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Splitting the Difference

If someone says you must pick a capacity level to meet a given demand profile, what level should you pick? We’ll look at the problem a simple way and then in a more realistic way.

We’ve already mentioned that if capacity is greater than demand, we incur a penalty due to excess capacity. It would be like buying three plane tickets, when we only need one, or buying three cars, when we can only drive one at a given time: We are unnecessarily incurring costs such as leases, financing, or depreciation.

Conversely, if we need a car, but we have none, we end up paying some kind of penalty by not having it. For example, if we need the car to get to work, we lose the wages associated with the job.

To keep things simple, we will assume a few things for now. First, we will assume that the cost of excess capacity is exactly the same as the cost of insufficient capacity. In effect, if we have one car too many, we are paying a penalty that is identical as having one car too few.

Second, we will assume that the penalty cost is linear. In other words, having three cars too many costs three times as much as much as having one car too many.

Last, we will assume that the demand is uniformly distributed. In other words, every level of demand between two select numbers is equally likely. For the sake of simplicity, let’s assume that a demand of zero units—say, cars—is as likely as one unit is as likely as two units is as likely as three units is as likely as. . .is as likely ...