No-wait Job Shop Scheduling Problem 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.

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.

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.

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.

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.

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.

A tabu search algorithm for no-wait job shop scheduling problem

In this paper, we consider no-wait job shop scheduling problem with makespan objective. In the no-wait problem two consecutive operations in each job must be processed without any interruption. No-wait job shop problem is strongly NP-hard. Mascis and Pacciarelli proposed an algorithm for no-wait job shop problem that produces good quality solution for benchmark problems but it mostly failed in finding a feasible solution. Therefore, we introduce a new neighbourhood structure in our tabu search to resolve this problem.

Studying the effect of different combinations of timetabling with sequencing algorithms to solve the no-wait job shop scheduling problem

This paper considers the no-wait job shop (NWJS) problem with makespan minimisation criteria. It is well known that this problem is strongly NP-hard. Most of the previous studies decompose the problem into a timetabling sub-problem and a sequencing sub-problem. Each study proposes a different sequencing and timetabling algorithm to solve the problem. In this research, this important question is aimed to be answered: is the timetabling or the sequencing algorithm more important to the effectiveness of the developed algorithm? In order to find the answer, three different sequencing algorithms are developed; a tabu search (TS), a hybrid of tabu search with variable neighbourhood search (TSVNS), and a hybrid of tabu search with particle swarm optimisation (TSPSO). Afterwards, the sequencing algorithms are combined with four different timetabling methods. All the approaches are applied to a large number of test problems available in the literature. Statistical analysis reveals that although some of the sequencing and timetabling algorithms are more complicated than the others, they are not necessarily superior to simpler algorithms. In fact, some of the simpler algorithms prove to be more effective than complicated and time-consuming methods.

Two-machine, no-wait job shop problem with separable setup times and single-server constraints

No-wait job shop scheduling problems refer to the set of problems in which a number of jobs are available for processing on a number of machines in a job shop context with the added constraint that there should be no waiting time between consecutive operations of the jobs. In this paper, a two-machine, no-wait job shop problem with separable setup times and a single-server constraint is considered. The considered performance measure is the makespan. This problem is strongly NP-hard. A mathematical model of the problem is developed and a number of propositions are proven for the special cases. Moreover, a genetic algorithm is proposed in this paper to find the optimal (or near-optimal) solutions. In order to evaluate the developed algorithm, a number of small instances are solved to optimality using the developed mathematical model. The proposed algorithm is able to find the optimal solution of all of these cases. For larger instances, the developed algorithm has been compared with the 2-opt algorithm as well as a proposed lower bound. Computational results show the efficiency of the proposed algorithm in generating good quality solutions compared to the developed lower bounds and 2-opt algorithm.

A Cross Entropy-Genetic Algorithm for m-Machines No-Wait Job-ShopScheduling Problem

No-wait job-shop scheduling (NWJSS) problem is one of the classical scheduling problems that exist on many kinds of industry with no-wait constraint, such as metal working, plastic, chemical, and food industries. Several methods have been proposed to solve this problem, both exact (i.e. integer programming) and metaheuristic methods. Cross entropy (CE), as a new metaheuristic, can be an alternative method to solve NWJSS problem. This method has been used in combinatorial optimization, as well as multi-external optimization and rare-event simulation. On these problems, CE implementation results an optimal value with less computational time in average. However, using original CE to solve large scale NWJSS requires high computational time. Considering this shortcoming, this paper proposed a hybrid of cross entropy with genetic algorithm (GA), called CEGA, on m-machines NWJSS. The results are compared with other metaheuritics: Genetic Algorithm-Simulated Annealing (GASA) and hybrid tabu search. The results showed that CEGA providing better or at least equal makespans in comparison with the other two methods.

Optimal Real-Time Traffic Control in Metro Stations

Train movements across railway stations are still operated by human dispatchers. Motivated by an application provided by Azienda Trasporti Milanesi (ATM), the major Italian municipal transport company, we developed a real-time automated traffic control system to operate trains in metro stations. The system optimally controls the trains in a metro station by identifying a suitable routing and by establishing an optimum schedule of the performed operations. For each candidate routing an instance of the blocking, no-wait job-shop scheduling problem with convex costs is solved to optimality by branch and bound. A new, effective lower bound is developed to speed up the enumeration process. Computational testing in a real environment proved that the algorithm is able to solve relevant practical instances within the very tight time limit imposed by the application. The system has been in operation in the Milan metro since July 2007. To our knowledge, this is the first example of successful application of optimization methods to real-time traffic control in metro stations.

A hybrid genetic algorithm for no-wait job shop scheduling problems

A no-wait job shop (NWJS) describes a situation where every job has its own processing sequence with the constraint that no waiting time is allowed between operations within any job. A NWJS problem with the objective of minimizing total completion time is a NP-hard problem and this paper proposes a hybrid genetic algorithm (HGA) to solve this complex problem. A genetic operation is defined by cutting out a section of genes from a chromosome and treated as a subproblem. This subproblem is then transformed into an asymmetric traveling salesman problem (ATSP) and solved with a heuristic algorithm. Subsequently, this section with new sequence is put back to replace the original section of chromosome. The incorporation of this problem-specific genetic operator is responsible for the hybrid adjective. By doing so, the course of the search of the proposed genetic algorithm is set to more profitable regions in the solution space. The experimental results show that this hybrid genetic algorithm can accelerate the convergence and improve solution quality as well.

Minimizing Makespan in No-Wait Job Shops

In this paper, we study polynomial time approximation schemes (PTASes) for the no-wait job shop scheduling problem with the makespan objective function. It is known that the problem is MaxSNP-hard in the case when each job is allowed to have three operations or more. We show that if each job has at most two operations, the problem admits a PTAS if the number of machines is a constant (i.e., not part of the input). If the number of machines is not a constant, we show that the problem is hard to approximate within a factor better than 5/4.