Heuristics for the Hybrid Flow Shop Scheduling Problem with Parallel Machines at the First Stage and Two Dedicated Machines at the Second Stage (original) (raw)
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Scheduling a two-stage hybrid flow shop with parallel machines at the first stage
Annals of Operations Research, 1997
This paper considers a non-preemptive two-stage hybrid flow shop problem in which the first stage contains several identical machines, and the second stage contains a single machine. Each job is to be processed on one of the first-stage machines, and then on the second-stage machine. The objective is to find a schedule which minimizes the maximum completion time or makespan. The problem is NP-hard in the strong sense, even when there are two machines at the first stage. Several lower bounds are derived and are tested in a branch and bound algorithm. Also, constructive heuristics are presented, and a descent algorithm is proposed. Extensive computational tests with up to 250 jobs, and up to 10 machines in the first stage, indicate that some of the heuristics consistently generate optimal or near-optimal solutions.
The hybrid flow shop scheduling problem
2010
The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper discusses several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.
A heuristic method for two-stage hybrid flow shop with dedicated machines
2013
Two-stage hybrid flow shop Dedicated machine Branch and bound Makespan Heuristic a b s t r a c t This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.
Invited Review The hybrid flow shop scheduling problem
The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.
A Heuristic for Group Scheduling the Multi-stage Hybrid Flow Shop Problems
According to the practical relevance, the Hybrid Flow Shop (HFS) has attracted many researchers recently. This paper addresses a special case of group scheduling problem in a multi-stage HFS with optimization of throughput related objectives. The aim of the work is to simplify the solution procedure through a heuristic approach to reach the optimal solution, i.e., minimal makespan with optimal flow parameters. The heuristic solution was tested with all possible group schedules encountered in the HFS problem to ensure the compatibility of the optimal solution and its consistency with the throughputs. The throughput related measures other than makespan such as queue status and machine utilization were considered to evaluate the performance of the heuristic. The heuristic performs well to reach the optimal solution with minimal makespan and queue status with effective machine utilization. A case study was done in a pulley manufacturing plant and a global solution was suggested.
World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 2010
This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems. Keywords—Flow Shop, Genetic Algorithm, Simulated Annealing, Tabu Search.
Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage
Computers & Operations Research, 2012
This study deals with the two-stage hybrid flow shop (HFS) problem with precedence constraints. Two versions are examined, the classical HFS where idle time between the operations of the same job is allowed and the no-wait HFS where idle time is not permitted. For solving these problems an adaptive randomized list scheduling heuristic is proposed. Two global bounds are also introduced so as to conservatively estimate the distance to optimality of the proposed heuristic. The evaluation is done on a set of randomly generated instances. The heuristic solutions for the classical HFS in average are provably situated below 2% from the optimal ones, and on the other hand, in the case of the no-wait HFS the average deviation is below 5%.
Computers & Operations Research, 2010
In this paper, an extensive review of recently published papers on hybrid flow shop (HFS) scheduling problems is presented. The papers are classified first according to the HFS characteristics and production limitations considered in the respective papers. This represents a new approach to the classification of papers in the HFS environment. Second, the papers have been classified according to the solution approach proposed. These two classification categories give a comprehensive overview on the state of the art of the problem and can guide the reader with respect to future research work.
Heuristic algorithms for scheduling hybrid flow shops with machine blocking and setup times
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018
We investigate a new variant of the hybrid flow shop problem (HFSP) considering machine blocking and both sequence-independent and sequence-dependent setup times. Since the HFSP is NP-hard, we propose heuristic algorithms along with priority rules based on the traditional SPT and LPT rules. We carried out computational experiments on simulated problem instances to test the performance of the priority rules. The objective function adopted was makespan minimization, and we used the rate of success and the relative deviation as performance criteria. The results indicate superiority of LPT-based rules. On instances with sequence-independent setup times, the LP rule, which is based on the non-increasing sorting of total processing times, outperformed other rules in most tested instances. In instances with sequence-dependent setup times, the LPS rule, which is based on the non-increasing sum of processing time and average setup times, outperformed other rules in most tested instances.
Computers and Operations Research, Vol. 36, No.2, 2009, 358 - 378
This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0-1 mixed integer program is formulated. The problem is however a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operation time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing, tabu search and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion based approach is superior to the others, whereas the proposed simulated annealing algorithms are better than tabu search and genetic algorithms among the iterative metaheuristic algorithms.