this article addresses a multi-stage flowshop scheduling problem with equal number of unrelated parallel machines. the objective is to minimize the makespan for a given set of jobs in the system. this problem class is np-hard in the strong sense, so a hybrid heuristic method for sequencing and then allocating operations of jobs to machines is developed. a number of test problems are randomly ge...

In this study, we consider the production environment of no-wait reentrant flow shop with the objective of minimizing makespan of the jobs. In a reentrant flow shop, at least one job should visit at least one of the machines more than once. In a no-wait flowshop scheduling problem, when the process of a specific job begins on the first machine, it should constantly be processed without waiting ...

No-Wait Flowshop Permutation Scheduling Problem (NWPFSP) is a scheduling problem that states every job completed on machine n must be processed immediately the next machine. The NWPFSP an extension of flowshop problem. This article proposes two new algorithms fire hawk optimization and beluga whale optimization, to solve minimize makespan. developed are tested three different cases. Each algori...

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines at the first stage and a single machine at the second stage. At the first stage, jobs use some additional resources which are available in limited quantities at any time. The resource requirements are of 0-1 type. The objective is the minimization of makespan. The problem is NP-ha...

Two-machine flowshop scheduling to minimize makespan is one of the most well-known classical scheduling problems. Johnson's rule for solving this problem has been widely cited in the literature. We introduce in this paper the concept of composite job, which is an artificially constructed job with processing times such that it will incur the same amount of idle time on the second machine as that...

It is well known that except in the case of makespan problems, there are hardly any analytical results for flowshop problems. This paper considers of a class of flowshop problems where job processing time at a machine is proportionate to the processing time on the first machine. We show that for the pre-emptive version of the problem, in order to minimize any regular measure of performance, it ...

Flowshop is an example of a classic hard combinatorial problem. Branch-and-bound is a technique commonly used for solving such hard problems. Together, the two can be used as a benchmark of maturity of parallel processing environment. Grid systems pose a number of hurdles which must be overcome in practical applications. We give a report on applying parallel branch-and-bound for flowshop in gri...

In this article, we present a study that compares variants of two ACO algorithms designed to tackle a biobjective permutation flowshop scheduling problem where the makespan and the total tardiness are the objectives considered. These two algorithms use respectively one and two pheromone matrices. The analysis of the results gives indications on the choices to adopt when designing an ACO approac...

We study a 2-machine flowshop in which all processing times are independently and identically distributed, with values known to the scheduler. We are able to describe in detail the expected behavior of the flowshop under optimal and under heuristic schedules. Our results suggest that minimizing makespan might be a superfluous objective: Scheduling the jobs randomly requires less information and...

The flowshop problem (FSP) is one of the most thoroughly studied scheduling problems. In the FSP, a set N = {1, . . . , n} of n independent jobs has to be processed on a set M = {1, . . . ,m} of m machines. Every job j, j ∈ N , requires a given fixed, non-negative processing time pij on every machine i, i ∈ M . In a flowshop, all n jobs are to be processed on the m machines in the same order, t...