# Question: Reconsider the example illustrating the use of chance constraints that

Reconsider the example illustrating the use of chance constraints that was presented in Sec. 7.5. The concern is that there is some uncertainty about how much production time will be available for Wyndorís two new products when their production begins in the three plants a little later. Table 7.11 shows the initial estimates of the mean and standard deviation of the available production time per week in each of the three plants.

Suppose now that a more careful investigation of these available production times has considerably narrowed down the range of what these times might turn out to be with any significant likelihood. In particular, the means in Table 7.11 remain the same but the standard deviations have been cut in half. However, to add more insurance that the original constraints still will hold when production begins, the value of a has been increased to α = 0.99. It is still assumed that the available production time in each plant has a normal distribution.

(a) Use probability expressions to write the three chance constraints. Then show the deterministic equivalents of these chance constraints.

Suppose now that a more careful investigation of these available production times has considerably narrowed down the range of what these times might turn out to be with any significant likelihood. In particular, the means in Table 7.11 remain the same but the standard deviations have been cut in half. However, to add more insurance that the original constraints still will hold when production begins, the value of a has been increased to α = 0.99. It is still assumed that the available production time in each plant has a normal distribution.

(a) Use probability expressions to write the three chance constraints. Then show the deterministic equivalents of these chance constraints.

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