Job shop scheduling with unit processing times under uncertainties: Sequential flexibility and new lower-bound

The job-shop scheduling problem is one of the hardest problems (NP-complete problem) {Garey and Johnson 1979, Computer and Intractability: A Guide to the Theory of NP-completeness (San Francisco: Freeman)}. In lots of cases, the combination of goals and resources exponentially increases the search space, and the generation of consistent and satisfying schedules is more and more difficult. This article shows the coupling of three approaches in order to contribute to the solving of the job-shop scheduling problem: genetic algorithms (GAs); constraint logic programming (CLP); and multi-criteria decision-making (MCDM). The GAs are searching algorithms based on the mechanics of natural selection. They employ a probabilistic search for locating the globally optimal solution. They start with an initial population often randomly generated. The difficulty holds in the creation of this initial population which is considered an important parameter of GAs. CLP is a concept based on operation research (OR) and artificial intelligence (AI). It tends to rid itself of their drawbacks and to regroup their advantages. It aims at providing a set of solutions to a problem expressed in term of constraints. A MCDM approach aims at providing an analysis of a set of possible alternatives according to a set of conflicting criteria in order to help the user. This article explains first how to use the CLP to generate a first population. Second it describes the application of GAs to provide a set of job-shop scheduling minimizing the global makespan. Among the set of job-shop scheduling minimizing the global makespan, it is then possible for the decision-maker to select the most satisfying scheduling according to other criteria, e.g. balance of workload or makespan of each manufacturing order. A large-sized example illustrates clearly the advantages of our hybrid method.

Genetic Programming based hyper-heuristics (GP-HH) for dynamic job shop scheduling (JSS) problems are approaches which aim to address the issue where heuristics are only effective for specific JSS problem domains, and that designing effective heuristics for JSS problems can be difficult. This paper is a preliminary investigation into improving the robustness of heuristics evolved by GP-HH by evolving ensembles of dispatching rules from a single population of GP individuals. The results show that the current approach does not evolve significantly better or more robust rules than a standard GP-HH approach of evolving single constituent rules.

An effective job shop scheduling (JSS) in the manufacturing industry is helpful to meet the production demand and reduce the production cost, and to improve the ability to compete in the ever increasing volatile market demanding multiple products.In so many combinatorial optimization problems, job shop scheduling problems have earned a reputation for being difficult to solve. Job-shop scheduling is essentially an ordering problem. A new encoding scheme for a classic job-shop scheduling problem is presented. The aim is to find an allocation for each job and to define the sequence of jobs on each machine so that the resulting schedule has a minimal completion time.Genetic algorithm that has demonstrated considerable success in providing efficient solutions to many non polynomial-hard optimization problems is used to solve job-shop scheduling problem. The schedules given by genetic algorithms are constructed using a priority rule and under several constraints. After a schedule is obtained a checking operation is applied to ensure that the solution is feasible. The approach is tested on a set of instances. The results validate the effectiveness of the algorithm.

The new challenges of "Agile Manufacturing" and distributed decision making entailed by decentralized organizations led to our interest in the study of computational cooperative problem solving models and coordination techniques for distributed production management. The goal of our research is to address the technical need of distributed production management and develop appropriate computational approaches to support adaptive, cost-effective responsiveness. In particular, we focus on the challenging problem of job shop scheduling, which has been one of the primary foci of production scheduling research. This paper presents a multi-agent problem solving model and an effective coordination technique for job shop scheduling. The model involves a group of agents; each agent is associated with either a job or a resource. A solution to a production scheduling problem is the result of coordinated conflict resolution in the iterative and asynchronous multi-agent decision making process. It is well known in distributed systems research that for tightly interacting, non-decomposable problems, such as job shop scheduling, the need for communicating partial solution results among parts of the system rapidly degrades system performance. On the other hand, limiting communication degrades solution quality. One can limit communication by employing shared memory, but this has the drawback that the shared memory becomes a bottleneck and, in addition, using shared memory limits decentralization. In our approach, we judiciously balance the above concerns. We limit interagent communication through a scheme that employs efficient, small and distributed shared memories, each of which is associated with and shared by a limited number of agents. We also exploit problem characteristics (e.g. disparity among subproblems) to design an effective coordination technique for the job shop scheduling problem. We have evaluated the utility of our approach through extensive experimentation on a variety of job shop constraint satisfaction and optimization problems with different optimization objectives. Our results show that our approach outperforms or gives comparative results with other state-of-the-art scheduling techniques on benchmark problems.

In the just-in-time job-shop scheduling (JIT–JSS) problem every operation has a distinct due-date, and earliness and tardiness penalties. Any deviation from the due-date incurs penalties. The objective of JIT–JSS is to obtain a schedule, i.e., the completion time for performing the operations, with the smallest total (weighted) earliness and tardiness penalties. This paper presents a matheuristic algorithm for the JIT–JSS problem, which operates by decomposing the problem into smaller sub-problems, optimizing the sub-problems and delivering the optimal schedule for the problem. By solving a set of 72 benchmark instances ranging from 10 to 20 jobs and 20 to 200 operations we show that the proposed algorithm outperforms the state-of-the-art methods and the solver CPLEX, and obtains new best solutions for nearly 56% of the instances, including for 79% of the large instances with 20 jobs.

Job-shop scheduling is a difficult problem, both theoretically and practically. This problem is a combinatorial optimization of considerable industrial importance. Although the job-shop scheduling problem has often been investigated, very little of this research is concerned with the uncertainty characterized by the imprecision in problem variables. In this paper, we investigate the job-shop scheduling problem with imprecise processing times. We first use triangular fuzzy numbers to represent imprecise processing times, and then construct a fuzzy job-shop scheduling model. Our work intends to extend the deterministic job-shop scheduling problem into a more generalized problem that would be useful in practical situations.KeywordsFuzzy NumberTriangular Fuzzy NumberMembership GradeFuzzy Processing TimeShifting BottleneckThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

The Job shop scheduling problem with generic time lags is a generalization of the job shop problem. It is defined as a job shop problem with minimal and maximal delays between starting times of operations of different jobs. In this paper, we propose a combination of genetic algorithm and tabu search to solve Job Shop Problem with Generic Time Lags. Benchmark instances are used to investigate the performance of the proposed metaheuristic. The results show that the proposed combination of metaheuristics improves the efficiency.

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, when we attempt to formulate job shop scheduling problems which closely describe and represent the real world problem, various factors involved are often imprecisely or ambiguously known to the analyst. Also, in the real situations, machines are not continuously available due to preventive maintenance activity. Besides, in the production system, there are many users and machines in various priorities. Often, user satisfactions, machine stability and schedule itself are in conflict. By considering the imprecise or fuzzy nature of the data in real world problem, job shop scheduling with uncertain processing time and machine available constraint is introduced. Under the fuzzy circumstance, we attempt to make a feasible solution for flexible job shop scheduling problem (FJSSP) based on a hybrid optimization approach with multi-objective which not only to minimize the makespan, but also maximize the user satisfaction and machine stability. In the experiment, we make the comparisons with some other algorithms, such as genetic algorithm, to demonstrate the hybrid approach is much better on efficient search and stability with three benchmark examples. Sensitivity analysis is conducted to study the impact, in term of total objective, when the proportion of machine stability is varied.

A Petri net with controller is used to model discrete events in flexible job shop scheduling, the objective of scheduling problems is to minimize make-span, the scheduling results is obtained based on genetic and Tabu Search (TS) algorithm. It is proved capable of providing optimized schedule to the job-shop where the machine tool and manpower resources are both constrained. After crossover and mutation operations, an optimal or suboptimal scheduling plan can be found. The result of the test shows that this method is feasible and efficient. Job shop scheduling is the primary content and critical technology of the production management of CIMS, in the past during 30 years, a lot of researchers and results focus on it, but most of them deal with single objective and resource scheduling problems which are fixed processing route and constrained by machine, and production period is its optimal objective. Nevertheless, the production styles are variable and processing route is determined under the special condition. Moreover, job shop scheduling problem is the most difficult combined constraints optimal problem and typical NP hard problem which can't be solved in polynomial time by an effective algorithm. Up to date, there are some traditional algorithms to solve JSP problem (1-2). About paper (3), Petri net is used to construct JSP model and L1 which combines branch and bound algorithm with dynamic program is used to search its optimal solution. And paper (4), the job sequence is assigned by genetic code firstly, and then filtered beam search which based on breadth-first algorithm is adopted to search. In recent years, the Petri net as a discrete event dynamic system modeling and analysis tool(5), has been successfully applied to the flexible manufacturing system modeling, analysis and control. Some researchers put forward to be based on Petri network scheduling method, but only on the production line itself can not reflect the modeling, as in the production line of external control scheduling strategy influence. A hybrid algorithm is proposed to solve dual-resource scheduling problem in flexible production environment, and Petri net model with a controller, which can effectively model control. It combines the advantage of global search ability of GA with the self-adaptive merit of Tabu Search (TS) and improves its convergence. It is proved capable of global and part searching ability and efficient.

In job shop scheduling problems, the previously used nonpreemptive schedules are semiactive, active, and non-delay schedules, and they are initially designed for traditional scheduling performances and do not take energy efficiency into consideration. To fill the gap, this article presents a novel class of nonpreemptive schedules by investigating the special properties of job shop scheduling problems. Then, an energy-efficient generation procedure of the novel nonpreemptive schedules and the standby policy are proposed. An improved genetic algorithm is introduced with three superior features, including the elitist selection, the improved generation alternation model, and the operator decision mechanism. The Friedman test and the Holm multiple comparison test are conducted on experimental results to determine the appropriate parameter for the proposed genetic algorithm. Finally, the computation results and two-sample t-tests show that both energy-efficient generation procedure and standby policy help to reduce energy consumption without worsening production efficiency.

The issue in Lot Streaming is how to split lots into sublots in order to improve the makespan (or some other criterion). We present a model and an iterative procedure for a general job-shop environment. The procedure alternates between solving a lot-sizing problem with a given sequence of sublots on the machines, and a standard job-shop scheduling problem with fixed sublot sizes. We report the computational results on a significant sample of 120 job-shop and flow-shop scheduling problems (including the famous 10–10). In case of no setup, in a few iterations, the makespan approaches a lower bound using very few sublots, suggesting that the procedure yields a global optimum. As a by-product, this result somehow validates the capacitated lot-sizing models in which the detailed capacity constraints, induced by the sequencing of operations, are ignored.

For pt.I. see ibid., p.1006-15. This paper presents the application of parallel dynamic interaction (PDI) to three real problem domains: the flowshop scheduling problem, the job-shop scheduling problem and the vertex cover problem. Specific examples are provided as to how the general PDI framework, introduced in part I of this paper, can be applied to a particular problem. The results of an empirical study of 90 example instances of these problems indicate that PDI consistently out-performs previously published heuristics for the vertex cover problem, and can typically generate solutions within a few percent of optimal for flow-shop and job-shop problems. Out of the 76 examples for which the optimal solution could be determined, PDI was able to produce results averaging within 4% of optimal. In over 30% of the cases, PDI was able to find the optimal solution. In no case did the PDI solution deviate more than 15% from optimal. It is also seen that the time taken by PDI to arrive at these solutions is negligible compared to that taken by conventional search techniques. This provides strong empirical evidence that PDI is capable of generating high quality solutions to exponentially and super-exponentially hard problems in reasonably short periods of time. >

Integrated Lot-sizing and Job Shop Scheduling Benefiting From Reconfigurable Machine Tools

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes an improved immune clonal selection algorithm, called improved clonal selection algorithm for the JSSP. The new algorithm has the advantage of preventing from prematurity and fast convergence speed. Numerous well-studied benchmark examples in job-shop scheduling problems were utilized to evaluate the proposed approach. The computational results show that the proposed algorithm could obtain the high-quality solutions within reasonable computing times, and the results indicate the effectiveness and flexibility of the immune memory clonal selection algorithm.