Why Risk Pooling is important to understand for modelers
From a Supply Chain Network Design perspective, risk pooling refers to facility consolidation, which leads to inventory consolidation. As you may know, consolidating facilities obviously reduces Supply Chain costs like holding cost, Inbound transportation costs, facilities cost etc. but may also end up increasing costs like outbound transportation. The biggest drawback of consolidation, if not done prudently might be loss of customer service levels, which in this age is unacceptable.
In this article, we will look at Risk pooling purely from an Inventory aspect by using an example to understand the principle. Having an idea about this will help you model the impact of Inventory cost reduction more accurately and precisely in your Network modeling initiatives.
Three Basic Principles of Risk Pooling
Three basic principles of risk pooling are as follows:
 Use of fewer warehouses or DCs to supply customers by consolidating customer regions
 Aggregating customer demand reduces demand risk
 Reduction in demand risk reduces total inventory in the supply chain
Remembering the Key Relationships
They key formula that you need to remember for Inventory Risk pooling is ???/
Let us assume that the number of DCs in the optimized scenario is N.

I = Total Inventory in the Supply Chain

IHC = Total Inventory holding cost
I will now illustrate the principle of Risk pooling using a simple example.
Risk pooling impact illustrated through an example
A very simplified Scenario
A company’s distribution network has 10 regional warehouses for the U.S market. The customer zones are assigned to the warehouses in such a way that their demands are equal. The company decides to close four warehouses and assign their customer demand equally to the remaining six.
We need to evaluate:
 What will be the impact of this risk pooling strategy on the total inventory carried in the supply chain ?
 Suppose the company wants to reduce the inventory by 50%, how many warehouses should it close ?
To evaluate the impact on total inventory, the formula that you need to remember is:
Inventory Future State/Inventory current state = √(Number of future state locations/Number of current state locations)
In this example: Inventory Future State/Inventory current state = √(6/10) = .775
Hence, due to the consolidation of facilities, the Supply Chain inventory is reduced by 22.5%
Using the same formula above, we can solve the second part of our example as well. We assume that the number of locations in the future state will be n. So the equation becomes: √(n/10) = .5 => n =2.5 hence the number of warehouses in future state should be 3.
Real world modeling challenges
We know that Safety Stock (SS) for any product, say i, held at any DC depends on two key parametersExpected Demand and the Standard Deviation of Demand.
We also know that the relationships between these quantities and the Optimal Safety stock is nonlinear and implicit functions of probability distribution. These aspects make it a difficult exercise in optimization modeling to explicitly model safety stock decisions and costs based on SS equations.