4.4 Risk pooling and the square root theory of inventory
Until now we have been discussing inventory decisions with regard to a single warehouse or facility. A large manufacturing or distribution firm would market its products through a number of facilities to cover a large, spatially dispersed region. The warehouses and distribution facilities would be centrally located to serve a particular market. These decentralised facilities require inventories at each location and each manager would decide on replenishment on the basis of the inventory position of each individual facility. We have seen in the previous sections that warehouses or inventory keeping units would require a level of inventory which guarantees the level of service to which the firm is committed.
One component of the average inventory level at each location is the safety stock. This safety stock represents idle capital for the firms; and it is a logical and reasonable approach to look at ways to minimise the level of inventory throughout the system without sacrificing the quality of service. One possible strategy is the centralisation of inventory.
Figure 4.4 Decentralised inventory - warehouses serving distinct markets
The concept of risk pooling is connected to the decision to centralise a firm's inventory by locating it in fewer locations. The strategy of risk pooling is based on the logic that if warehouses are centralised and inventories are aggregated, there will be an opportunity to reduce total inventory without reducing service level. This could happen because, since demands are aggregated across regions, it is quite possible that high demand in one location will be offset by low demand in another location. This concept of risk pooling has been derived from the well known 'square root theory of inventory' proposed by Maister (1976).
The following case in your text shows how this concept works in practice.
In your text
The Acme Case. p.64.
This case also introduces you to a very useful measure of uncertainty associated with a sample, the co-efficient of variation . This is defined as standard deviation of a sample divided by the average value of the sample.
Both standard deviation and co-efficient of variation are measures of variability, but the co-efficient of variation indicates something which the standard deviation cannot. If there is a product with a mean demand of 100 and the standard deviation of demand is also 100, the demand uncertainty is very large compared to another product with an average demand of 1000 and standard deviation of 100 (Chopra & Meindl, 2001). We cannot capture this degree of uncertainty by only considering standard deviation alone.
Co-efficient of variation allows us to capture the uncertainty associated with a particular distribution at a glance. The Acme case shows how the co-efficient of variation can be used in practice.
Activity 4.2
Can you recall the definition of standard deviation? Sketch simple normal distribution curves on a graph illustrating the following mean and standard deviation figures:
1 |
Mean 50 |
St. dev 15 |
2 |
Mean 80 |
St. dev 25 |
3 |
Mean 100 |
St. dev 30 |
4 |
Mean 60 |
St. dev 45 |
Remember that the area under the normal curve is 1. What percentage of the total area is under the curve between 1 standard deviation from the mean on each side? (This will help you to construct the curves.)
Which combination above represents maximum uncertainty by the look of the curves?
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