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)
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.
Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion
In the paper, the flow-shop scheduling problem with parallel machines at each stage (machine center) is studied. For each job its release and due date as well as a processing time for its each operation are given. The scheduling criterion consists of three parts: the total weighted earliness, the total weighted tardiness and the total weighted waiting time. The criterion takes into account the costs of storing semi-manufactured products in the course of production and ready-made products as well as penalties for not meeting the deadlines stated in the conditions of the contract with customer. To solve the problem, three constructive algorithms and three metaheuristics (based one Tabu Search and Simulated Annealing techniques) are developed and experimentally analyzed. All the proposed algorithms operate on the notion of so-called operation processing order, i.e. the order of operations on each machine. We show that the problem of schedule construction on the base of a given operation processing order can be reduced to the linear programming task. We also propose some approximation algorithm for schedule construction and show the conditions of its optimality. r Hybrid flow-shop problems have received considerable attention from researchers during the last two decades. However, the scheduling criterion most frequently considered in those papers was the maximum completion time, see , , , and . Furthermore, these studies propose either an exact algorithm, which can solve only up to moderate size problem instances, or different types of heuristic and approximation algorithms .
Scheduling two-stage hybrid flow shop with availability constraints
Computers & Operations Research, 2006
Most of the literature on scheduling assumes that machines are always available. However, in real life industry, machines may be subject to some unavailability periods due to maintenance activities such as breakdowns (stochastic case) and preventive maintenance (deterministic case). In this paper we investigate the two-stage hybrid flow shop scheduling problem with only one machine on the first stage and m machines on the second stage to minimize the makespan. We consider that each machine is subject to at most one unavailability period. The start time and the end time of each period are known in advance (deterministic case) and only the non-resumable case is studied. First we discuss the complexity of the problem. Afterwards, we give the Branch and Bound model for this problem. Last, we calculate the worst-case performances of three heuristics: LIST algorithm, LPT algorithm and H-heuristic.
International Journal of Advanced Manufacturing Technology, Vol. 37, 2008, 354 - 370
In textile industries, production facilities are established as multi-stage production flow shop facilities where a production stage may be made up of parallel machines. It is known as flexible or hybrid flow shop environment. This paper considers the problem of scheduling n independent jobs in such an environment. In addition, we also consider the general case in which parallel machines in each stage may be unrelated. Each job is processed in ordered operations on a machine of each stage. Its release date and due date are given. Preemption of jobs is not permitted. We consider both sequence- and machine-dependent setup times. The problem is to determine a schedule that minimizes a convex combination of makespan and the number of tardy jobs. A 0-1 mixed integer program of the problem is formulated. Since this problem is NP-hard in the strong sense, we develop heuristic algorithms to solve it approximately. Firstly, several basic dispatching rules and well-known constructive heuristics for flow shop makespan scheduling problems are generalized to the problem under consideration. We sketch how from a job sequence a complete schedule for the flexible flow shop problem with unrelated parallel machines can be constructed. To improve the solutions, polynomial heuristic improvement methods based on shift moved of jobs are applied. Then genetic algorithms are suggested. We discuss the components of these algorithms and test their parameters. 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.
Minimizing makespan in a three-stage hybrid flow shop with dedicated machines
International Journal of Industrial Engineering Computations
In recent years, many studies on scheduling problems with dedicated machines have been carried out. But, few of them have considered the case of more than two stages. This paper aims at filling this gap by addressing the three-stage hybrid flow shop scheduling problem with two dedicated machines in stage 3. Each job must be processed, consecutively, on the single machines of stages 1 and 2, and depending on its type, it will be further processed on one of the two dedicated machines of stage 3. The objective is to find an optimal schedule that minimizes the maximum completion time (makespan). Since this problem is strongly NP-hard, we first provide some basic results including solutions for several variations of the problem. Then, for the general case we adapt a set of lower bounds from the literature and propose a heuristic approach that is based on the dynamic programming technique, which uses a local search procedure. Finally, various experimentations on several problems with different sizes are conducted and the computational results of the heuristic show that the mean percentage deviation value from the lower bound was lower than 0.8 percent for some instances with 40 to 200 jobs in size.
Cyclic Hybrid Flow-shop Scheduling Problem with Machine Setups
Procedia Computer Science, 2014
In this paper we consider an NP-hard hybrid flow shop problem with machine setups and cycletime minimization. The above issue is an important generalization of a flow-shop problem with minimization of a cycle time, and it stays in a direct relationship with a flexible job shop problem. In the hybrid problem task operations are performed by machines arranged in slots, i.e., a set of machines with the same functional properties. In this work we presented a graph model, properties of the problem and methods of determining approximate value of the optimal cycle duration. The above mentioned concepts have been used in the construction of tabu search algorithm. Computational experiments were conducted on well-known in literature examples, which confirmed high efficiency of the algorithm.
Most scheduling problems are combinatorial optimization problems which are too difficult to be solved optimally, and hence heuristics are used to obtain good solutions in reasonable times. The specific goal of this paper is to investigate scheduling heuristics to seek the minimum of a positively weighted convex sum of makespan and the number of tardy jobs in a static hybrid flow shop environment, where at least one production stage is made up of unrelated parallel machines. In addition, sequence -and machine -dependent setup times are considered. Some simple dispatching rules and flow shop makespan heuristics are adapted for the sequencing problem under consideration. The improvement heuristic algorithm proposed is a reinsertion algorithm. A simulated annealing algorithm is presented in this paper. Three basic parameters (i.e., cooling schedules, neighborhood structures, and initial temperatures) of a simulated annealing algorithm 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.
2007
Most scheduling problems are combinatorial optimization problems which are too difficult to be solved optimally, and hence heuristics are used to obtain good solutions in a reasonable time. The specific goal of this paper is to investigate scheduling heuristics, to seek the minimum of a positively weighted convex sum of makespan, and the number of tardy jobs, in a static hybrid flow shop environment, where at least one production stage is made up of unrelated parallel machines. In addition, sequence-and machine-dependent setup times are considered. Some simple dispatching rules and flow shop makespan heuristics are adapted for the sequencing problem under consideration. Then, this solution may be improved by a fast polynomial reinsertion algorithm. Moreover, a simulated annealing algorithm is presented in this paper. Three basic parameters (i.e., cooling schedules, neighborhood structures, and initial temperatures) of a simulated annealing algorithm 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.
Multicriteria Hybrid Flow Shop Scheduling Problem: Literature Review, Analysis, and Future Research
Independent Journal of Management Production, 2014
This research focuses on the Hybrid Flow Shop production scheduling problem, which is one of the most difficult problems to solve. The literature points to several studies that focus the Hybrid Flow Shop scheduling problem with monocriteria functions. Despite of the fact that, many real world problems involve several objective functions, they can often compete and conflict, leading researchers to concentrate their efforts on the development of methods that take this variant into consideration. The goal of the study is to review and analyze the methods in order to solve the Hybrid Flow Shop production scheduling problem with multicriteria functions in the literature. The analyses were performed using several papers that have been published over the years, also the parallel machines types, the approach used to develop solution methods, the type of method develop, the objective function,