When is it Feasible to Model Low Discrete Demand by a Normal Distribution?

Inventory control systems used in practice are quite often modeling the lead-time demand by a normal distribution. This may result in considerable errors when the real demand is low and discrete. For such demand, it is usually better to use a discrete demand distribution. However, this will increase the computational effort. A natural question is under what circumstances a normal approximation is feasible. This paper analyzes this question in a numerical study. Our study indicates that a normal approximation works reasonably well when the average lead-time demand is something like 10 or higher and the coefficient of variation is bounded by something like 2. The normal approximation works better for a high backorder cost or, equivalently, a high service level.