Classical Job Shop Research Articles

Scheduling manufacturing systems with blocking: a Petri net approach

This paper introduces a Petri net-based approach for scheduling manufacturing systems with blocking. The modelling of the job routings and the resource and blocking constraints is carried out with the Petri net formalism due to their capability of representing dynamic, concurrent discrete-event dynamic systems. In addition Petri nets can detect deadlocks typically found in systems with blocking constraints. The scheduling task is performed with an algorithm that combines the classical A* search with an aggressive node-pruning strategy. Tests were conducted on a variety of manufacturing systems that included classical job shop, flexible job shop and flexible manufacturing scheduling problems. The optimisation criterion was makespan. The experiments show that the algorithm performed well in all types of problems both in terms of solution quality and computing times.

A new neighborhood and tabu search for the Blocking Job Shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature.

A modified shifting bottleneck heuristic for the reentrant job shop scheduling problem with makespan minimization

This paper proposes a modified shifting bottleneck heuristic (MSBH) for the reentrant job shop scheduling problem (RJSSP) with makespan minimization objective. Recently, the reentrant job shop has come into prominence as a new type of manufacturing shop. The principle characteristic of a reentrant job shop is that a job may visit certain machines more than once during the process flow, whereas in the classic job shop, each job visits a machine only once. The shifting bottleneck heuristic (SBH) is one of the most successful heuristic approaches for the classical job shop scheduling problem, which decomposes the problem into a number of single-machine subproblems. This paper adapts the SBH for the RJSSP and proposes a new sequencing heuristic for the single-machine maximum lateness subproblem considering the reentrant jobs in order to handle large-size RJSSPs. It also uses a subproblem criticality measure that further shortens the implementation time. The proposed MSBH is tested by using instances up to 20 machines and 100 jobs, and it is illustrated that good quality solutions can be obtained in reasonable computational times. A real-life application of the MSBH is also given as a case study to evaluate its performance.

An evolutionary algorithm for assembly job shop with part sharing

Assembly job shop problem (AJSP) is an extension of classical job shop problem (JSP). AJSP first starts with a JSP and appends an assembly stage after job completion. Lot Streaming (LS) technique is defined as the process of splitting lots into sub-lots such that successive operation can be overlapped. In this paper, the previous study of LS to AJSP is extended by allowing part sharing among distinct products. In addition to the use of simple dispatching rules (SDRs), an evolutionary approach with genetic algorithm (GA) is proposed to solve the research problem. A number of test problems were conducted to examine the performance of the proposed algorithm. Computational results suggested that the proposed algorithm can outperform the previous one, and can work well with respect to the objective function. Also, the inherent conflicting relationship between the primary objective and the system measurements can be addressed.

The Application of Lot Streaming to Assembly Job Shop under Resource Constraints

Assembly job shop problem (AJSP) is an extension of classical job shop problem (JSP). AJSP first starts with a JSP and appends an assembly stage after job completion. Lot Streaming (LS) technique is defined as the process of splitting lots into sub-lots such that successive operation can be overlapped. In this paper, the previous study of LS to AJSP will be extended by introducing resource constraints. To reduce the computational effort, we propose a new Genetic Algorithm (GA) approach which is the modification of the algorithm in our previous paper. A number of test problems are conducted to examine the performance of the new GA approach. Moreover, the single GA approach will be compared with a single Particle Swarm Optimization (PSO) approach. Computational results suggest that the new algorithm can outperform the previous one and the PSO approach with respect to the objective function.

A genetic-search-guided greedy algorithm for multi-resource shop scheduling with resource flexibility

The Multi-Resource Job-Shop Problem with resource Flexibility (MJSPF) provides a framework for realistic modeling of a wide range of problems encountered in manufacturing systems. The problem is a generalization of the classical job shop problem. Each operation may require a combination of more than one resource and there may be several feasible resource combinations for each operation. The scheduling problem consists in both assigning resources to operations and sequencing operations on the selected resources in order to minimize the makespan. In this paper, a polynomial algorithm for solving a special case with two jobs is proposed, and the concept of a combined job is introduced. Building on these results, a greedy heuristic that considers jobs sequentially according to a given job sequence is proposed for scheduling any number of jobs. The greedy heuristic is guided by a genetic algorithm in order to identify effective job sequences. Computational results on benchmark instances for special cases of the MJSPF show that the general method is competitive with respect to the best known heuristic approaches dedicated to these special cases.

New local diversification techniques for flexible job shop scheduling problem with a multi-agent approach

The Flexible Job Shop problem is among the hardest scheduling problems. It is a generalization of the classical Job Shop problem in that each operation can be processed by a set of resources and has a processing time depending on the resource used. The objective is to assign and to sequence the operations on the resources so that they are processed in the smallest time. In our previous work, we have proposed two Multi-Agent approaches based on the Tabu Search (TS) meta-heuristic. Depending on the location of the optimisation core in the system, we have distinguished between the global optimisation approach where the TS has a global view on the system and the local optimisation approach (FJS MATSLO) where the optimisation is distributed among a collection of agents, each of them has its own local view. In this paper, firstly, we propose new diversification techniques for the second approach in order to get better results and secondly, we propose a new promising approach combining the two latter ones. Experimental results are also presented in this paper in order to evaluate these new techniques.

Simulation-based performance comparison between dynamic cells, classical cells and job shops: a case study

This paper presents the results of a simulation-based performance comparison between dynamic cellular (DC) manufacturing systems and two other well-known systems, namely classical cells (CC) and job shop systems (JS). The performance comparison is made at different levels of turbulence. The experiment contains 13 independent variables, most of them related to demand turbulence, and 17 dependant variables related to performance measure. A stochastic simulation model developed on Microsoft Visual FoxPro 5.0 was used in combination with LINDO (a linear/integer programming software) to obtain the initial results. In view of the large number of variables and the time required to run each experiment, a Taguchi plan was used to optimize the model. The results obtained from the analysis of variance indicate that dynamic cellular manufacturing systems are generally more efficient than classical cellular systems or job shop systems, especially with respect to the average and maximum throughput time, mean and maximum work-in-process, mean and maximum tardiness, and the total marginal cost for a given horizon.

The Application of Lot Streaming to Assembly Job Shop under Resource Constraints

Assembly job shop problem (AJSP) is an extension of classical job shop problem (JSP). AJSP first starts with a JSP and appends an assembly stage after job completion. Lot Streaming (LS) technique is defined as the process of splitting lots into sub-lots such that successive operation can be overlapped. In this paper, the previous study of LS to AJSP will be extended by introducing resource constraints. To reduce the computational effort, we propose a new Genetic Algorithm (GA) approach which is the modification of the algorithm in our previous paper. A number of test problems are conducted to examine the performance of the new GA approach. Moreover, the single GA approach will be compared with a single Particle Swarm Optimization (PSO) approach. Computational results suggest that the new algorithm can outperform the previous one and the PSO approach with respect to the objective function.

A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems

Flexible job shop scheduling problem (fJSP) is an extension of the classical job shop scheduling problem, which provides a closer approximation to real scheduling problems. This paper addresses the fJSP problem with three objectives: min makespan, min maximal machine workload and min total workload. We develop a new genetic algorithm hybridized with an innovative local search procedure (bottleneck shifting) for the problem. The genetic algorithm uses two representation methods to depict solution candidates of the fJSP problem. Advanced crossover and mutation operators are proposed to adapt to the special chromosome structures and the characteristics of the problem. The bottleneck shifting works over two kinds of effective neighborhood, which use interchange of operation sequences and assignment of new machines for operations on the critical path. In order to strengthen search ability, the neighborhood structure can be adjusted dynamically in the local search procedure. The performance of the proposed method is tested by numerical experiments on a large number of representative problems.

Lot streaming for product assembly in job shop environment

Assembly job shop scheduling problem (AJSP) is an extension of classical job shop scheduling problem (JSP). AJSP starts with JSP and appends an assembly stage to the completed jobs. Lot streaming (LS) technique is a process of splitting jobs into smaller sub-jobs such that successive operations can be overlapped. This paper combines, for the first time, LS and AJSP, extending LS applicability to both machining and assembly. To solve this complex problem, an efficient algorithm is proposed using genetic algorithms and simple dispatching rules. Experimental results suggest that equal size LS outperforms varied size LS with respect to the objective function.

Feasible insertions in job shop scheduling, short cycles and stable sets

Insertion problems arise in scheduling when additional activities have to be inserted into a given schedule. This paper investigates insertion problems in a general disjunctive scheduling framework capturing a variety of job shop scheduling problems and insertion types. First, a class of scheduling problems is introduced, characterized by disjunctive graphs with the so-called short cycle property, and it is shown that in such problems, the feasible selections correspond to the stable sets of maximum cardinality in an associated conflict graph. Two types of insertion problems are then identified where the underlying disjunctive graph is through- or bi-connected. For these cases, it is shown that the short cycle property holds and the conflict graph is bipartite, allowing to derive a polyhedral characterization of all feasible insertions. An efficient method for deciding whether there exists a feasible insertion, and a lower and upper bound procedure for the minimum makespan insertion problem are developed. For bi-connected graphs, this procedure solves the insertion problem to optimality. The obtained results are applied to three extensions of the classical Job Shop, the Multi-Processor Task, Blocking and No-Wait Job Shop, and two types of insertions, job and block insertion.

Modular Simulated Annealing in Classical Job Shop Scheduling

Modular Simulated Annealing in Classical Job Shop Scheduling

Coalitions in coordinated multi-agent production scheduling: A computational study

This paper studies distributed production scheduling where agents control dispersed information and decentralized decision authority. Using the classical job shop scheduling model, the effects of coalition formation and local communication in an iterative auction are studied. The case is investigated where job agents are allowed to form coalitions, where coalition members share private information and resolve resource conflicts among themselves, while intercoalition communication is limited to bidding. The computational study shows that when the size, type, and timing of the coalitions are properly determined, it is possible to produce a high-quality schedule with a reasonable number of iterations. The results show further improvement in convergence and in solution quality when coalition size and update frequency increase. However, these improvements show diminishing return; thus, it is concluded that a high-quality schedule can be achieved with manageable coalition sizes and a moderate level of information sharing.

A Study on the Aviation Manufacture Cell Scheduling Based on Adaptive Ant Colony Algorithm

Aviation manufacture cell scheduling is generally multi-constraint and multi-objective flexible job-shop scheduling, and is more complicated than classical job-shop because of flexible processing route, multi-restriction, multi-objective, dynamic disturb and complex model. The model of aviation manufacture cell scheduling is set up, and accordingly adaptive ant colony algorithm is brought forward. The adaptive mechanism and the genetic principle are introduced into the algorithm to accelerate convergence and avoid stagnation. Finally, the aviation manufacture cell scheduling of Xi’an Aero-Engine (Group) Ltd. is well solved by the proposed methods.

Ant colony optimization combined with taboo search for the job shop scheduling problem

In this paper, we present a hybrid algorithm combining ant colony optimization algorithm with the taboo search algorithm for the classical job shop scheduling problem. Instead of using the conventional construction approach to construct feasible schedules, the proposed ant colony optimization algorithm employs a novel decomposition method inspired by the shifting bottleneck procedure, and a mechanism of occasional reoptimizations of partial schedules. Besides, a taboo search algorithm is embedded to improve the solution quality. We run the proposed algorithm on 101 benchmark instances and obtain competitive results and a new best upper bound for one open benchmark instance is found.

Minimizing Total Weighted Tardiness in a Generalized Job Shop

We consider a generalization of the classical job shop scheduling problem with release times, positive end---start time lags, and a general precedence graph. As objective we consider the total weighted tardiness. We use a tabu search algorithm to search for the order in which the operations are processed on each machine. Given a sequence of operations on each machine, we determine optimal starting times by solving a maximum cost flow problem. This solution is used to determine the neighborhood for our tabu search algorithm. All sequences in our neighborhood are obtained by swapping certain pairs of adjacent operations. We show that only swaps that possess a certain property can improve the current solution; if no such swap is available in the neighborhood, then the current solution is globally optimal. In the computational results we compare our method with other procedures proposed in literature. Our tabu search algorithm seems to be effective both with respect to time and solution quality.

APPROXIMATION ALGORITHMS FOR FLEXIBLE JOB SHOP PROBLEMS

The Flexible Job Shop problem is a generalization of the classical job shop scheduling problem in which for every operation there is a group of machines that can process it. The problem is to assign operations to machines and to order the operations on the machines so that the operations can be processed in the smallest amount of time. This models a wide variety of problems encountered in real manufacturing systems. We present a linear time approximation scheme for the non-preemptive version of the problem when the number m of machines and the maximum number μ of operations per job are fixed. We also study the preemptive version of the problem when m and μ are fixed, and present a linear time approximation scheme for the problem without migration and a (2+ε)-approximation algorithm for the problem with migration.

Efficient heuristic approaches to transform job shops into flow shops

In this paper, we address the problem of transforming a job shop layout into a flow shop with the objective of minimizing the length of the resulting flow line. Since this problem is NP-hard, we focus our attention on developing high quality approximate solutions. We start by reviewing existing heuristics for the problem as well as some heuristics developed for the Shortest Common Supersequence problem, a well-known stringology problem similar to the one under consideration. We then present a new decomposition approach for the problem that allows the application of local search techniques. We have embedded this approach into a tabu search procedure that is shown to be effective in subsequent computational experiments. Finally, we provide best-so-far solutions for classical job shop problem instances, so they can be used as benchmark instances for further research.

An approach using petri nets and improved heuristic search for manufacturing system scheduling

Petri nets have been extensively used to model the dynamics of various types of manufacturing systems due to their power to capture the complex characteristics of many of such systems. However, the “state explosion” has prevented their use for solving real scheduling problems. To date, Petri net based algorithms have only been tested with relatively small problems with few machines and few jobs. This paper proposes an algorithm that combines the A* search with both an aggressive node-pruning strategy and improved evaluation functions to generate near-optimal schedules. Extensive computational tests were conducted on a wide variety of scenarios ranging from classical job shop to complex FMS scheduling problems. The obtained results show very promising results in terms of solution quality and computing times.