M-machine Flow Shop Research Articles

Evolutionary algorithms for scheduling m-machine flow shop with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs– m-machines flow shops under lot sizing environment. Lot streaming (Lot sizing) is the process of creating sub lots to move the completed portion of a production sub lots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. Evolutionary algorithms that belong to search heuristics find more applications in recent research. Genetic algorithm (GA) and hybrid genetic algorithm (HEA) also known as hybrid evolutionary algorithm fall under evolutionary heuristics. On this concern this paper proposes two evolutionary algorithms namely, GA and HEA to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set-up time. The following two algorithms are used to evaluate the performance of the proposed GA and HEA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) simulated annealing algorithm (SA) for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.

Minimising total tardiness in the m-machine flowshop problem: A review and evaluation of heuristics and metaheuristics

In this work, a review and comprehensive evaluation of heuristics and metaheuristics for the m-machine flowshop scheduling problem with the objective of minimising total tardiness is presented. Published reviews about this objective usually deal with a single machine or parallel machines and no recent methods are compared. Moreover, the existing reviews do not use the same benchmark of instances and the results are difficult to reproduce and generalise. We have implemented a total of 40 different heuristics and metaheuristics and we have analysed their performance under the same benchmark of instances in order to make a global and fair comparison. In this comparison, we study from the classical priority rules to the most recent tabu search, simulated annealing and genetic algorithms. In the evaluations we use the experimental design approach and careful statistical analyses to validate the effectiveness of the different methods tested. The results allow us to clearly identify the state-of-the-art methods.

7102 List-based Squeezing Branch and Bound法におけるノード選択方法の改良(OS7 学生研究課題発表)

The "list-based squeezing branch and bound (LSQ) algorithm" is a kind of local search algorithms, which searches neighborhood of an initial schedule in an enumerative manner by using a branching procedure in a branch and bound algorithm (B & B) in parallel. In the LSQ, some initial schedules are found first by using promising heuristic methods, and then a B & B-based parallel local search is implemented for obtaining an optimal (or a near-optimal) schedule. In this paper, the LSQ is applied to n-job, m-machine flowshop scheduling problems to minimize makespan. A new procedure for selecting promising nodes to be branched is proposed and incorporated into the searching process of the LSQ to improve the efficiency and accuracy. Numerical experiments are implemented through benchmark problems to demonstrate that the proposed method can efficiently obtain a near optimal schedule with high accuracy.

Flowshop/No-idle Scheduling to Minimize Total Elapsed Time

This paper studies four n-job, m-machine flowshop problems when processing times of jobs on various machines follow certain conditions. The objective is to obtain a sequence, which minimizes total elapsed time under no-idle constraint. Under no-idle constraint, the machines work continuously without idle-interval. We prove two theorems. We introduce simple algorithms without using branch and bound technique. Numerical examples are also given to demonstrate the algorithms.

Environmental compliance impacts China job shops

We address a batch scheduling problem of n identical processing time jobs on an m-machine flow-shop and a 2-machine job-shop. The objective is makespan minimization. Both problems are shown to be solved in O(n).

A heuristic for minimizing the makespan in no-idle permutation flow shops

The paper deals with the problem of finding a job sequence that minimizes the makespan in m-machine flow shops under the no-idle condition. This condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. Since the problem is NP-hard, we propose a constructive heuristic for solving it that significantly outperforms heuristics known so far.

A note on flow-shop and job-shop batch scheduling with identical processing-time jobs

We address a batch scheduling problem of n identical processing time jobs on an m-machine flow-shop and a 2-machine job-shop. The objective is makespan minimization. Both problems are shown to be solved in O( n).

Flow‐shop batch scheduling with identical processing‐time jobs

AbstractIn many practical situations of production scheduling, it is either necessary or recommended to group a large number of jobs into a relatively small number of batches. A decision needs to be made regarding both the batching (i.e., determining the number and the size of the batches) and the sequencing (of batches and of jobs within batches). A setup cost is incurred whenever a batch begins processing on a given machine. This paper focuses on batch scheduling of identical processing‐time jobs, and machine‐ and sequence‐independent setup times on an m‐machine flow‐shop. The objective is to find an allocation to batches and their schedule in order to minimize flow‐time. We introduce a surprising and nonintuitive solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Total flowtime and makespan for a no-wait m-machine flowshop with set-up times separated

This paper addresses the m-machine no-wait flowshop problem where the set-up time of a job is separated from its processing time. The performance measures considered are the total flowtime and makespan. The scheduling problem for makespan reduces to the travelling salesman problem (TSP), and the scheduling problem for total flowtime reduces to the time-dependent travelling salesman problem (TDTSP). Non-polynomial time solution methods are presented, along with a polynomial heuristic.

Multi-objective lot splitting for a single product m-machine flowshop line

In this paper, the mean flowtime and the makespan objectives are simultaneously investigated in a single product, m-machine, flowshop system. For this purpose, an efficiency frontier approach is applied and an optimal algorithm for generating all efficient solutions is developed. A comprehensive computational experiment is performed for analyzing the tradeoff between the two objectives and evaluating the proposed algorithm performance. The most-balanced-solution, MinMax, is defined and recommended as a desirable alternative for either the flowtime or the makespan optimal solutions. Results show that when the system is optimized for either the mean flowtime or the makespan, a significant loss in the nonoptimized objective value is observed. On the other hand, adopting the MinMax solution obtains a close to optimal solution in both objectives.

Comparing scheduling rules for flexible flow lines

This paper explores scheduling flexible flow lines with sequence-dependent setup times. Three major types of heuristics are explored. Insertion heuristics (based on insertion heuristics for the traveling salesman problem) attempt to simultaneously equalize workload on all processors at a stage, and minimize total or single-stage flowtimes. Johnson's algorithm for two-stage flow shops and its heuristic extensions to m-machine flow shops are modified for parallel processors and the flexible flow-line environment. A set of naı̈ve greedy heuristics is investigated for comparison purposes. The performance of the heuristics is compared on a set of test problems. Results indicate the range of conditions under which each method performs well.

The two- and m-machine flowshop scheduling problems with bicriteria of makespan and mean flowtime

This paper considers the flowshop scheduling problem with the objective of minimizing the weighted sum of makespan and mean flowtime. Even though the two-machine problem has been addressed and several heuristics have been established in the literature, these heuristics have not been compared. In this paper, a comparison of these available heuristics in the literature is conducted. Moreover, three new heuristic algorithms are proposed, which can be utilized for both the two-machine and m-machine problems. Computational experiments indicate that the proposed heuristics are superior to all the existing heuristics in the literature including a genetic algorithm. Two dominance relations are also developed; one for the two-machine and the other for the three-machine problem. Experimental results show that both relations are efficient.

Scheduling unit processing time jobs on an m-machine flow-shop

The sequential production of identical jobs and the flow-shop machine setting are extremely common in real-life applications. We study a scheduling problem that combines these two elements: jobs of identical processing time, with job-dependent weights, and a given common due date processed on an m-machine flow-shop. The (just-in-time) objective is to minimize the maximum earliness/tardiness cost. We introduce a polynomial time solution in both cases of (i) a non-restrictive (ie, sufficiently large) due date, and (ii) a restrictive due date (which restricts the number of early jobs).

A new heuristic for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness

This paper addresses the m-machine flowshop problem with the objective of minimizing a weighted sum of makespan and maximum tardiness. Two types of the problem are addressed. The first type is to minimize the objective function subject to the constraint that the maximum tardiness should be less than a given value. The second type is to minimize the objective without the constraint. A new heuristic is proposed and compared to two existing heuristics. Computational experiments indicate that the proposed heuristic is much better than the existing ones. Moreover, a dominance relation and a lower bound are developed for a three-machine problem. The dominance relation is shown to be quite efficient. Scope and purpose The majority of research on scheduling problems addresses only a single criterion while the majority of real-life problems require the decision maker to consider more than a single criterion before arriving at a decision. The scheduling literature reveals that the research on multi-criteria is mainly focused on the single-machine problem as a result of the difficulty of the multiple machines problem. This paper addresses an m-machine flowshop scheduling problem with a multi-criteria objective function.

Minimizing tardiness in a two-machine flow-shop

The two-machine flow-shop scheduling problem with the objective of minimizing total tardiness is considered in this paper. Dominance criteria are developed to establish the precedence constraints between jobs in an optimal schedule. A lower bound on the total tardiness of the problem is derived by constructing the sequence of jobs from front to back to simplify the bounding procedure. A branch-and-bound algorithm incorporating these properties is proposed to expedite the search for an optimal sequence. Computational experiments are conducted and the results demonstrate that the proposed algorithm surpasses an existing one in terms of both computation times and sizes of the problems solved. Scope and purpose An m-machine flow-shop requires all the n jobs to be processed following the same path from one to another on these m machines. For a two-machine flow-shop problem, however, one needs to consider only permutation schedules [1] on which both machines process the jobs in the same order. Besides the flow-shops that actually consist of two machines, there are many occasions in which a large complex facility can be viewed as though it performs two major operations. Even if a shop has several machines, two of them may be so restrictive and function as bottleneck ones. Total tardiness is a widely used scheduling performance measure in practical production environments for which there is no benefit for finishing jobs early, and the tardiness penalty is proportional to the delay over all jobs. The two-machine flow-shop problem with total tardiness as the scheduling criterion is NP-complete [2] and has been solved by branch-and-bound algorithms. However, more properties of the problem can be exploited and developed to enhance the computational efficiency of the algorithm.

Part location algorithms for an intelligent fixturing system, part 1: System description and algorithm development

The purpose of this paper is to point out that the programming model proposed by Eren [A bicriteria m-machine flowshop scheduling with sequence-dependent setup times, Appl. Math. Model. 34 (2010) 284–293] is incorrect. We propose a mixed 0–1 programming model for the same scheduling problem based on their model.

New heuristics to minimize total completion time in m-machine flowshops

We consider the m-machine permutation flowshop with the objective of minimizing total completion time. We compare few recent heuristics that are independently developed and propose several new heuristics. Our computational analysis shows that a small proposed modification (pairwise exchange) improves the error performance of the best existing algorithms almost 50% with negligible CPU time. Moreover, some of our proposed heuristics outperform the modified existing heuristics in both error and CPU time. For example, for U(1, 100) and number of jobs 500 and number of machines 20, our proposed heuristic IH3 yields an error of 0.287 at a CPU time of 144 seconds whereas the modified existing WY heuristic gives an error 0.325 at a CPU time of 2665 seconds.

Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date

We consider two problems of m-machine flow shop scheduling in this paper: one, with the objective of minimizing the variance of completion times of jobs, and the other with the objective of minimizing the sum of squares of deviations of job completion times from a common due date. Lower bounds on the sum of squares of deviations of job completion times from the mean completion time of jobs for a given partial sequence are first presented. Using these lower bounds, a branch and bound algorithm based on breadth-first search procedure for scheduling n jobs on m-machines with the objective of minimizing completion time variance (CTV) is developed to obtain the best permutation sequence. We also present two lower bounds and thereafter, a branch and bound algorithm with the objective of minimizing the sum of squares of deviations of job completion times from a given common due date (called the MSD problem). The computational experience with the working of the two proposed branch and bound algorithms is also reported. Two heuristics, one for each of the two problems, are developed. The computational experience on the evaluation of the heuristics is discussed.

Minimizing makespan in a blocking flowshop using genetic algorithms

We consider the problem of minimizing the makespan of n jobs in an m-machine flowshop operating without buffers. Since there is no intermediate storage, a job here cannot leave a machine until the machine downstream is free. When that is the case, the job is said to be blocked. This “blocking flowshop” problem is known to be strongly NP-hard for the shop having more than two machines. In this paper, we develop a genetic algorithmic approach to solve large size restricted slowdown flowshop problems of which blocking flowshop problems are a special case. Abadi (Flowshop scheduling problems with no-wait and blocking environments: A mathematical programming approach. Ph.D Thesis, Department of Industrial Engineering, University of Toronto, Canada, 1995) has established a connection between the blocking flowshop problem and a no-wait flowshop in which jobs do not wait between operations. He uses the idea of deliberately slowing down the processing of certain operations. We utilize this concept to evaluate the makespan (fitness) of the solutions generated by genetic algorithms. Computational results indicate that a genetic algorithm with optimized parameters for controlling the evolution of solutions consistently performs significantly better than the heuristic for blocking flowshops developed in a recent Ph.D. thesis by Abadi. The comparison is made for the problems with sizes up to 20 machines and 250 jobs.

Scheduling no-wait robotic cells with two and three machines

A no-wait robotic cell is an automated m-machine flow shop in which one robot is used to move the parts from a machine to the next, as well as between the machines and the input/output devices. Parts are not allowed to wait, either on a machine or on the robot. The problem is to sequence the parts and, concurrently, schedule the robot moves in order to maximize productivity. In the two-machine case, we show that the problem is solvable in time O( nlog n) by reducing it to the classical two-machines no-wait flow shop. For the three-machine case and identical parts, it is shown that it is sufficient to consider robot move cycles in which all the machines are visited once or twice.