Demand fulfillment probability in a multi-item inventory system with limited historical data

ABSTRACT In a budget-constrained multi-item inventory system with independent demands, we consider the case of unknown demand parameters that are estimated from limited amounts of historical demand data. In this situation, the probability of satisfying all item demands, as a measure of demand fulfillment, is a function of the finite-sample estimates of the unknown demand parameters; thus, the demand fulfillment probability is a random variable. First, we characterize the properties of an asymptotical approximation to the mean and variance of this random variable due to the use of limited data for demand parameter estimation. Second, we use the characterization of the variance of the demand fulfillment probability for quantifying the impact of demand parameter uncertainty on demand fulfillment via numerical experiments. Third, we propose an inventory optimization problem that minimizes the variance of the demand fulfillment probability due to demand parameter uncertainty subject to a budget constraint on the total inventory investment. Our numerical experiments demonstrate that, despite the availability of limited amounts of historical demand data, it is possible to manage inventory with significantly reduced variance in the demand fulfillment probability.

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