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Asymmetric Penalty Functions, Perfect Capacity, and On Demand

Given these arguments, we can formalize a penalty cost for incorrect capacity. We denote the unit cost of an excess resource by cr and denote the unit cost of an insufficient resource by cd. In some cases, we keep things simple and assume that cd = cr. Generally, though, we assume that cd > cr.

In other words, there is a cost associated with having too little or too much capacity. Having the exactly correct amount of capacity at all times—which we call perfect capacity—ensures that this penalty function is zero. We can formalize this cost over the period [t1,t2] as:

In other words, the penalty function is the cost of undercapacity times the amount of undercapacity over time, plus the cost of overcapacity times the amount of overcapacity over time.

On-demand capacity is one way of achieving perfect capacity. If we can respond to any shift in demand by instantaneously adjusting the resources, we will always have the correct capacity. However, on-demand capacity is not equivalent to perfect capacity: For some types of demand curves and resource provisioning strategies (e.g., flat demand and fixed capacity or step-increasing demand with enough forecast visibility to meet it and provision capacity), it is possible to achieve perfect capacity without on-demand resources. Generally, however, the ability to dynamically ensure ...