HW8+Solution

HW8+Solution - IOE543Winter2010 Homework8Solution Problem1...

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IOE 543 Winter 2010 Homework 8 Solution Problem 1 (a) (b) (c) Since all 3 jobs are probabilistically identical, a static list policy performs just as well as a dynamic policy. Without loss of generality, we can assume the order of jobs in the priority list is 1 2 3 X1 X2 X3 Makespan Total Completion Time .5 .5 .5 1 2 .5 .5 1.5 2 3 .5 1.5 .5 1.5 3 .5 1.5 1.5 2 4 1.5 .5 .5 1.5 3 1.5 .5 1.5 2 4 1.5 1.5 .5 2 5 1.5 1.5 1.5 3 6 Total 15 30 Expected makespan=15/8 Expected total completion time=15/4 (d) If all 3 jobs have processing time 1, the makespan is 2 and the total completion time is 4. Thus, the expected outcomes for the stochastic case are better than their respective outcomes in the deterministic case. Problem 2 For job 1, X 1 א {9, 10, 11}, each with probability of 1/3 For job 2, X 1 א {8, 9, 10, 11, 12}, each with probability of 1/5 For job 3, X 1 א {7, 8, 9, 10, 11, 12, 13}, each with probability of 1/7 ( 20) () ( 20) 20 j j j j C C hC C = > (a) LV rule implies that we schedule the job following the sequence 3 >2 >1 Eሺ෍ h ሺC ሻሻ ൌ 1 5ൈ7
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This note was uploaded on 03/16/2012 for the course IEOR 466 taught by Professor Richard during the Spring '12 term at Columbia.

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HW8+Solution - IOE543Winter2010 Homework8Solution Problem1...

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