## Inventory Risk Pooling

Inventory risk pooling refers to a strategy used in supply chain management where a company centralizes its inventory in a single location or a fewer number of locations rather than spreading it across multiple locations. The rationale behind this strategy is the concept of “risk pooling,” which is based on the statistical principle of the law of large numbers.

The benefit of inventory risk pooling is primarily that it allows companies to keep less total inventory while still being able to meet customer demand. The reason is that the variability in demand tends to be less at an aggregated level than at an individual level.

For example, let’s say a company sells a product and has a 50% chance of selling one unit at each of its two stores in different locations. If the company keeps one unit at each store, then there’s a 50% chance that it will have either too much inventory (if no units are sold) or too little inventory (if a unit is sold at both stores) at the individual store level. But if the company keeps its inventory at a central location and can quickly ship a unit to whichever store makes a sale, then it can meet any combination of demand from the two stores (0, 1, or 2 units) with just two units of inventory.

Of course, the effectiveness of inventory risk pooling depends on various factors such as the ability to quickly move inventory to where it’s needed, the correlation of demand between different locations (risk pooling works better when demand is not perfectly positively correlated), and the costs associated with holding and transporting inventory. The potential trade-offs must be carefully considered when implementing this strategy.

This concept is used in various supply chain strategies, like centralized warehousing and cross-docking. It can also be extended to other types of “pools,” such as pooling demand across different products or pooling supply risk across different suppliers.

## Example of Inventory Risk Pooling

Imagine that a company, say, ABC Toys, sells toys in two cities – City A and City B. The demand for a particular toy in both cities can be either 0, 1, or 2 units each day, and all possibilities are equally likely.

If ABC Toys decides to keep the inventory decentralized (i.e., one unit of the toy at each store in each city), then on any given day:

- There’s a 1 in 9 chance (11.1%) that both cities will demand two units, and the company will be short by one unit in each city.
- There’s a 2 in 9 chance (22.2%) that the demand in each city will be one unit, and the company will meet the demand perfectly.
- There’s a 1 in 9 chance (11.1%) that both cities will demand zero units, and the company will have an excess of one unit in each city.
- The remaining possibilities involve the company having too much inventory in one city and too little in the other.

However, if ABC Toys decides to use risk pooling and keep the inventory centralized (i.e., two units at a central warehouse), then on any given day:

- There’s a 1 in 9 chance (11.1%) that the total demand will be four units (two units in each city), and the company will be short by two units.
- There’s a 3 in 9 chance (33.3%) that the total demand will be two units (which could involve one unit in each city or two units in one city and zero in the other), and the company will meet the demand perfectly.
- There’s a 1 in 9 chance (11.1%) that the total demand will be zero units, and the company will have an excess of two units.
- The remaining possibilities involve the company having either a slight excess or a slight shortage of inventory.

So, by centralizing its inventory, ABC Toys has reduced the chance of having a severe inventory mismatch from 22.2% to 11.1%. Even though there’s still a chance of having an inventory mismatch, the severity of the mismatches has been reduced. This shows how inventory risk pooling can help a company reduce its inventory costs and better match supply with demand.