14 anyspt1lpt2scheduleisoptimalforf2 6 cmax

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Unformatted text preview: : – Jobs in Set I go first and in an increasing (non­ decreasing) order of p1j => SPT(1) – Jobs in Set II go last and in a decreasing (non­ increasing) order of p2j => LPT(2) Theorem 6.1.4 – Any SPT(1)­LPT(2) schedule is optimal for F2|| 6 Cmax Fm|prmu|Cmax Theorem 6.1.7 – F3|prmu|Cmax is strongly NP­hard – 3­Partition reduces to F3|prmu|Cmax 7 Mixed integer programming formulation of Fm|prmu|Cmax Notation – xjk=1 if job j is the kth job in the sequence and 0 otherwise – Iik is the idle time on machine i between jobs in the kth and (k+1)th position – Wik is the waiting time after it has finished on the ith machine of the job in the kth position – ∆ ik is the difference between the time when the job in the (k+1)th position starts on machine i+1 and the time the job in the kth position finishes on machine i – pi(k) is the processing time on machine i of the job in the kth position 8 Proportionate flow shops The processing time (work) for job j is pij=pj Theorem 6...
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This note was uploaded on 10/09/2012 for the course MAST 901 taught by Professor King during the Spring '10 term at British Columbia Institute of Technology.

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