Tractable (Q, R) Heuristic Models for Constrained Service Levels

The fill rate (the proportion of demand that is satisfied from stock) is a viable alternative in inventory models to the hard-to-quantify penalty cost. However, a number of difficulties have impeded its implementation, among them that the existing cycle-based approximate solutions do not reflect the possibility of multiple outstanding orders and that the optimal policy cannot be found directly, but must be iteratively calculated. We show that for a large family of leadtime demand distributions, the optimal policy depends on only two parameters: the fill rate and the economic order quantity (EOQ) scaled by the standard deviation of demand over the constant leadtime. If we then assume that the leadtime demand is normally distributed, we can use the asymptotic results as the EOQ goes to zero and to positive infinity to fit atheoretic curves for the order quantity Q and the reorder point R. These fitted curves yield a good (Q, R) policy without iteration. We also find that, among the set of simple heuristics, the limit form as EOQ goes to positive infinity provides a better alternative to simply setting Q equal to the EOQ.