We consider the NP-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson’s rule. For m = 2, we present a 32 -approximation algorithm, and for m = 3, we present a 12 7 -approximation algori...

A flow shop scheduling problem involves scheduling jobs on multiple machines in series in order to optimize a given criterion. The flow time of a job is the amount of time the job spent before its completion and the stretch of the job is the ratio of its flow time to its processing time. In this paper, a hybrid genetic algorithm (HGA) approach is proposed for minimizing the total stretch in flo...

In this paper, the problem of finding an assignment “n” surgeries to be presented in one “m” identical operating rooms (ORs) or machines as surgical case scheduling (SCSP) is proposed. Since ORs are among NP-hard optimization problems, mathematical and metaheuristic methods address OR problems used. The job operation ordering any a permanent part all sequencing problems. transportation times be...

We consider the scheduling problems F 2 j j C max and F 2 j no-wait j C max , i.e. makespan minimization in a two machine ow shop, with and without no wait in process. For both problems solution algorithms based on sorting with O(n log n) running time are known, where n denotes the number of jobs Johnson 1954, Gilmore & Gomory 1964]. We prove that no asymptotically faster algorithms can solve t...

In this paper the resource-constrained flow shop (RCF) problem is addressed. A number of realistic extensions are incorporated, including non-serial precedence requirements, mixed flow shop situations, and the distribution of the human workforce among a number of pre-determined groups. The RCF is then solved by meta-heuristics, primarily of the evolutionary type. An extensive numerical investig...

In this paper, we propose 260 scheduling problems whose size is greater than that of the rare examples published. Such sizes correspond to real dimensions of industrial problems. The types of problems that we propose are : the permutation flow shop, the job shop and the open shop scheduling problems. We restrict us to basic problems : the processing times are fixed, there are neither set-up tim...

The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5approximation algorithm and an improved 1.4-approximation algorithm.