Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipments

Abstract

ABSTRACTThis paper extends an economic production quantity (EPQ) model for deteriorating items when the delivery policy is based on multiple shipments. A continuous inventory policy for satisfying demand has been considered in the classic EPQ model. While in an integrated production–inventory–delivery system, the multi-shipment approach is actually used instead of the continuous issuing policy. On the other hand, the EPQ model has not been developed for deteriorating items with multiple shipments. This paper considers the time-varying deterioration rate and finds optimal replenishment lot size which minimises the long-run average cost function after proving its convexity. Finally, mathematical modelling and analysis are employed for a laboratory kit production system. Then, impact factors which can modify total cost are recognised and optimal replenishment lot size, as well as optimal quantity of each shipment, is found in different situations.