Fixed non-stockout-probability policies for the single-item lost-sales model

Abstract

We consider the classical discrete time lost-sales model under stationary continuous demand and linear holding and penalty costs and positive constant lead time. To date the optimal policy structure is only known implicitly by solving numerically the Bellman equations. In this paper we derive an optimality equation for the lost-sales model. We propose a fixed non-stockout-probability (FP3) policy, implying that each period the order size ensures that P3, the probability of no-stockout at the end of the period of arrival of this order, equals some target value. The FP3-policy can be computed efficiently and accurately from an exact recursive expression and two-moment fits to the emerging random variables. We use the lost-sales optimality equation to compute the optimal FP3-policy. Comparison against the optimal policy for discrete demand suggests that the fixed P3-policy is close-to-optimal. An extensive numerical experiment shows that the FP3-policy outperforms other policies proposed in literature in 97% of all cases. Under the FP3-policy, the volatility of the replenishment process, measured as coefficient of variation (cv) is much lower than the volatility of the demand process. This cv-reduction holds a promise for substantial cost reduction at upstream stages in the supply chain of the end-item under consideration, compared to the situation with backlogging.