Monte Carlo Determination of Stock Redistribution

Abstract

A model was designed for the purpose of studying stock distribution policies in an inventory system consisting of a number of demand points distributed through space. The model is limited to items that are not centrally repaired and that are procured only once for the life of the item, since both centralized repair and recurrent procurement offer opportunities to correct an imbalance in the distribution of stock among bases at little or no cost to the system. Assuming then an initial distribution of stock among bases, an analytical solution to the redistribution of stock between a pair of bases is obtained in each time period of the model, in terms of (1) the cost of transportation, (2) the stock on hand, depletion penalty, and demand probability function at each of the bases, and (3) a controlled variable βt representing the per cent of the transportation cost to be charged in the tth period in the analytical solution. The expected system costs associated with alternative β functions are then determined by Monte Carlo methods, with each function beginning at a value between zero and one in the first period, and rising to one in the last period. The methodology is extended to include the redistribution decision among three or more bases.