The economic order quantity taking into account additional information about the known quantile of the cumulative distribution function of the product's sales volume

Abstract

In modern logistics and supply chain management, the task of inventory management is paramount. The total costs of the enterprise and consequently, its profit, directly depend on the accuracy of calculating the volumes and terms of orders. In this work, the problem of increasing the accuracy of calculating the economic order quantity for a product was solved by involving additional information about the known quantile of a given level of the distribution function of the volume of product's demand. The quantile information was used to recalculate the annual demand for the product, based on a modified estimator of the sales expectation for the period. The modified estimator is asymptotically unbiased, normal, and more accurate than the traditional sample mean in the sense of mean squared error. New formulas for calculating the economic order quantity and its confidence interval were presented and tested on real data on the monthly sales volumes of goods of a large retail store network over two years. It is shown that the classic way of mean calculation led to an underestimation of the volume of the economic order quantity, which in turn increased the risk of a shortage, and hence a drop in the quality of logistics services. The new calculation method also showed that the period between orders should be one day shorter. The work is practically significant; according to its results, recommendations are given to the enterprise.