Applying the Root Rule in safety stock sizing in a network change

In a construction project or revision of the logistics network, among the costs that must be evaluated is the cost of inventory. This is because the number of storage points directly impacts the need for safety stock in the chain (to learn more about other types of stock, read: The five functions of inventory). As the safety stock acts as a shield against variability in demand and delivery time, the more dispersed the stock is in the chain, the greater the uncertainties and the greater this shield must be to maintain the same level of product availability.

To help us measure the impact of decentralization or centralization of inventories on the safety stock level, we can make use of what is popularly known as the “Square Root Rule”. By this rule, the impact factor of safety stock levels (FIE) in a network of facilities is expected to be equal to the square root of the ratio of the initial number of facilities in stock (NIIE) to the final number of facilities with stock (NFIE). The following image shows this formula and an application example for a centralization case in which a network composed of two distribution centers will be replaced by a single central warehouse.

Figure 1 – Square Root Rule and application in a hypothetical example
Source: Adapted from WANKE (2006)

However, this resource must be used sparingly, as it does not apply to every case and some simplifications must be made. Considering the hypothetical example above, regarding the expected reduction in safety stock levels, two conditions must be observed:

1. Systematically, when the demand in the market region served by DC1 varies upwards, the demand in the market region served by DC2 varies downwards and vice versa. If both variations go in the same direction, there is no possible trade-off in inventory levels between facilities.
2. The magnitude of demand variation in the market region served by DC1 is the same order of magnitude as the magnitude of demand variation in the market region served by DC2. If the magnitudes have different orders and magnitudes, the effect of compensation is also reduced.

The example illustrated below presents good conditions for reducing safety stocks by replacing two DCs with a single central DC.

Figure 2: Demand analysis for two distribution centers – variation in opposite directions
Source: Adapted from WANKE (2006)

A network design goes far beyond the assessment of impacts on stocks. Other costs such as transport, storage, tax benefits, in addition to impacts on the level of service offered to the customer, must be considered in a construction project or revision of the logistics network. Consultant Bernardo Falcão wrote about this topic in: The importance of correctly defining a logistics network. If you want to know more about this, the ILOS can help through courses ou projects of logistic network revision.

References:
WANKE, Peter. Inventory Management in the Supply Chain: Decisions and Quantitative Models. Atlas Publisher. São Paulo, 2006.