Procedure: the modified WCSA for the parallel machine scheduling problem |
Inputs:ββ, , , , for ,β¦, |
Output: the near optimal scheme S_optββand the associated total completion time TC |
Begin |
βlet ββbe the sequence that sorts all the jobs by ascending order of their |
βnormal time , |
βset TC = infinity, and ββfor βββ% initialize the and |
βset ββββββββββββ% initialize the ranges of and |
βfor (;ββ++) |
βββ |
βββfor (++) |
ββββ |
ββββ |
ββββset |
ββββset for ββββββββββ% initialize the scheme |
ββββset , for βββββββ% initialize the completion |
βββββββββββββββββββββββtime of all machines |
ββββset , for ββββββββ% initialize the completion |
βββββββββββββββββββββββtime of all jobs |
ββββfor (;ββ;ββ++) |
βββββselect the machine that has the least completion time in all machines |
βββββselect the job that has the least normal time from |
βββββ |
βββββ |
βββββ |
βββββdelete job from |
βββend for |
βββfor (; ;β β++) |
ββββselect the machine that has the least completion time in all machines |
ββββif β ββββ% tardy jobs are sequenced in the |
ββββββββββββββββββββββnondecreasing order of |
βββββselect the job with the smallest from |
βββββ |
βββββ |
βββββ |
βββββdelete job from |
ββββelseβββββββββββββββββ% arrange the jobs in a ascending |
βββββββββββββββββββββββorder of the weight of combination |
βββββset |
βββββselect job ββwith the smallest ββββ |
βββββ |
βββββ |
βββββ |
βββββdelete job from |
ββββend if |
βββend for |
βββ,ββforββ |
βββifβββββββββββββββ% update the scheme and the |
βββββββββββββββββββββββassisted completion time |
ββββ |
ββββ |
βββend if |
ββend for |
βend for |
End |