Capacity Choice in the Presence of Demand Uncertainty

Consider a company that is planning capacity but is unsure of the potential demand for products. Suppose the cost per unit of capacity is 25. Next, if demand is satisfied, the company gets revenue of 100 per unit. Leftover capacity can be used to satisfy secondary demand but generates revenue of only 10 per unit. There is sufficient capacity for this secondary demand. For purposes of clarity, assume that demand can take the values with associated probabilities as shown in Table 4.1. 

Now suppose the company were to obtain a capacity of 300 units. The associated expected profit can be calculated as 

Repeating this exercise for each of the possible choices of capacity, i.e., 100, 300, and 500, provides the results in Table 4.2. 

The decision described above is commonly termed the newsboy model. The optimal capacity decision can be obtained by identifying two costs the marginal cost of excess capacity Q and the marginal cost of capacity shortage Q. In the example above, the marginal cost of excess capadty is 

Now suppose it was possible for the company to obtain a perfect forecast of demand and then choose capacity. In such a case, it is optimal to choose a capacity level that matches demand. Such a context is called the perfect-information expected profit. The expected capacity would be 

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This example shows the close interaction between information, lead time, and capacity choice in the presence of demand uncertainty. In the absence of information, capacity buffers are optimal. However, lower lead times may permit better demand information, thus leading to a better match between demand levels and capacity. This enables additional capacity to be planned when there is an upside potential associated with high demand and simultaneously lower capacity when demand levels are anticipated to be low. The net result is a higgler profitability with lowered average capacity levels. 

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