Ending Inventory Valuation in Multiperiod Production Scheduling

When making lot-sizing decisions, managers often use a model horizon T that is much smaller than any reasonable estimate of the firm's future horizon. This is done because forecast accuracy deteriorates rapidly for longer horizons, while computational burden increases. However, what is optimal over the short horizon may be suboptimal over the long run, resulting in errors known as end-effects. A common end-effect in lot-sizing models is to set end-of-horizon inventory to zero. This policy can result in excessive setup costs or stock-outs in the long run. We present a method to mitigate end-effects in lot sizing by including a valuation term V(I_T) for end-of-horizon inventory I_T, in the objective function of the short-horizon model. We develop this concept within the classical EOQ modeling framework, and then apply it to the dynamic lot-sizing problem (DLSP). If demand in each period of the DLSP equals the long-run average demand rate, then our procedure induces an optimal ordering policy over the short horizon that coincides with the long-run optimal ordering policy. We test our procedure empirically against the Wagner-Whitin algorithm and the Silver Meal heuristic, under several demand patterns, within a rolling horizon framework. With few exceptions, our approach significantly outperforms the other approaches tested, for modest to long model horizons. We discuss applicability to more general lot-sizing problems.