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 pe nalty cost. However, a number of difficulties have impeded its impleme ntation, among them that the existing cycle-based approximate solution s do not reflect the possibility of multiple outstanding orders and th at the optimal policy cannot be found directly, but must be iterativel y calculated. We show that for a large family of leadtime demand distr ibutions, the optimal policy depends on only two parameters: the fill rate and the economic order quantity (EOQ) scaled by the standard devi ation of demand over the constant leadtime. If we then assume that the leadtime demand is normally distributed, we can use the asymptotic re sults as the EOQ goes to zero and to positive infinity to fit atheoret ic curves for the order quantity Q and the reorder point R. These fitt ed curves yield a good (Q, R) policy without iteration. We also find t hat, among the set of simple heuristics, the limit form as EOQ goes to positive infinity provides a better alternative to simply setting Q e qual to the EOQ.