Efficiency of reductions of job-shop to flow-shop problems

We study the problem of scheduling N independent jobs in a job-shop environment. Each job must be processed on at most M machines according to individual routes. The objective is to minimise the maximum completion time of the jobs. First, the job-shop problem is reduced to a flow-shop problem with job precedence constraints. Then, an extension of Johnson's rule is defined to solve it. The optimality of the extended Johnson's rule is proved for two machine jobshop problems and the rule efficiency for some three and four machine job-shop problems is shown. (C) 2000 Elsevier Science B.V. All rights reserved.