Better Safe than Sorry

In the analysis just described, we assumed a symmetric penalty function. In other words, being one resource too high cost us exactly as much as being one resource too low; being 100 resources too high cost us just as much as being 100 resources too low. Typically this is not the case, though. We invest in resources to receive a net return.

We don’t spend an extra dollar on computers to receive an extra dollar in income from the Web site that they power. By “spend,” here, let’s assume that we have converted investments and the income generated from them into similar units; otherwise, we will have to worry about the weighted average cost of capital and depreciation schedules and the time value of the net operating profit after taxes and things like that. But let’s keep it simple.

If spending $1 only returned us $1, we wouldn’t be any better off than not spending that dollar. Instead, we would expect that spending a dollar would gain us $2, $3, or $10, for example.

Therefore, an asymmetric penalty function makes more sense. Let’s take a look at the same set of capacity strategies as before, but this time, assuming that the net cost of resources is only 50 cents, but the net revenue that they generate is $2. Then, having two unneeded resources costs us $1, but being two resources short loses us $4. What happens under those assumptions?

Exhibit 9.3 graphically illustrates the effect: Triangles that slope to the left (indicating overcapacity) are shallower than ...

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