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Demand and Resource Functions

Often demand and resources are measured in separate units—for example, the demand is for sweaters, and the resources needed are knitting machines, operators, and wool. Sometimes resources are in integer units, say, planes, but demand is in fractional quantities, say, plane seats; or the reverse may occur. Here we ignore all these complicating factors and simply assume that demand and resources are in the same units, for example, kilowatts of demand for electricity and kilowatts of electrical generating capacity. This assumption does not impact the generality of the insights that we derive in the next few pages.

We assume that the demand for resources over time is a function, D(t), and the resources available to meet that demand is also a function, R(t). At any given time, say, t1, one of these must hold:

• D(t1) < R(t1)—We have excess resources deployed
• D(t1) > R(t1)—We have too few resources (i.e., excess demand)
• D(t1) = R(t1)—The amount of resources we have is just right

In the best of all worlds, at all times we would have exactly the correct amount of resources to satisfy demand or D(t) = R(t). We can call this perfect capacity. However, depending on the demand function and the resource function, it certainly is possible—or even likely—that the resources will be either insufficient or excess, and this situation will incur a penalty, or cost.

In attempting to match resources to capacity, there are six major areas to consider.

1. Frequency of demand ...