M-machine Flow Shop Research Articles

An upper bound for the inter-exit time of two jobs in an m-machine flow shop

This paper addresses the class of permutation flow shop scheduling where jobs, after their completion, must be grouped in batches. This is a common scheme in industrial environments, where products undergo multiple process steps in different shops and, when completed, must be transported to customers or the next production step. A new optimisation criterion is used, the inter-exit time, i.e., the difference between the completion times of two jobs. An upper bound is proposed and demonstrated for a general permutation flow shop with m machines.

An algorithm for a no-wait flowshop scheduling problem for minimizing total tardiness with a constraint on total completion time

We consider a no-wait m-machine flowshop scheduling problem which is common in different manufacturing industries such as steel, pharmaceutical, and chemical. The objective is to minimize total tardiness since it minimizes penalty costs and loss of customer goodwill. We also consider the performance measure of total completion time which is significant in environments where reducing holding cost is important. We consider both performance measures with the objective of minimizing total tardiness subject to the constraint that total completion time is bounded. Given that the problem is NP-hard, we propose an algorithm. We conduct extensive computational experiments to compare the performance of the proposed algorithm with those of three well performing benchmark algorithms in the literature. Computational results indicate that the proposed algorithm reduces the error of the best existing benchmark algorithm by 88% under the same CPU times. The results are confirmed by extensive statistical analysis. Specifically, ANOVA analysis is conducted to justify the difference between the performances of the algorithms, and a test of hypothesis is performed to justify that the proposed algorithm is significantly better than the best existing benchmark algorithm with a significance level of 0.01.

Robust and Stable Flow Shop Scheduling Problem under Uncertain Processing Times and Machines’ Disruption

This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs’ completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NP-hard problem; a method based on decomposing the problem into sub-problem and solving each sub-problem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.

Bounding Strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimizing the total flowtime of jobs

In this paper, bounding strategies for determining a lower bound on the completion time of a job sequenced in each position in the permutation sequence on each machine in permutation flowshop scheduling problem with minimisation of total flowtime of jobs as objective are discussed. Basically, the bounding strategies are machine-based bounding strategies used for determining the lower bound on total flowtime of jobs for all the small-sized and large-sized benchmark flowshop scheduling problem instances proposed by Vallada et al. (2015). The lower bound matrix can be pruned as tightening constraints into the mixed integer linear programming (MILP) model with objective of minimisation of total flowtime of jobs. Since the flowshop scheduling problem with total flowtime objective is difficult, two kinds of linear programming (LP) relaxation methods are used for determining an LP-based lower bound on total flowtime of jobs for some benchmark problem instances proposed by Vallada et al. (2015).

Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

A better heuristic approach for n-job m-machine flow shop scheduling problem

Scheduling problem has its origin in manufacturing industry.In this paper we describe a simple approach for solving the flow shop scheduling problem. The result we obtained has been compared with Palmers Heuristic and CDS algorithms along with NEH. It was found that our method will reach near optimum solution within few steps compared to CDS and NEHalgorithm and yield better result compared to Palmers Heuristic with objective of minimizing the Makespan for the horizontal rectangular matrix problems.

Some Results on Shop Scheduling with S-Precedence Constraints among Job Tasks

We address some special cases of job shop and flow shop scheduling problems with s-precedence constraints. Unlike the classical setting, in which precedence constraints among the tasks of a job are finish–start, here the task of a job cannot start before the task preceding it has started. We give polynomial exact algorithms for the following problems: a two-machine job shop with two jobs when recirculation is allowed (i.e., jobs can visit the same machine many times), a two-machine flow shop, and an m-machine flow shop with two jobs. We also point out some special cases whose complexity status is open.

Solving Flow Shop Scheduling Problems with Blocking by using Genetic Algorithm

Flow shop scheduling problems have been analyzed worldwide due to their various applications in industry. In this article, a new genetic algorithm (NGA) is developed to obtain the optimum schedule for the minimization of total completion time of n-jobs in an m-machine flow shop operating without buffers. The working process of the present algorithm is very efficient to implement and effective to find the best results. To implement the proposed algorithm more effectively, similar job order crossover operators and inversion mutation operators have been used. Numerous examples are illustrated to explain proposed approach. Finally, the computational results indicate that present NGA performs much superior to the heuristics for blocking flow shop developed in the literature.

Batching and resource allocation decisions on an m-machine proportionate flowshop

This article considers an m-machine proportionate flowshop scheduling problem where each stage of production consists of a batching operation. Moreover, we assume that the job processing times are controllable through the allocation of a non-renewable resource. The objective consists of minimising the makespan. The scheduler’s task consists of (1) allocating jobs to batches; (2) scheduling batches on the m-machine flowshop; (3) allocating resources to batches; and (4) allocating the resources within each batch to jobs. We show that there exists an optimal solution to the problem that consists of sequencing the jobs in Λ-shape order based on their workloads. Furthermore, the jobs that are sorted in non-decreasing order of workload are scheduled in batches of equal size, whereas the remaining jobs are allocated to batches of different sizes. We present an time algorithm based on the observation that all jobs scheduled in the first segment of the Λ-shape have workloads that are smaller than (or equal to) that of the last job in the sequence.

Minimization of total energy consumption in an m-machine flow shop with an exponential time-dependent learning effect

Minimization of total energy consumption in an m-machine flow shop with an exponential time-dependent learning effect

Computational Study of N-Job M-Machine Flow Shop Scheduling Problems: SPT, EDD, NEH, NEH-EDD, and Modified-NEH Algorithms

This paper discusses about the flow shop scheduling problems using shortest processing time, earliest due date (EDD), Nawaz, Enscore, and Ham (NEH), NEH-EDD, and modified-NEH methods. The objective of this research is to determine the performance of these methods in minimizing makespan and total tardiness. Processing times and due dates were randomly generated, and computational studies were performed in Microsoft Visual Basic 6.0. The experiments are performed for small and medium data sets. Efficiency index, relative error, and run time measure the performance of each method. Experimental results showed that NEH has the best performance in minimizing the makespan in both data sets; these are 53.35 time unit for small data sets and 83.803 time unit for medium data sets. NEH-EDD has the best performance in minimizing total tardiness with 9.37 time unit for small data sets and 231.02 time unit for medium data sets. Modified-NEH, as the proposed method for minimizing makespan and total tardiness at the same time, has good enough result. For minimizing the makespan, modified-NEH results in 57.15 time unit for small data sets and 88.107 time unit for medium data sets. For minimizing total tardiness, the modified-NEH results in 14.21 time unit for small data sets and 246.57 time unit for medium sets.

Special Case Algorithm for N-jobs M-machines Flow Shop Scheduling Problems

In this paper we have developed an algorithm for n-jobs with m-machine flow shop scheduling problems in order to handle variety of data type than Geleta [3]. In other hands, as in Geleta [3] it main objective is how to obtain optimal sequence of jobs with aim of minimum squared value of lateness.

New Algorithm for N-jobs on M-machine Flow Shop Scheduling Problems

Because of flow shop scheduling is one of the most important problems in the area of production management, In this paper, what I have did is that, I have developed a new algorithm for n-jobs m-machine flow shop scheduling problem for special case of n-jobs m-machine flow shop scheduling problem. And also, there is a good self explanatory example to explain the algorithm very well.

A hybrid discrete firefly algorithm to solve flow shop scheduling problems to minimise total flow time

In this paper, we consider m-machine flow shop scheduling problems (FSSPs). The objective is to schedule the available n jobs to minimise the total flow time. The flow shop scheduling problems have been proved to be strongly non-deterministic polynomial-time hard (NP-hard). Hence, exact methods cannot be used to solve even small size problems. Researchers addressed many heuristics and meta-heuristics to solve the problems. Firefly algorithm (FA) is one of the recently developed meta-heuristic algorithms. We propose a hybrid discrete firefly algorithm (HDFA) to solve the FSSPs to minimise the total flow time. To validate the performances of the HDFA, computational experiments are conducted on a number of randomly generated test problems with different parameters and the results proved the effectiveness of the proposed algorithm.

A hybrid discrete firefly algorithm to solve flow shop scheduling problems to minimise total flow time

In this paper, we consider m-machine flow shop scheduling problems (FSSPs). The objective is to schedule the available n jobs to minimise the total flow time. The flow shop scheduling problems have been proved to be strongly non-deterministic polynomial-time hard (NP-hard). Hence, exact methods cannot be used to solve even small size problems. Researchers addressed many heuristics and meta-heuristics to solve the problems. Firefly algorithm (FA) is one of the recently developed meta-heuristic algorithms. We propose a hybrid discrete firefly algorithm (HDFA) to solve the FSSPs to minimise the total flow time. To validate the performances of the HDFA, computational experiments are conducted on a number of randomly generated test problems with different parameters and the results proved the effectiveness of the proposed algorithm.

Min-Max Regret Version of an m-Machine Ordered Flow Shop with Uncertain Processing Times

We consider an m-machine flow shop scheduling problem to minimize the latest completion time, where processing times are uncertain. Processing time uncertainty is described through a finite set of processing time vectors. The objective is to minimize maximum deviation from optimality for all scenarios. Since this problem is known to be NPhard, we consider it with an ordered property. We discuss optimality properties and develop a pseudo-polynomial time approach for the problem with a fixed number of machines and scenarios. Furthermore, we find two special structures for processing time uncertainty that keep the problem NP-hard, even for two machines and two scenarios. Finally, we investigate a special structure for uncertain processing times that makes the problem polynomially solvable.

Heuristics for an <i>m</i>-Machine Re-Entrant Permutation Flowshop with the Objective of Total Tardiness

We focus on an m-machine re-entrant flowshop scheduling problem with the objective of minimizing total tardiness. In the re-entrant flowshop considered here, routes of all jobs are identical as in ordinary flowshops, but the jobs must be processed multiple times on the machines. We present heuristic algorithms, which are modified from well-known existing algorithms for the general m-machine flowshop problem or newly developed in this paper. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported.

한정된 크기의 버퍼가 있는 흐름 공정 일정계획의 스트레치 최소화

In this paper, a hybrid genetic algorithm (HGA) approach is proposed for an n-job, m-machine flow shop scheduling problem with limited capacity buffers with blocking in which the objective is to minimize the total stretch. The stretch of a job is the ratio of the amount of time the job spent before its completion to its processing time. HGA adopts the idea of seed selection and development in order to improve the exploitation and exploration power of genetic algorithms (GAs). Extensive computational experiments have been conducted to compare the performance of HGA with that of GA.

A Heuristic Algorithm for Flow Shop Scheduling Problem

This paper considers the m-machine flow shop problem to minimize weighted completion time. A heuristic algorithm is presented to deal with the problem for large size problem. At the end of the paper, some numerical experiments show the effectiveness of the heuristic.

Comparison of Improved Sheep Flock Heredity Algorithm and Artificial Bee Colony Algorithm for lot Streaming in m-Machine Flow Shop Scheduling

Lot streaming is a technique used to split the processing of lots into several sublots (transfer batches) to allow the overlapping of operations in a multistage manufacturing systems thereby shortening the production time (makespan). The objective of this paper is to minimize the makespan and total flow time of n-job, m-machine lot-streaming problem in a flow shop with variable size sublots and also to determine the optimal sublot size. In recent times researchers are concentrating and applying intelligent heuristics to solve Flow shop problems with lot streaming. In this research, Improved Sheep Flock Heredity algorithm (ISFHA) and Artificial Bee Colony (ABC) algorithms are used to solve the problem. The results obtained by the proposed algorithms are also compared with the performance of other worked out traditional heuristics. The computational results show that the identified algorithms are more efficient, effective and better than the algorithms already tested for this problem.