Cost accounting methods and periodic-review policies for serial inventory systems

Abstract

For reasons of mathematical tractability and historic convention, previous studies on periodic-review inventory control policies under uncertainty have typically accounted inventory related costs at the end of each review period. Inventory holding and shortage costs in reality, however, often accrue continuously in time. Given this discrepancy, it is necessary to understand the impact of end-of-period cost accounting. We address this issue for serial inventory systems adopting fixed-interval ordering in this paper. Our contribution is two-fold. First, we develop a model to evaluate and optimize a serial inventory system where inventory holding and shortage costs accrue continuously in time. This model includes discrete-time cost accounting that evaluates inventory holding and shortage costs at a single or multiple discrete points in a reorder interval as a special case. Second, we assess the effect of applying discrete-time cost accounting when inventory holding and shortage costs actually accrue continuously in time. We make three observations. First, for single-stage systems, end-of-period cost accounting generally results in very significant cost inefficiency and this cost inefficiency is bounded below by the ratio of inventory holding cost to backordering cost asymptotically as the reorder interval increases. Second, for multiple-stage systems, the cost inefficiency of end-of-period cost accounting decreases with the number of stages but is still significant for a typical serial system. Finally, extending cost accounting from the end to multiple discrete points in a reorder interval does not provide a significant modelling and computational advantage as compared to our continuous-time cost accounting model.