveness of the method. A sensitivity analysis has also been presented to study the effect of changes in the system parameters on the optimal cost.