No-wait Job Shop Research Articles

A Radial Memetic Algorithm to Resolve the No-Wait Job-Shop Scheduling Problem

A new radial memetic algorithm is proposed to resolve the no-wait job-shop scheduling problem. Basically, each sequencing solution is factorized as a distance-based ranking model, i.e., each solution is decomposed in n − 1 terms, where n is the number of jobs to be sequenced. After that, a cumulative radial distribution of hydrogen is considered to produce new factorizations using the offspring information (genes). Such radial distribution is applied in the local optimization procedure of the memetic algorithm. A benchmarking dataset is used to show the performance of this new experimental technique, as well as other current procedures. Statistical tests were implemented to confirm the performance of the proposed scheme.

A simple migrating birds optimization algorithm with two search modes to solve the no-wait job shop problem

The no-wait job shop problem has important applications in various industries such as steel-making and chemical processes, and its mainstream approaches are metaheuristics with timetabling methods. Inspired by the characteristics of the problem, we consider both left and right shifts for some jobs and present an effective timetabling method called left–right shift (LRS) method. The LRS method schedules jobs as far left as possible and tries all the possible right shifts for some jobs to expand the search space. We propose a simple migrating birds optimization (SMBO) algorithm for searching the space of job sequences. The population of the proposed algorithm is equally divided into two subpopulations with two search modes, one for the original instance and the other for the inverse instance. Local exploitation and global exploration are well balanced in the population evolution scheme of the proposed algorithm. To enhance the run efficiency of the algorithm, we introduce a speedup method for left timetabling and employ the simultaneous multithreading technique for the parallel evolution of subpopulations. Experimental results show that the proposed SMBO algorithm outperforms the state-of-the-art by a significant margin and obtains new upper bounds for a large number of benchmark instances.

Solve no –wait job shop scheduling problem using a local search algorithm

In this paper, no-wait job shop problems with makespan minimization are considered. It is well known that these problems are strongly NP-hard. The problem is decomposed into the sequencing and the timetabling components. The results showed that the new PNS method gives less makespan value with different problems size (15x15, 20x15, 20x20, 30x15, 30x20, 50x15, 50x20 and 100x20) taken from the OR- library compared to previous well known neighborhood search methods. In independent setup times we compared the result with the best solution from OR- library, and have been results indicates the proposed neighborhood search structure near from best solution compare with other methods of NS.

Minimizing total completion time in the no-wait jobshop scheduling problem using a backtracking metaheuristic

This study focused on the no-wait jobshop scheduling problem (NWJSP), which is NP-hard in the strong sense. A new benchmarking algorithm, named backtracking multi-start simulated annealing (BMSA), is presented in this study for minimizing the total completion time in NWJSPs. To effectively and efficiently find (near-) optimal schedules, the simulated annealing algorithm is strengthened by integrating the multi-start and backtracking mechanisms that enable the search processes to escape from the local optimum. The performance of the BMSA algorithm is assessed by comparing its experimental results to those of the best available metaheuristics on three well-known benchmark problem sets. Computational results and statistical analyses confirm that the BMSA algorithm significantly outperforms these benchmark metaheuristics. This study mainly contributes to providing an innovative approach for solving this highly intractable scheduling problem, which is also worth applying to solve a practical NWJSP.

A cooperative coevolutionary algorithm approach to the no-wait job shop scheduling problem

The no-wait job shop is an extension of the well-known job shop scheduling subject to the constraint that the operations of any job, once started, must be processed immediately, one after the other, until the completion of the job. The problem is NP-hard and exact methods can only solve small instances. In the last two decades of advances on this problem, one aspect became central for the success of metaheuristics to tackle it, namely the decomposition of solution into two parts: sequencing and timetabling. Most of these metaheuristics use a permutation to represent the sequencing part, while the timetabling part uses specific rules that differentiate one approach from the other. The main contribution of this work is the proposal of a cooperative coevolutionary algorithm where the sequencing and the timetabling parts interact with each other to evolve quasi-optimal sequencing and timetabling decisions. To this aim, the algorithm co-evolves a population of permutations with a population of binary chains. The permutation decides the sequencing while each bit in the binary chain decides whether or not a job is shifted to the left-most position on its corresponding machine. Therefore, the whole binary chain defines a timetabling rule that is automatically optimized during the evolution process. The algorithm also includes one-step perturbation mechanisms that help improve the solution quality. The proposed algorithm is tested on a set of benchmark instances to compare it with seven state-of-the-art methods. Computational experiments show that the proposed algorithm produces competitive results, furthermore, new best values for four instances are obtained.

No-Wait Job Shop Scheduling Using a Population-Based Iterated Greedy Algorithm

When no-wait constraint holds in job shops, a job has to be processed with no waiting time from the first to the last operation, and the start time of a job is greatly restricted. Using key elements of the iterated greedy algorithm, this paper proposes a population-based iterated greedy (PBIG) algorithm for finding high-quality schedules in no-wait job shops. Firstly, the Nawaz–Enscore–Ham (NEH) heuristic used for flow shop is extended in no-wait job shops, and an initialization scheme based on the NEH heuristic is developed to generate start solutions with a certain quality and diversity. Secondly, the iterated greedy procedure is introduced based on the destruction and construction perturbator and the insert-based local search. Furthermore, a population-based co-evolutionary scheme is presented by imposing the iterated greedy procedure in parallel and hybridizing both the left timetabling and inverse left timetabling methods. Computational results based on well-known benchmark instances show that the proposed algorithm outperforms two existing metaheuristics by a significant margin.

New controllable processing time scheduling with subcontracting strategy for no-wait job shop problem

ABSTRACT This paper addresses the no-wait job shop scheduling problem with due date and subcontracting cost constraints. For the no-wait job shop problem, it does not allow for waiting or interruption between any two consecutive operations of the same job. Considering the deadline and controllable processing time requirements in the real world, due date and subcontracting cost constraints are integrated into the problem as a new extension. The problem has two objectives which are associated with makespan and subcontracting cost. The extended problem focuses on a special case that some jobs cannot satisfy their deadlines no matter how they are scheduled. To satisfy the deadlines, a subcontracting strategy, i.e. buying semi-finished products for processing, is put forward. Two mathematical models are proposed. One is an integrated MILP (MILP-IS), and the other is a rolling time line MILP (MILP-RTL). According to the idea of rolling time line, an artificial bee colony algorithm based on rolling time line (RTL-ABC) is developed. Comprehensive computational analysis is carried out. For small size problems, the optimal solutions are obtained by using these two mathematical models. For large size problems, RTL-ABC is able to find good-quality solutions in a reasonable time and improves the best-found solutions.

Efficient scheduling of a stochastic no-wait job shop with controllable processing times

This work derives a novel effective and efficient algorithm for a stochastic no-wait job-shop scheduling problem with controllable processing times. Some of the processing times are stochastic and the proposed solution effectively minimizes the makespan and increases the robustness of the makespan against deviating processing times. Therefore, a no-wait job shop with controllable deterministic processing times is solved by a decomposition into timetabling and sequencing. During timetabling, extra safety margins are added to the scheduled processing times without delaying jobs. In the sequence optimization subproblem, an extra penalty term is added to the cost function which punishes uncertain tasks at positions that have an impact on the makespan. Simulation results based on real plant data and tailor-made benchmark problems show that these measures can reduce the standard deviation of the makespan dramatically. This significantly improves the prediction accuracy of the scheduling method.

A Study Review of Completion Multi Job on Job Shop Scheduling Technique To Minimize Make Span

In this paper, the development of flexibility job shop scheduling problem was many discussed before globally. The concept job shop scheduling had discussion like minimize total make span, throughput approaching, lot streaming, no-wait job shop, and many more. Also, into job shop scheduling always consider deadline or due date for job load into machine available with target at the end how to optimize machine capacity and minimum make span.

Solving no-wait job-shop scheduling problems using a multi-start simulated annealing with bi-directional shift timetabling algorithm

This paper presents a multi-start simulated annealing with bi-directional shift timetabling (MSA-BST) algorithm for solving the no-wait jobshop scheduling problem (NWJSP). To enhance the quality of the solution, a bi-directional shift timetabling procedure that allows delay timetabling and consequently enlarges the search space is embedded into the multi-start simulated annealing algorithm. The performance of the proposed MSA-BST algorithm is evaluated with respect to the makespan by comparing its computational results to those of the best-to-date meta-heuristic algorithm, the hybrid artificial bee colony (HABC) algorithm, in the literature. Experimental results that were obtained by applying the proposed algorithm to a set of benchmark problems in the literature indicate that it significantly outperforms HABC. The main contribution of this study is to provide a novel and effective alternative method for solving the complex NWJSP.

A population-based iterated greedy algorithm for no-wait job shop scheduling with total flow time criterion

The no-wait job shop where no waiting time is allowed between two successive operations of a job has a strong industrial background, especially in steel-making industry and concrete manufacturing. This study formulates the no-wait job shop problem with a total flow time criterion based on time difference and decomposes the problem into timetabling and sequencing subproblems. Several timetabling methods are designed for the total flow time criterion to generate a sequence timetable. By adopting favourable features of the iterated greedy algorithm, the population-based iterated greedy (PBIG) algorithm for the sequencing subproblem is proposed. The individuals in the population evolve by means of a destruction and construction perturbator and an insertion-based local search. In each iteration, a tournament selection is designed to replace a relatively worse solution. In order to generate starting solutions with a certain quality and diversity, the Nawaz–Enscore–Ham-based heuristics for flow shop scheduling are extended in no-wait job shops. In computational experiments based on well-known benchmark instances, timetabling methods are investigated, and it is shown that the left timetabling is superior to other timetabling methods for the total flow time minimisation. Computational results also show that the proposed algorithm significantly outperforms several state-of-the-art metaheuristics, and it could be applicable to practical production environment.

Solving the no-wait job shop scheduling problem with due date constraints: A problem transformation approach

This paper addresses the job shop scheduling problem with the additional condition that no waiting time is allowed between the operations of the jobs. Moreover, jobs must be fully processed by their respective due dates. The goal is to minimize the makespan. The problem is strongly NP-Hard. This paper transforms the mentioned problem to another scheduling problem and proposes mathematical models for both. The mathematical models proposed for the transformed problem demonstrate a better performance compared to the models developed for the original problem. A genetic algorithm is developed to deal with larger instances of both the original and the transformed problems. The evidence gathered from the computational results confirm that the proposed GA has better performance when applied to the transformed problem.

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.

A column generation-based approach for proportionate flexible two-stage no-wait job shop scheduling

Job shop scheduling, as one of the classical scheduling problems, has been widely studied in literatures, and proved to be mostly NP-hard. Although it is extremely difficult to solve job shop scheduling with no-wait constraint to optimality, the two-machine no-wait job shop scheduling to minimise makespan could be solvable in polynomial time when each job has exactly two equal length operations (proportionate job shop). In the present paper, an extension is attempted by considering a proportionate flexible two-stage no-wait job shop scheduling problem with minimum makespan, and a set-covering formulation is put forward which contains a master problem and a pricing problem. To solve this problem, a column generation (CG)-based approach is implemented. In comparison, a mixed integer programming model is constructed and optimised by Cplex. A series of randomly generated numerical instances are calculated. And the testing result shows that the mixed integer model handled by Cplex can only solve small scale cases, while the proposed CG-based method can conquer larger size problems in acceptable time.

A new exact algorithm for no-wait job shop problem to minimize makespan

In this paper, the no-wait job shop scheduling problem with a makespan objective is considered. A new exact algorithm, which is based on the dynamic programming (DP), is proposed. We introduce a dominance relation between two timetables. Several theorems are provided showing the application of the dominance. Despite the theoretical interest, experimental results prove that the proposed algorithm is able to optimally solve moderate benchmark instances within a reasonable time limit. Moreover, we have shown that the use of the dominance effectively reduces the state space of the algorithm. As an extension of the DP algorithm, we also present its heuristic version. It is shown that good quality upper bounds for large-size benchmark instances can be obtained. A comparison among several algorithms presented in the literature shows that the DP algorithm is quite competitive in terms of the computational time and the quality of obtained solutions.

New index priority rules for no-wait flow shops

We derive an index priority rule for an m-machine no-wait flow shop with the minimum makespan objective and specially-structured job processing times. Our rule generalizes the previously known rules for two special cases of the problem. We also derive an index priority rule for a two-machine no-wait flow shop with the minimum weighted total job completion time objective when all jobs have the same processing time on the first machine. We then show that additional index priority rules can be derived for the latter problem with other scheduling objectives. Finally, we discuss extensions to flow shops with blocking and no-wait job shops and open shops.

The no-wait job shop with regular objective: a method based on optimal job insertion

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.

The proportionate two-machine no-wait job shop scheduling problem

We consider the two-machine no-wait job shop minimum makespan scheduling problem. We show that when each job has exactly two equal length operations (also called a proportionate job shop), the problem is solvable in O(nlog n) time. We also show that the proportionate problem becomes strongly NP-hard when some jobs are allowed to visit only one machine. Finally, we show that the proportionate problem with missing operations becomes solvable in O(nlog n) time when all missing operations are on the same machine.

A two-stage no-wait job shop scheduling problem by using a neuro-evolutionary variable neighborhood search

A two-stage order scheduling problem with an additional no-wait condition is studied in this article. All orders must be processed from start to completion without any waiting between operations and any interruption within operations. Examples of such a problem occur in steel pro- duction and pharmaceutical, chemical, and construction in- dustries. A new optimization method which is based on a combination of an enhanced variable neighborhood search (VNS) and an artificial neural network (ANN) is devised in this paper. The aim is to simultaneously employ the key characteristicsoftwoapproachestoachieve superiorsolutions in solving the addressed optimization problem. In proposed algorithm, the VNS performs a global search whereas the ANNplaystheroleofintensiveinitialsolution.Theindividual obtained by feed forward back-propagation ANN is improved within enhanced VNS iterations. The two techniques comple- ment each other when ANN feeds its best solution to the VNS algorithm.Furthermore,toestablishthebestsequenceoforder pairs,ateamprocessalgorithmisalsoembeddedintotheVNS to enhance the search diversification as well as its intensifica- tion. The performance of proposed neuro-evolutionary algo- rithm is investigated via computational experiments, and the results prove the appropriate performance of suggested VNS- ANN algorithm.

Branch-and-bound and PSO algorithms for no-wait job shop scheduling

This paper deals with the no-wait job shop scheduling problem resolution. The problem is to find a schedule to minimize the makespan ($$C_{max}$$Cmax), that is, the total completeness time of all jobs. The no-wait constraint occurs when two consecutive operations in a job must be processed without any waiting time either on or between machines. For this, we have proposed two different resolution methods, the first is an exact method based on the branch-and-bound algorithm, in which we have defined a new technique of branching. The second is a particular swarm optimization (PSO) algorithm, extended from the discrete version of PSO. In the proposed algorithm, we have defined the particle and the velocity structures, and an efficient approach is developed to move a particle to the new position. Moreover, we have adapted the timetabling procedure to find a good solution while respecting the no-wait constraint. Using the PSO method, we have reached good results compared to those in the literature.