Capacity Choice Given Lead Time

This section presents an example to illustrate the capacity impact of long lead times. Consider a manufacturer who faces demand for a fashion product that can take one of two levels, low and high. If the demand level is hig i, then the demand is expected to follow a uniform distribution between six and ten units. If the demand is low, then it is expected to be uniformly distributed between one and five units. Given the nature of manufacturing, capacity decisions have to be made many months in advance of demand. At the point in time that a capacity decision is made, suppose the manufacturer does not know if demand will be high or low, but the best estimate is that demand will be high or low with a 50% probability. 

Suppose the cost of capacity for a certain manufacturer is 100 per unit and has to be incxured in advance, independent of actual demand. Suppose the revenue associated with satisfying demand is 200 per unit. The maximum quantity that can be produced is limited to the available capacity. Any unused capacity can be used to satisfy demand for low-margin products but yields a revenue of only 20 per unit. Any unsatisfied demand is estimated to have a goodwill impact of 200 per unit. 

Given the lack of information regarding the demand level, the demand faced by the manufacturer is illustrated in Table 4.3. 

Now suppose the manufacturer has access to data from related markets that enables a reliable estimate of whether the demand level is high or low. How does this affect the choice of capacity Note that if the capacity decision has to be made when demand is low, it is optimal to have a capacity of four units to ensure a service level of 78.9%. Similarly when the demand is high, it is optimal to have a capacity of nine units to ensure a service level of 78.9%. Thus the expected capacity chosen is (0.5 X 4) -P (0.5 X 9) — 6.5 units. In addition, because the capacity level is chosen to be synchronized with demand level, the expected profit when demand is low (with a capacity of four units) is 144, and the expected profit when demand is high (with a capacity of nine units) is 644. Thus the expected profit across demand levels is (0.5 X 144) + (0.5 X 644) = 394. 

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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In this example the lead times that the firm proposes are accepted with a certain probability i4. The values of these probabilities have been given in the formulae (7.3.1) and (7.3.2). The normal available capacity on each machine will be 9 units. If no orders would be withdrawn and if we have one set-up on each machine every period, the machines would be occupied more than 90 percent (25 out of 27 units). Due to the withdrawals the real occupancy rate will be around 85 percent. For this example we will first make an arbitrary choice for the penalty points and for the additional elements. We start with ci = 3, D = 3 and mcl = 3. The 2 value is chosen arbitrarily as 2 =2 for all types and priorities. The choices for the other parameters are given in the matrix XQC. ... 

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