9.7 Tools: Risk Pooling

Let's review. Throughout this chapter we have emphasized two points about uncertainty:

1. Uncertainty complicates your decision-making regarding inventory management.

2. Uncertainty drives costs, especially inventory holding and stockout costs.

Simply put, uncertainty is your enemy. As you strive to reduce costs and boost profitability, one of your goals should be to reduce uncertainty. We call efforts that help you reduce uncertainty "risk poolingSet of management techniques aimed at reducing exposure to (demand and/or lead time) uncertainty by spreading risk across broader sets of customers and/or suppliers.." One risk-pooling practice is warehouse (or DC) consolidation. For example, every retailer interested in growing its eCommerce business is trying to figure out how to use fewer, larger DCs to handle both bricks-and-mortar and Internet distribution channels.

Let's take a closer look to see how warehouse consolidation can reduce your uncertainty—and costs. Imagine your firm has two warehouses located relatively close to one another. Both warehouses carry the same products and serve neighboring market areas. This two-warehouse distribution systemA system of stocking locations used to get products from suppliers or a manufacturing facility to end customers. is illustrated in the left-hand panel in Figure 9-9. Each of the two warehouses faces lead time demand uncertainty ( sLD ₁ and sLD ₂ , respectively). As a result, you need to hold safety stock in each warehouse. The question is, "Can you reduce your costs and improve your service by centralizing the two warehouses into a single stocking location?" Take a look at the right-hand panel of Figure 9-9. In theory, you can reduce your overall safety stock by consolidating warehouses.

Now, consider the following scenario:

What are the costs for each warehouse? Your London warehouse incurs stockout costs. Your Birmingham warehouse incurs holding costs. What happens if you pool demand risk across both markets? In other words, what would happen if you could use the inventory from Birmingham to satisfy demand for fans in London? This would be a win-win situation! The following mathematical model supports your intuition by calculating the degree of risk ( sLD _c ) after consolidation:

$$sL{D}_c=\sqrt{sL{D}_1^2+sL{D}_2^2+2\cdot sL{D}_1\cdot sL{D}_2\cdot p_{12}}$$

Where ρ12 is the correlation of demands between locations 1 and 2. 1

Let's look at a numerical example where sLD ₁ is 250 and sLD ₂ is 350. You also need to know that ρ ₁₂ is 0 and you are targeting a 96% in-stock rate, which corresponds to a z value of about 1.75. With these numbers, you can calculate safety stock requirements for both your current two-warehouse system as well as your proposed consolidated, single-warehouse system (see Table 9-2).

First, let's do the math for your current two-warehouse system:

Now, let's run the numbers for the consolidated, one-warehouse system. However, before we can calculate the safety stock, we need to calculate the combined standard deviation of lead time demand: sLD _c

$$sL{D}_c=\sqrt{sL{D}_1^2+sL{D}_2^2+2\cdot sL{D}_1\cdot sL{D}_2\cdot p_{12}}=\sqrt{{250}^2+{350}^2+2\cdot 250\cdot 350\cdot 0}=430.1$$ $$ConsolidatedWarehouse:S{S}_c=z\cdot sL{D}_c=1.75\cdot 430.1=752.7$$

Based on your analysis, consolidation allows you to reduce your total safety from 1,050 to 753 units—that's a 28.3% reduction! Pooling risk by consolidating warehouses enables you to partially offset some of the lead time demand fluctuations. Less uncertainty then means lower safety stocks and lower costs.

Now let's do a thought experiment: What would happen if lead time demands between your London and Birmingham warehouse were perfectly positively correlated ( ρ 12 = 1)? By how much could safety stocks be reduced as a result of centralization? As you redo the calculations, you will notice that the safety stock reduction would be zero. This makes sense since there is no "offsetting effect" if lead time demands are simultaneously high in both markets. Conversely, what would happen if lead time demand were perfectly negatively correlated ( ρ 12 = -1)? This negative correlation would imply that lead time demand for London is high when it is low for Birmingham and vice versa. This will maximize the "offsetting effect" and result in greater safety stock savings (-83.3%). Watch the following video for step-by-step instructions.