Robustness of the normal approximation of lead‐time demand in a distribution setting

Abstract: Previous studies criticize the general use of the normal approximation of lead-time demand on the grounds that it can lead to serious errors in safety stock. We reexaminethis issue for the distribution of fast-moving finished goods. We first determine the optimalreorder points and quantities by using the classical normal-approximation method and atheoretically correct procedure. We then evaluate the misspecification error of the normalapproximation solution with respect to safety stock, logistics-system costs, total costs (logis-tics costs, including acquisition costs), and fill rates. The results provide evidence that thenormal approximation is robust with respect to both cost and service for seven major industrygroups. q 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 165–186, 1997 INTRODUCTIONThe (s, Q) continuous-review inventory model has been widely used and extensivelystudied in the literature. In the stochastic version of this model, where demand (D) andlead time (L) are independent random variables, the analyst must know the distributionlead-time demands (X ) to assess stockout risks or expected shortages. The simplest wayto model lead-time demand is to determine the first two moments ofX and then assumethat X has a normal distribution. This classic approach, found in virtually every textbookon production-inventory, operations, and logistics management, rests on two premises:1. The underlying distribution of X is not important.2. The first two moments are the only relevant parameters.Many scholars, however, have criticized the use of this normal theory approach on twogrounds. First, the distribution of X is likely to have a nonnormal shape, which means thatthe normal approximation will produce errors in the estimates of replenishment levels andthus the amount of safety stock needed to support customer-service targets or to counterbal-ance stockout costs. Second, if the coefficient of variation ofX is large—say, greater than