Two-machine No-wait Flowshop Problem Research Articles

A two-machine no-wait flow shop problem with two competing agents

A two-machine no-wait flow shop problem with two competing agents

A branch and bound algorithm to solve a two-machine no-wait flowshop scheduling problem with truncated learning function

ABSTRACTThis paper addresses a two-machine no-wait flowshop problem with the effect of the truncated learning function of jobs whose actual processing times depend on their positions in the sequence. By considering truncated learning effect, the actual processing time of a job is a function of its position index in the schedule and a control parameter. In a production scenario with truncated learning effect, the actual processing time of a job will not be lower than a threshold when the number of processed jobs increases. We develop a branch and bound algorithm to minimize the makespan. A lower bound and a dominance property have been proposed to increase the speed of elimination process in the branch and bound algorithm.

The two-machine no-wait general and proportionate open shop makespan problem

We consider the two-machine no-wait open shop minimum makespan problem in which the determination of an optimal solution requires an optimal pairing of the jobs followed by the optimal sequencing of the job pairs. We show that the required enumeration can be curtailed by reducing the pair sequencing problem for a given pair set to a traveling salesman problem which is equivalent to a two-machine no-wait flow shop problem solvable in O(nlogn) time. We then propose an optimal O(nlogn) algorithm for the proportionate problem with equal machine speeds in which each job has the same processing time on both machines. We show that our O(nlogn) algorithm also applies to the more general proportionate problem with equal machine speeds and machine-specific setup times. We also analyze the proportionate problem with unequal machine speeds and conclude that the required enumeration can be further curtailed (compared to the problem with arbitrary job processing times) by eliminating certain job pairs from consideration.

An efficient hybrid algorithm for the two-machine no-wait flow shop problem with separable setup times and single server

We consider the two-machine no-wait flow shop problem with separable setup times and single server side constraints, and makespan as the performance measure. This problem is strongly NP-hard. A mathematical model of the problem is developed and a number of propositions are proven for the special cases. Furthermore, a hybrid algorithm of variable neighbourhood search (VNS) and Tabu search (TS) is proposed for the generic case. For evaluation, a number of test problems with small instances are generated and solved to optimality. Computational results show that the proposed algorithm is able to reproduce the optimal solutions of all of the small-instance test problems. For larger instances, proposed solutions are compared with the results of the famous two-opt algorithm as well as a lower bound that we develop in this paper. This comparison demonstrates the efficiency of the algorithm to find good-quality solutions. [Received 25 November 2009; Revised 26 February 2010; Revised 19 March 2010; Accepted 20 March 2010]

Formula omitted]-approximation for two-machine no-wait flowshop scheduling with availability constraints

We consider in this paper the two-machine no-wait flowshop problem in which each machine may have an unavailable interval. We present 3 2 -approximation algorithms for the problem when the unavailable interval is imposed on only one machine, or the unavailable intervals on the two machines overlap. These algorithms improve on existing results.

Heuristics for two-machine no-wait flowshop scheduling with an availability constraint

In this paper we study the two-machine no-wait flowshop problem with an availability constraint. The problem has been shown to be NP-hard, and some heuristics with a worst-case error bound of 2 have been developed for it. We provide two improved heuristics for the problem, and show that each has a worst-case error bound of 5/3.

A new heuristic and dominance relations for no-wait flowshops with setups

The two-machine no-wait flowshop problem, where setup times are considered separate from processing times and sequence independent, is addressed with respect to minimizing total flowtime. A local and a global dominance relation are developed and a new heuristic is provided. Furthermore, a lower bound is obtained and used along with the dominance relations in a branch-and-bound algorithm in order to evaluate the efficiency of the heuristic. Computational experience demonstrates the superiority of the local dominance relation and the new heuristic. Scope and purpose No-wait flowshop problems, where jobs have to be processed without interruption between consecutive machines, represent an important area in scheduling. There are several industries where the no-wait flowshop problem applies including the metal, plastic, and chemical industries. For instance, in the case of steel production, the heated metal must continuously go through a sequence of operations before it is cooled in order to prevent defects in the composition of the material. Another important area arises when setup time is considered separate from processing time. Such a consideration is particularly justified when the ratio of setup to processing time is non-negligible. Many applications warrant separate consideration of setup; examples include the re-tooling of multi-tool equipment. Other applications can be found in textile, plastic, chemical, and semi-conductor industries. This paper develops a new heuristic and dominance relations for the two-machine no-wait separate setup flowshop problem, where the performance criterion is total flowtime.

Complexity results and approximation algorithms for the two machine no-wait flow-shop with limited machine availability

The scheduling problems studied in this paper concern a two-machine no-wait flow shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (Cmax). We prove that the problem is NP-hard even if only one non-availability period occurs on one of machines, and NP-hard in the strong sense for arbitrary numbers of non-availability periods. We also provide heuristic algorithms with error bounding analysis.

Minimizing the makespan in the two-machine no-wait flow-shop with limited machine availability

This paper deals with the two-machine no-wait flow-shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (C max). We prove that the problem is NP-Hard even if only one unavailability period occurs on one single machine, and NP-Hard in the strong sense for arbitrary numbers of unavailability periods. We also provide heuristic algorithms with error bounding analysis.

Total flowtime in no-wait flowshops with separated setup times

An important class of scheduling problems is characterized by a no-wait constraint where the jobs have to be processed continuously without waiting between or on consecutive machines. This constraint of no-waiting arises from the characteristics of the processing technology itself. Considering setup times separate from processing times of the jobs forms another important class of scheduling problems. This is particularly important when the ratio of the setup time to the processing time is non-negligible. This paper addresses a scheduling problem which falls in the combined category of no-wait and separate setup times. The performance measure considered is the total flowtime. This paper addresses the two-machine no-wait flowshop problem where the setup time of a job is separated from its processing time. The performance measure considered is the total flowtime. An elimination criterion is developed and optimal solutions are obtained for two special cases. For the generic case, a heuristic algorithm is provided. Computational experience shows that the algorithm yields good solutions.