The Regression Model and the Problem of Inventory Centralization: Is the 'Square Root Law' Applicable?

The research problem undertaken by the authors of this article concerns the optimization of the size of the distribution network (the number of warehouses). The authors developed regression models, which are an alternative to the classical “Square Root law” optimization formula. The models were built for the two distributions of demand most commonly used in the literature: Gaussian and Gamma distribution. They allow the calculation of the level of inventory with a given number of warehouses and the level of stock availability as a measure of logistic customer service. The aim was to create a useful tool for decision-makers in companies. The models were elaborated on the base of the simulations carried out for various products (loading parameters, value), sales volumes, number of warehouses, and different standard deviations. Both regression models were statistically significant; the coefficients of determination are relevant. A slightly better value was obtained in the case of Gaussian distribution. The results obtained with the use of the classic “Square Root law” were in some cases quite similar. However, the type of distribution and the variability of demand, measured by standard deviation, have a significant influence here. Thus, the authors believe that the models developed may give more accurate results and that the “Square Root law” formula should be modified taking into account the characteristics of the demand. After completing the regression models with cost components, the total costs were calculated for selected cases of product groups (food, electronics, garments), different levels of the availability of stocks, and different number of warehouses. As it turned out, centralization may not necessarily be the optimal strategy for the most expensive goods. Loading parameters are also important, as they have a significant impact on the costs of storage and, above all, transport.