An empirical examination of the assumptions of the Square Root Law for inventory centralisation and decentralisation

The Square Root Law (SRL) is a popular formula for assessing inventory levels at varying numbers of warehouses. Its popularity is probably due to its simplicity and the ample opportunities for its application to the managerial dilemma of inventory centralisation vs. decentralisation. However, researchers disagree about which parts of inventory it can be applied to and its underlying assumptions. To address these questions, this study algebraically derives the assumptions necessary for the SRL to apply to regular, safety and total stock. Afterwards, the paper empirically examines to what extent these assumptions hold in practice by analysing four case studies and data from a sample of 280 German manufacturing and trading companies. Most companies do not fulfil the assumptions of the SRL and therefore cannot apply it with accurate results. Trading companies, however, seem to fulfil more assumptions than manufacturing ones, retailers more than wholesalers, industrial goods manufacturers more than consumer goods manufacturers. Although the SRL has traditionally been mainly considered for safety stock, companies, especially trading companies, appear to rather fulfil the assumptions for applying the SRL to cycle stock. Some assumptions seem to be complementary, whereas others appear to be competing, so that it is difficult to fulfil all of them.