In this paper we study the classical no-wait flowshop scheduling problem with makespan objective (F |no−wait|Cmax in the standard three-field notation). This problem is well-known to be a special case of the asymmetric traveling salesman problem (ATSP) and as such has an approximation algorithm with logarithmic performance guarantee. In this work we show a reverse connection, we show that any p...

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...

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...

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...

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 traditional focus of scheduling research is on finding schedules with a low implementation cost. However, in many real world scheduling applications finding a robust or flexible schedule is just as important. A robust schedule is a quality schedule expected to still be acceptable if something unforeseen happens, while a flexible schedule is a quality schedule expected to be easy to change. ...

This research presents a formal model of the one machine job shop scheduling problem with variable machine and labor capacity. Primary interest is focused on the trade-off between overtime and detailed scheduling costs. The detailed scheduling problem considered is minimizing the sum of weighted tardiness and weighted flow-time costs for a given capacity plan (e.g., a given overtime schedule). ...

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...