Lec 18 - Lecture 19 Team 5 Sati Houston Ashley McIntyre...

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Team 5 11/29/10 Sati Houston, Ashley McIntyre, Amber Richter, Michelle Vu Scheduling I. Operating Room Scheduling ܨሺܵሻൌ Proof by contradiction (continued from last lecture) Assume S is optimal, but S is not SPT S: C(A): sum of completion time of jobs in A C(B): sum of completion time of jobs in B (note: C(B) S = C(B) S’ ) Now consider S’, a new sequence similar to S except i and j are switched S’: Flow/total completion time: P i > P j A j i B ൣܥሺܣሻ൅ ሺܥሺܣሻ൅ܲ ሻ൅ ൫ܥሺܣሻ൅ ܲ ൅ ܲ ൯൅ ܥሺܤሻ൧ ܨሺܵԢሻൌ 1 ݊ A i j B ൣܥሺܣሻ൅ ൫ܥሺܣሻ൅ܲ ൯൅ ൫ܥሺܣሻ൅ ܲ ൅ ܲ ൯ ൅ ܥሺܤሻ൧ ss And since P i > P j , F(S) > F(S’). Thus, S is not optimal and we have reached a contradiction. As a result, SPT has to be followed in the optimal schedule. II. Minimize the max latene n patients, 1 operating room P i : processing time d i : due time L i : C i – d
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Lec 18 - Lecture 19 Team 5 Sati Houston Ashley McIntyre...

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