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Two-stage Assembly Flowshop Scheduling Problem With Bi-objective of Number of Tardy and Makespan Minimization.
Abstract
In this paper the two stage assembly flow shop problem (TSAFSP) with bi-objective of number of tardy and makespan minimization is addressed. The problem is known to be NP-hard and is thus solved with two metaheuristics: Simulated Annealing (SA) and Variable Neighborhood Search (VNS) and the Pareto-optimal solutions approach is taken to find optimal solutions of the problem. Computational experiments have been executed and a comparison of the metaheuristics has been carried out. It is indicated that for this problem SA works better in small problems, but is outperformed by VNS as the size of the problem grows; while in general SA is faster than VNS.
... For this reason, some researchers turned their attention to the use of meta-heuristics for the solution of TSAFSP. The most notable of these algorithms are evolutionary computation methods such as evolutionary algorithms (Allahverdi and Al-Anzi 2008), simulated annealing (Navaei, Mozdgir, and Hidaji 2010;Javadian et al. 2009), VNS (Navaei, Mozdgir, and Hidaji 2010;Javadian et al. 2009), tabu-search (Hatami et al. 2010;Allahverdi and Al-Anzi 2006), particle swarm optimisation (PSO) (Allahverdi and Al-Anzi 2006) and genetic algorithm (Zhao and Wu 2000). ...
... For this reason, some researchers turned their attention to the use of meta-heuristics for the solution of TSAFSP. The most notable of these algorithms are evolutionary computation methods such as evolutionary algorithms (Allahverdi and Al-Anzi 2008), simulated annealing (Navaei, Mozdgir, and Hidaji 2010;Javadian et al. 2009), VNS (Navaei, Mozdgir, and Hidaji 2010;Javadian et al. 2009), tabu-search (Hatami et al. 2010;Allahverdi and Al-Anzi 2006), particle swarm optimisation (PSO) (Allahverdi and Al-Anzi 2006) and genetic algorithm (Zhao and Wu 2000). ...
... VNS is a powerful local search method which has been shown as a powerful algorithm in solving scheduling problems (Navaei, Mozdgir, and Hidaji 2010;Javadian et al. 2009;Mladenovic and Hansen 1997). VNS begins with an initial solution and searches for better solutions through manipulation in a nested loop of neighbourhoods. ...
In this paper, we address the two stage assembly flow-shop problem with multiple non-identical assembly machines in stage two to minimise weighted sum of makespan and mean completion time. Also, sequence dependent setup times are considered for the first stage. This problem is a generalisation of previously proposed two stage assembly flow-shop problems (TSAFSP). In many real world industrial and production systems, there is more than one assembly machine to assemble job components. After extending a mathematical mixed-integer linear programming model to solve the problem, we use GAMS software. The TSAFSP has been known as NP-hard. Therefore, our more general problem is NP-hard too and so for large sized problems the right way to proceed is with the use of heuristic algorithms. So in this paper a hybrid VNS heuristic, which is a combination of the variable neighbourhood search (VNS) algorithm and a novel heuristic is developed and its solutions compared with solutions obtained by GAMS. Computational experiments reveal that the hybrid VNS heuristic performs much better than GAMS with respect to the percentage errors and run times.
... In TSAFSP, researchers have used different objectives such as makespan, mean completion time, lateness, tardiness, number of tardy jobs and so on [2,3,24,29,39]. In real life many managers are curious about total cost in order to find the best sequence of jobs to minimize their expenditures. Two important types of costs derived by sequencing of jobs are holding and delay costs. ...
... Some researchers have used meta-heuristic algorithms to solve the TSAFSP. The most notable of this group of algorithms used in optimization problems are evolutionary computation methods such as evolutionary algorithms [2], simulated annealing (SA) [2,22,24,27,29], variable neighborhood search [24,29], self-adaptive differential evolution (SDE) [2], genetic algorithm (GA) [10,16,4], tabu-search [1,18], particle swarm optimization [1] and hybrid of them [38]. On account of the fact that this problem contains two phases which are finding a sequence of jobs at the first stage and assigning addressed jobs to w assembly machines at the second stage, more than one heuristic or meta-heuristic to solve the problem is required. ...
... Some researchers have used meta-heuristic algorithms to solve the TSAFSP. The most notable of this group of algorithms used in optimization problems are evolutionary computation methods such as evolutionary algorithms [2], simulated annealing (SA) [2,22,24,27,29], variable neighborhood search [24,29], self-adaptive differential evolution (SDE) [2], genetic algorithm (GA) [10,16,4], tabu-search [1,18], particle swarm optimization [1] and hybrid of them [38]. On account of the fact that this problem contains two phases which are finding a sequence of jobs at the first stage and assigning addressed jobs to w assembly machines at the second stage, more than one heuristic or meta-heuristic to solve the problem is required. ...
... Hence, when jobs (e.g., raw material, parts, tasks and items) are early or late, the fixed and variable penalties are incurred (Lann and Mosheiov, 1996). (Navaei et al., 2010) presented a two-stage assembly flow-shop scheduling problem with bi-objectives minimizing the makespan and the number of tardy jobs. (Javadian et al., 2009) solved an assembly flowshop scheduling problem with parallel machines by the use of variable neighborhood search (VNS). ...
This paper presents a new mathematical model for a two-stage assembly flowshop scheduling problem that minimizes the mean tardiness and earliness penalties. This problem is an extension of the assembly flow shop problem with simultaneous operations in the first stage and a single assembly operation in the second stage. The problem is known to be NP-hardness; therefore, we propose three meta-heuristic algorithms, namely variable neighborhood search (VNS), genetic algorithm (GA) and simulated annealing (SA), in order to solve such a hard problem. To tune the parameters of the foregoing algorithms, the Taguchi method is used. A number of test problems are considered and the associated data are generated at random. Furthermore, a comprehensive computational experiment is conducted to compare the performance of the proposed meta-heuristics. The related results and statistical experiments show that the proposed VNS outperforms the proposed GA and SA in terms of both the standard deviation and average percentage error measures.
Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult.
In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.
In this paper, we address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the jobs on the machines so that total completion time of all n jobs is minimized. Optimal solutions are obtained for two special cases. A simulated annealing heuristic, a tabu search heuristic, and a hybrid tabu search heuristic are proposed for the general case. The proposed heuristics are compared with the existing heuristics and shown to be more efficient. The computational analysis shows that the proposed hybrid tabu search heuristic improves the error rate by about 60 and 90 percent over tabu search and simulated annealing heuristics, respectively, where the CPU time of all the three heuristics is almost the same.
We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.
The two-stage flowshop scheduling problem with the objective of minimizing total flowtime subject to obtaining the optimal makespan is discussed. A branch-and-bound algorithm and two heuristic algorithms have been developed. The results of the experimental investigation of the effectiveness of the algorithms are also presented.
We study the problem of minimizing the makespan in a two-stage assembly flow shop scheduling problem with uniform parallel machines. This problem is a generalization of the assembly flow shop problem with concurrent operations in the first stage and a single assembly operation in the second stage. We propose a heuristic with an absolute performance bound which becomes asymptotically optimal as the number of jobs becomes very large. We show that our results slightly improve earlier results for the simpler assembly flow shop problem (without uniform machines) and for the two-stage hybrid flow shop problem with uniform machines.
We consider the two-stage flexible flow shop makespan minimization problem with uniform parallel machines. Soewandi and Elmaghraby [Soewandi, H., Elmaghraby, S., 2003. Sequencing on two-stage hybrid flowshops with uniform machines to minimize makespan. IIE Transaction 35, 467–477] developed a heuristic (S–E) and derived a machine speed-dependent worst-case ratio bound for it. We point out that this bound works well when the uniform machines have approximately equal speeds but is not indicative of the performance of the S–E heuristic when the machine speeds are in a wide range. Motivated by this observation, we propose an alternative tight machine-speed dependent worst-case bound for the S–E heuristic that works well when the machine speeds vary significantly. We then combine the two speed-dependent ratio bounds into a speed-independent bound. Our findings facilitate the narrowing of the gap between experimental performance and worst-case bound for the S–E heuristic.