A heuristic procedure for makespan minimization in job shops with multiple identical processors

Scheduling has been and continues to be a major issue in production planning. Job shop scheduling is one area where a considerable amount of research has been and continues to be pursued. Usual emphasis is on one machine per work center job shop scheduling. There appears to be very limited literature available on scheduling a job shop problem which requires scheduling of n jobs in m machine centers where each machine center may have k number of identical processors (though the number of identical processors may vary from one machine center to next). We discuss here, the problem of minimize of the makespan for such a job shop arrangement The problem can be represented by the symbol m x n x k.     

Modeling and heuristics for scheduling of distributed job shops

This paper deals with the problem of distributed job shop scheduling in which the classical single-facility job shop is extended to the multi-facility one. The mathematical formulation of the problem is comprehensively discussed. Two different mixed integer linear programming models in form of sequence and position based variables are proposed. Using commercial software of CPLEX, the small sized problems are optimally solved. To solve large sized problems, besides adapting three well-known heuristics, three greedy heuristics are developed. The basic idea behind the developed heuristics is to iteratively insert operations (one at each iteration) into a sequence to build up a complete permutation of operations. The permutation scheme, although having several advantages, suffers from redundancy which is having many different permutations representing the same schedule. The issue is analyzed to recognize the redundant permutation. That improves efficiency of heuristics. Comprehensive experiments are conducted to evaluate the performance of the two models and the six heuristics. The results show sequence based model and greedy heuristics equipped with redundancy exclusion are effective for the problem.     

作业车间调度转换瓶颈算法可行性研究

讨论了转换瓶颈( SB) 算法在解作业车间调度问题时需要解决的子问题。转换瓶颈算法是解决作业车间调度最小makespan( 完工时间) 问题的有效启发式算法。它是基于反复地解决某些单机调度问题这样的子问题。然而所解决的单机调度问题的解可能会导致算法最终得不到可行解, 即使是单机调度最优解也可能得到不可行解。为此, 给出了一个简单的反例证明了产生不可行解的情况, 并对产生不可行解的原因作了详细分析。该研究有利于对转换瓶颈技术进行更好的理解和应用。     

Algorithm based on taboo search and shifting bottleneck for job shop scheduling

In this paper, a computational effective heuristic method for solving the minimum makespan problem of job shop scheduling is presented. It is based on taboo search procedure and on the shifting bottleneck procedure used to jump out of the trap of the taboo search procedure. A key point of the algorithm is that in the taboo search procedure two taboo lists are used to forbid two kinds of reversals of arcs, which is a new and effective way in taboo search methods for job shop scheduling. Computational experiments on a set of benchmark problem instances show that, in several cases, the approach, in reasonable time, yields better solutions than the other heuristic procedures discussed in the literature.     

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck-tabu search (SB-TS) algorithm by replacing the re-optimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature.     

Decomposition methods for large job shops

A rolling horizon heuristic is presented for large job shops, in which the total weighted tardiness must be minimized. The method divides a given instance into a number of subproblems, each having to correspond to a time window of the overall schedule, which are solved using a shifting bottleneck heuristic. A number of rules for defining each time window are derived. The method is tested by using instances up to 10 machines and 100 operations per machine, outperforming a shifting bottleneck heuristic that has been shown to generate close to optimal results.Scope and purposeThere has been a significant amount of research focused on the scheduling of a job shop, either minimizing the makespan or the tardiness. Although the results for small-size problems are satisfactory, there has been no approach as for yet middle- and large-size problems. This paper presents a heuristic that decomposes the problems on a time window basis, solving each subproblem using a shifting bottleneck heuristic. Its results for a due-date-related objective function are promising.     

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.     

Discovering subproblem prioritization rules for shifting bottleneck algorithms

Shifting bottleneck (SB) algorithms have been successful in solving most real-sized scheduling problems. However, it is known that under certain conditions, solution quality degrades because of subproblem interactions. Changing the order in which subproblems are solved greatly affects the solution quality. We demonstrate that for some class of problems it is possible to induce production (IF–THEN) rules that determine the subproblem solution order and lead to good quality solutions, matching the performance of the SB algorithm in most other instances.     

Configuration and the advantages of the shifting bottleneck procedure for optimizing the job shop total weighted tardiness scheduling problem

This paper answers two fundamental questions concerning the usage of the shifting bottleneck (SB) procedure to optimize the criterion total weighted tardiness for the classical job shop scheduling problem. The first question is how to configure the SB procedure, as it is a divide-and-conquer method and consists of diverse subsolutions for each procedure phase. The second question is what the advantages of the SB procedure are, in comparison with other state-of-the-art approaches. To answer the first question, we evaluate the performance (i.e. the scheduling quality) and the efficiency (i.e. the computational time) of various SB variants using computational experiments and present guidelines for configuring the SB procedure. To respond to the second question, extensive computational experiments were conducted on various benchmark instances (up to 100 jobs \(\times \) 20 machines). Results show the superior performance/efficiency trade-off of the SB variants with certain configuration to local search methods. This excellent trade-off between performance and efficiency makes the SB procedure particularly promising for solving practical production scheduling problems.     

An adaptive branch and bound approach for transforming 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. First, we present five properties of the problem under consideration that are employed for constructing a branch and bound algorithm. The approach is named adaptive since the development of the children nodes depends on the particular instance in order to try tightening the lower bounds and hence performing faster. The computational experiments carried out show the approach to be effective for a variety of problem sizes.     

A heuristic algorithm for distributed control in manufacturing systems

Distributed Problem Solving Networks (DPSN) provide a means for interconnecting intelligent problem solver nodes that can solve only a part of a problem depending on their ability in the problem domain. The decomposition of a problem into subproblems, and the selection of nodes to solve them can be regarded as the generation of an AND/OR tree, and the solution of the problem as a search for a solution tree. Introducing measurements for the cost of a solution tree, we present an algorithm to find one having minimal cost under certain conditions. A Flexible Manufacturing System consisting of a network of flexible workcells is used as an example.     

A batch splitting heuristic for dynamic job shop scheduling problem

The job shop scheduling problem has been a major target for many researchers. Unfortunately, though, most of the past studies assumed that a job consists of only a single part. If we assume that a job consists of a batch as in many real manufacturing environment, then we can obtain an improved schedule. However, then, the size of the scheduling problem would become too large to be solved in practical time limit. So, we proposed an algorithm to get an improved schedule by splitting the original batch into smaller batches, and thereby can meet the due date requirement, and adapt to unexpected dynamic events such as machine failure, rush order and expediting.     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

Scheduling for on-time completion in job shops using feasibility function

This article focuses on job shop type manufacturing systems where a high variety of products of different volumes are requested to be produce on a tight due date. The feasibility function (FF) is addressed in this article to schedule jobs in multi-machine random job shop, where the purpose is to minimize unit penalty by achieving a balance between the number of tardy and early jobs, and reducing the difference between the maximum and the minimum lateness of jobs. A job shop simulation model based on multi-agent architecture developed by the authors provides an environment for comparing the FF to commonly used dispatching rules. The results show the benefit of using the FF. Discussions reveal that this concept is more reliable in case of due dates with different tightness level.     

A two-phased approach to setting due-dates in single machine job shops

This paper explores the characteristics of job flow time distributions resulting from the use of different priority rules via computer simulation and statistical analysis. Statistical analysis of results from phase I experimentation modeling traditional due-date setting practices are used to develop job flow time prediction models. In phase II simulation experiments, the regression models developed in phase I are used to establish due-date allowances to jobs based on their processing times. Forms of the prediction equations reveal the differences in resultant job flow distributions, and explain the underlying nature of interactions between due-date setting methods and shop performance characteristics of dispatching rules as reported in previous studies. Application of the prediction equations in phase II experimentation show the viability of improving shop floor performance without resorting to looser due-dates.     

A heuristic algorithm for the distributed and flexible job-shop scheduling problem

The distributed manufacturing takes place in a multi-factory environment including several factories, which may be geographically distributed in different locations, or in a multi-cell environment including several independent manufacturing cells located in the same plant. Each factory/cell is capable of manufacturing a variety of product types. An important issue in dealing with the production in this decentralized manner is the scheduling of manufacturing operations of products (jobs) in the distributed manufacturing system. In this paper, we study the distributed and flexible job-shop scheduling problem (DFJSP) which involves the scheduling of jobs (products) in a distributed manufacturing environment, under the assumption that the shop floor of each factory/cell is configured as a flexible job shop. A fast heuristic algorithm based on a constructive procedure is developed to obtain good quality schedules very quickly. The algorithm is tested on benchmark instances from the literature in order to evaluate its performance. Computational results show that, despite its simplicity, the proposed heuristic is computationally efficient and promising for practical problems.     

Stochastic dynamic job shops and hierarchical production planning

This paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products. The concept of a dynamic job shop is introduced by interpreting the system as a directed graph, and the structure of the system dynamics is characterized for its use in the asymptotic analysis. The optimal control problem for the system is a state-constrained problem, since the number of parts in any buffer between any two machines must remain nonnegative. A limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities, as the rate of change in machine states approaches infinity. The value function of the original problem is shown to converge to that of the limiting problem, and the convergence rate is obtained. Furthermore, near-optimal controls for the original problem are constructed from near-optimal controls of the limiting problem, and an error estimate is obtained on the near optimality of the constructed controls     

Makespan minimization in preemptive two machine job shops

In this note we investigate the NP-complete problem of minimizing the makespan in a preemptive two machine job shop. We present a polynomial time approximation algorithm with worst case ratio 3/2 for this problem, and we also argue that this is the best possible result that can be derived via our line of approach.     

Negotiation-based routing in job shops via collaborative agents

In recent years, the application of agent-based systems in manufacturing has received a lot of attention in several areas, particularly scheduling and shop-floor control. This paper explores two methods of enhancing the negotiation process employed by an agent-based system to support performance improvements in real-time routing of job orders within job-shop environments. The first method takes advantage of an extended negotiation period to provide a more complete picture of the shop's conditions in order to enhance the validity of the decisions made by individual agents. The second approach explores the possibility of process model data to increase the accuracy of time estimates used in the negotiation process. The resulting performance of the two methods is tested using a simulated job shop.     

An incentive-based heuristic job scheduling algorithm for utility grids

Job scheduling in utility grids should take into account the incentives for both grid users and resource providers. However, most of existing studies on job scheduling in utility grids only address the incentive for one party, i.e., either the users or the resource providers. Very few studies on job scheduling in utility grids consider incentives for both parties, in which the cost, one of the most attractive incentives for users, is not addressed. In this paper, we study the job scheduling in utility grid by optimizing the incentives for both parties. We propose a multi-objective optimization approach, i.e., maximizing the successful execution rate of jobs and minimizing the combined cost (incentives for grid users), and minimizing the fairness deviation of profits (incentive for resource providers). The proposed multi-objective optimization approach could offer sufficient incentives for the two parties to stay and play in the utility grid. A heuristic scheduling algorithm called Cost-Greedy Price-Adjusting (CGPA) algorithm is developed to optimize the incentives for both parties. Simulation results show that the CGPA algorithm is effective and could lead to higher successful execution rate, lower combined cost and lower fairness deviation compared with some popular algorithms in most cases.