INDUSTRIAL JOB-SHOP SCHEDULING WITH RANDOM OPERATIONS AND DIFFERENT PRIORITIES

A classical job-shop scheduling problem with n jobs (orders) and m mac hines is considered. Each job-operation O-il (the l(-th) Operation of job i, l = l,...,m, i = 1, 2,..., n) has a random time duration t(il) with the average value (t) over bar(il) and the variance V-il. Each jo b J(i) has its due date D-i and its priority index rho(i). Given rho(i ) the desired probability for job J(i) to be accomplished on time, an d p(i)*, the least permissible probability for the job to meet its du e date on time, the problem is to determine starting time values S-il for each job-operation O-il. Those values are not calculated beforehan d and are values conditioned on our decisions. Decision-making, i,e., determining values S, is carried out at the moments when at least one of the machines is free for service and at least one job is ready to b e processed on that machine. If at a certain moment t more than one jo b is ready to be processed, these jobs are compared pairwise. The winn er of the first pair will be compared with the third job, etc., until only one job will be left. The latter has to be chosen for the machine . The competition is carried out by calculating the job's delivery per formance, i.e., the probability for a certain job to meet its due date on time. Such a calculation is carried out by determining the probabi lity to meet the deadline for the chain of random operations. Two diff erent heuristics for choosing a job from the line will be imbedded in the problem. The first one is based on examining delivery performance values together with priority indices rho(i). The second one deals wit h examining confidence possibilities p(i) and p(i)** and does not tak e into account priority indices. A numerical example is presented. Bot h heuristics are examined via extensive simulation in order to evaluat e their comparative efficiency for practical industrial problems.