TWO- AND THREE-STAGE FLOWSHOP SCHEDULING WITH NO-WAIT IN PROCESS (original) (raw)
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Heuristics for no-wait flowshops with makespan subject to mean completion time
Applied Mathematics and Computation, 2012
The m-machine no-wait flowshop scheduling problem is addressed by taking into account two performance measures of makespan and mean completion time. The objective is to minimize makespan such that mean completion time is less than a certain value. A dominance relation is provided for a special case of the problem. Moreover, two new heuristics are proposed in this paper. Computational analysis indicates that one of the proposed heuristics (eSA) reduces the error of the previously best known heuristic for the problem (HH1) by 70% while the computational time of HH1 is 30% more than that of eSA. Furthermore, the computational analysis also indicates that the other proposed heuristic (eHH) reduces the error of HH1 by 80% while both eHH and HH1 have the same computational time. All the results have been statistically verified.
Minimizing makespan with multiple-orders-per-job in a two-machine flowshop
European Journal of Operational Research, 2007
We investigate a new scheduling problem, multiple-orders-per-job (MOJ), in the context of a two-machine flowshop. Lower bounds for the makespan performance measure are provided for combinations of lot-processing and item-processing machines. An optimization model is presented that addresses both job formation and job sequencing. We define a heuristic to minimize the makespan for the MOJ problem for two-machine item-processing flowshops. The heuristic obtains solutions within 2% of a tight lower bound and runs in O(HF) time, where H is the number of orders and F is the restricted number of jobs.
A Branch-and-Bound Algorithm to Minimize the Makespan in a Flowshop with Blocking
Annals of Operations Research, 2005
Resumo_ Este trabalho considera o critério de minimização do makespan para o problema de programação de tarefas no ambiente flowshop com bloqueio. Neste ambiente não existem espaços de armazenamento entre as máquinas, logo filas de tarefas esperando no sistema pelas próximas operações não são permitidas. Neste artigo, um limitante inferior que explora a ocorrência do bloqueio é proposto. Um algoritmo branch-and-bound que utiliza este limitante é descrito e sua eficiência é avaliada em diversos problemas. Resultados de experimentos computacionais são apresentados. Palavras-chave: flowshop com bloqueio, makespan, limitante inferior, branch-and-bound. Abstract_ This work addresses the minimization of the makespan criterion for the flowshop scheduling problem with blocking. In this environment there are no buffers between successive machines, and therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. We propose a lower bound which exploits the occurrence of blocking. A branch-and-bound algorithm that uses this lower bound is described and its efficiency is evaluated on several problems. Results of computational experiments are reported.
No-wait flowshops with bicriteria of makespan and maximum lateness
European Journal of Operational Research, 2004
In this work we study a flowshop scheduling problem in which jobs are not allowed to wait in-between machines, a situation commonly referred to as no-wait. The concerned criterion is to minimize a weighted sum of makespan and maximum lateness. A dominance relation for the case of three-machine is presented and evaluated by experimental designs. Several heuristics and local search methods are proposed for the general m-machine case. The local search methods are based on genetic algorithms and iterated greedy procedures. An extensive computational analysis is conducted where it is shown that the proposed methods outperform existing heuristics and metaheuristics in all tested scenarios by a considerable margin and under identical CPU times.
International Journal of Production Research, 2011
In this paper, we consider the two-machine no-wait flow-shop scheduling problem, when every machine is subject to one non-availability constraint and jobs have different release dates. The nonavailability intervals of the machines overlap and they are known in advance. We aim to find a nonresumable schedule that minimizes the makespan. We propose several lower bounds and upper bounds. These bounding procedures are used in a branch-and-bound algorithm. Computational experiments are carried out on a large set of instances and the obtained results show the effectiveness of our method.
Multi-Degree Cyclic Scheduling of Two Robots in a No-Wait Flowshop
IEEE Transactions on Automation Science and Engineering, 2005
This paper addresses multi-degree cyclic scheduling of two robots in a no-wait flowshop, where exactly ( 1) identical parts with constant processing times enter and leave the production line during each cycle, and transportation of the parts between machines is performed by two robots on parallel tracks. The objective is to minimize the cycle time. The problem is transformed into enumeration of pairs of overlapping moves that cannot be performed by the same robot. This enumeration is accomplished by enumerating intervals for some linear functions of decision variables. The algorithm developed is polynomial in the number of machines for a fixed , but exponential if is arbitrary. Computational results with benchmark instances are reported.
Sustainability
This paper is aimed at studying a two-machine flowshop scheduling where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. That is, when a job is processed completely on the first machine, a certain delay time is required before its processing on the second machine. If we would like to reduce the actual waiting time, the processing time of the job on the second machine increases. The objective is to minimize the makespan. When the processing time is reduced, it implies that the consumption of energy is reduced. It is beneficial to environmental sustainability. We show that the proposed problem is NP-hard in the strong sense. A 0-1 mixed integer programming and a heuristic algorithm with computational experiment are proposed. Some cases solved in polynomial time are also provided.
Scheduling three-operation jobs in a two-machine flow shop to minimize makespan
This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.
Cyclic scheduling in robotic flowshops
Annals of Operations …, 2000
Fully automated production cells consisting of flexible machines and a material handling robot have become commonplace in contemporary manufacturing systems. Much research on scheduling problems arising in such cells, in particular in flowshop-like production cells, has been reported recently. Although there are many differences between the models, they all explicitly incorporate the interaction between the materials handling and the classical job processing decisions, since this interaction determines the efficiency of the cell. This paper surveys cyclic scheduling problems in robotic flowshops, models for such problems, and the complexity of solving these problems, thereby bringing together several streams of research that have by and large ignored one another, and describing and establishing links with other scheduling problems and combinatorial topics.
Scheduling a two-stage flowshop under makespan constraint
Mathematical and Computer …, 2006
We consider selecting and sequencing jobs in a two stage flowshop so that the selected jobs are completed before a specified time limit (such as the end of a shift). The objective is to maximize the weighted (reward) sum of the selected jobs. We show that the problem is NP-hard, and present two procedures to find an optimum solution. The first procedure uses dynamic programming, and the second uses mixed integer programming. The integer programming formulation exploits special properties of the problem and solves large instances of the problem. We also develop heuristics and provide worst case performance guarantees. An improvement procedure is also developed. Extensive computational testing shows that our heuristics, when used jointly with the improvement procedure, yield excellent results (providing solutions within 3% of the optimum in an average sense) for both balanced and unbalanced shops.