Economic order quantity model for deteriorating items with time-dependent demand rate under time varying shortages

Abstract

This paper derives an economic order quantity model for deteriorating items with linearly time-dependent demand rate and shortages, where demand rate is differentiable function of time. Under these assumptions, mathematical formulations are derived for finding optimal time to finish positive inventory, cycle time, initial inventory and total cost per cycle. We show that the total cost per unit time is a concave function of cycle time. The results are illustrated with numerical example. Finally, sensitivity analyses have been performed to study the effects of changes with different parameters like: ordering cost, holding cost, purchase cost, deterioration rate, shortage cost and demand on optimal policies.