Managing Inventory with Limited History of Intermittent Demand

We consider a single-product discrete-time inventory model with intermittent demand. In every period, either zero demand or a positive demand is observed with an unknown probability. The distribution of the positive demand is assumed to be from the location-scale family with unknown mean and variance. The functional form of the optimal inventory target is available but it is a function of the unknown intermittent demand parameters that must be estimated from a limited amount of historical demand data. We first quantify the expected cost associated with implementing the optimal inventory policy using the point estimates of the unknown parameters by ignoring the uncertainty around them. We then minimize this expected cost with respect to a threshold variable that factors the statistical estimation errors of the unknown parameters into the inventory decision. We find that the use of an optimized threshold leads to a significant reduction in the a priori expected cost of the decision maker.

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