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– 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||
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
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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.
- Spring '10