4.4.1 The square root law (SRL) of inventory
This law was formulated by Maister (1976) and is the basis of the concepts of risk pooling and inventory centralisation. This law provides a formula for calculating the benefit obtainable by inventory centralisation. The law states that total safety stock inventories in a future number of facilities can be approximated by multiplying the total amount of inventory at existing facilities by the square root of the number of future facilities divided by the number of existing facilities :
Where 
= number of existing facilities
= number of future facilities
= total inventory in existing facilities
= total inventory in future facilities
Coyle et al (2001) provides the following data from an actual company which demonstrate how average inventory level increases as the number of stocking locations increase. Though the number is given as average inventory, this level is directly related with safety inventory.
Table 4.2 Source: (Coyle et al 2001) The management of business logistics , p.260.
Number of Warehouses |
|
Total Average Inventory (Units) |
Percent Change |
1 |
1.000 |
3885 |
- |
2 |
1.4142 |
5494 |
141% |
3 |
1.7321 |
6729 |
173% |
4 |
2.000 |
7770 |
200% |
5 |
2.2361 |
8687 |
224% |
10 |
31326 |
12285 |
316% |
15 |
38730 |
15047 |
387% |
20 |
44721 |
17374 |
447% |
25 |
50000 |
19425 |
500% |
There are a few reasonable assumptions attached to the SRL. These are:
- Inventory transfers between stocking locations at the same level are not common practice.
- Lead times do not vary.
- Customer service level is constant.
- Demand at each location is normally distributed.
Activity 4.3
Woolrich Zinc Mining Co. operates nine warehouses in Australia , each warehouse carries $2,500,000 of inventory on the average. The company wishes to consolidate inventories in two warehouses. Assuming demands across the markets during a period are negatively correlated, how much savings in inventory can the company achieve by consolidation?
The most important limitation attached to the effectiveness of SRL has been pointed out by Zinn, Levi and Bowersox (1989) and this relates to the demands across the markets served by the various stocking points. It has been shown that SRL will be most effective when markets have demands which are negatively correlated and there is little or no benefit from consolidation when demands faced by the various stocking points are positively correlated. Additionally, the more the uncertainty of demand at each location, measured by the coefficient of variation, the better the SRL of inventory works.
Reading 4.2
Zinn, W; Levy, M & Bowersox, DJ (1989) 'Measuring the effect of inventory centralization/decentralization on aggregate safety stock: the "square root law" revisited', Journal of Business Logistics , vol. 10, no. 1, pp.1-14.
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