Assignment4

# Assignment4 - 0 if site i is not assessed 1 Let Xi = 1 if...

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1) Let X i = assessed is i site if assessed not is i site if 1 0 binary X X X X X X X X X X X X i X i X C i x i 2 1 1 2 5 1 1 min 8 7 6 5 5 4 5 3 8 7 1 10 10 + + + + + + + = = = 4) a. Let M be a very large constant (on the order of j i ij t , ). Y ikj is an indicator variable that will be equal to 1 if job i comes before job k on machine j, and 0 otherwise. integer j i X binary Y j k i Y Y j k i t MY X X i t X X i t X X i t X L L ij kji ikj ij ikj kj ij i i i i i i i i , , , 0 , 1 , 0 min 1 1 2 2 2 3 3 3 = + + b. Now Y does not have to be machine specific; i.e., becomes simply Y ik . integer j i X binary Y k i Y Y k i t MY X X i t X X i t X X i t X L L ij kj ik ij ik kj ij i i i i i i i i , , , 0 1 0 min 1 1 2 2 2 3 3 3 = + +

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18) a) Optimal Tableau Row: x 1 + (2/5)x 3 – (1/5)x 4 = 16/5 Cut #1: (2/5)x 3 + (4/5)x 4 1/5 Î s 1 - (2/5)x 3 - (4/5)x 4 = -1/5 Optimal Tableau Row: x 2 + (1/5)x 3
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