A hybrid two-phase encoding particle swarm optimization for total weighted completion time minimization in proportionate flexible flow shop scheduling

A proportionate flow shop (PFS) is a special case of the m machine flow shop problem. In a PFS, a fixed sequence of machines is arranged in s stages (s?>?1) with only a single machine at each stage, and the processing time for each job is the same on all machines. Notably, PFS problems have garnered considerable attention recently. A proportionate flexible flow shop (PFFS) scheduling problem combines the properties of PFS problems and parallel-identical-machine scheduling problems. However, few studies have investigated the PFFS problem. This study presents a hybrid two-phase encoding particle swarm optimization (TPEPSO) algorithm to the PFFS problem with a total weighted completion time objective. In the first phase, a sequence position value representation is designed based on the smallest position value rule to convert continuous position values into job sequences in the discrete PFFS problem. During the second phase, an absolute position value representation combined with a tabu search (TS) is applied starting from the current position of particles that can markedly improve swarm diversity and avoid premature convergence. The hybrid TPEPSO algorithm combines the cooperative and competitive characteristics of TPEPSO and TS. Furthermore, a candidate list strategy is designed for the TS to examine the neighborhood and concentrate on promising moves during each iteration. Experimental results demonstrate the robustness of the proposed hybrid TPEPSO algorithm in terms of solution quality. Moreover, the proposed hybrid TPEPSO algorithm is considerably faster than existing approaches for the same benchmark problems in literature.     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

Lot streaming in a two-machine mixed shop

Most classical scheduling models overlook the fact that products are often produced in job lots and assume that job lots are indivisible single entities, although an entire job lot consists of many identical items. However, splitting an entire lot (process batch) into sublots (transfer batches) to be moved to downstream machines allows the overlapping of different operations on the same product while work needs to be completed on the upstream machine. This approach is known as lot streaming in scheduling theory. In this study, the lot streaming problem of multiple jobs in a two-machine mixed shop where there are two different job types as flow shop and open shop is addressed so as to minimize the makespan. The optimal solution method is developed for the mixed shop scheduling problem in which lot streaming can improve the makespan.     

Algorithms for flexible flow shop problems with unrelated parallel machines, setup times, and dual criteria

In textile industries, production facilities are established as multi-stage production flow shop facilities, where a production stage may be made up of parallel machines. This known as a flexible or hybrid flow shop environment. This paper considers the problem of scheduling n independent jobs in such an environment. In addition, we also consider the general case in which parallel machines at each stage may be unrelated. Each job is processed in ordered operations on a machine at each stage. Its release date and due date are given. The preemption of jobs is not permitted. We consider both sequence- and machine-dependent setup times. The problem is to determine a schedule that minimizes a convex combination of makespan and the number of tardy jobs. A 0–1 mixed integer program of the problem is formulated. Since this problem is NP-hard in the strong sense, we develop heuristic algorithms to solve it approximately. Firstly, several basic dispatching rules and well-known constructive heuristics for flow shop makespan scheduling problems are generalized to the problem under consideration. We sketch how, from a job sequence, a complete schedule for the flexible flow shop problem with unrelated parallel machines can be constructed. To improve the solutions, polynomial heuristic improvement methods based on shift moves of jobs are applied. Then, genetic algorithms are suggested. We discuss the components of these algorithms and test their parameters. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages.     

Makespan minimization in a job shop with a BPM using simulated annealing

A scheduling problem commonly observed in the metal working industry has been studied in this research effort. A job shop equipped with one batch processing machine (BPM) and several unit-capacity machines has been considered. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The BPM can process a batch of jobs as long as its capacity is not exceeded. The batch processing time is equal to the longest processing job in the batch. If no batches were to be formed, the scheduling problem under study reduces to the classical job shop problem with makespan objective, which is known to be nondeterministic polynomial time-hard. A network representation of the problem using disjunctive and conjunctive arcs, and a simulated annealing (SA) algorithm are proposed to solve the problem. The solution quality and run time of SA are compared with CPLEX, a commercial solver used to solve the mathematical formulation and with four dispatching rules. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using SA to solve large-scale problems.     

Minimizing makespan in a two-machine no-wait flow shop with batch processing machines

Given a set of jobs and two batch processing machines (BPMs) arranged in a flow shop environment, the objective is to batch the jobs and sequence the batches such that the makespan is minimized. The job sizes, ready times, and processing times on the two BPMs are known. The batch processing machines can process a batch of jobs as long as the total size of all the jobs assigned to a batch does not exceed its capacity. Once the jobs are batched, the processing time of the batch on the first machine is equal to the longest processing job in the batch; processing time of the batch on the second machine is equal to the sum of processing times of all the jobs in the batch. The batches cannot wait between two machines (i.e., no-wait). The problem under study is NP-hard. We propose a mathematical formulation and present a particle swarm optimization (PSO) algorithm. The solution quality and run time of PSO is compared with a commercial solver used to solve the mathematical formulation. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using PSO to solve large-scale problems.     

A general flow shop scheduling problem with consideration of position-based learning effect and multiple availability constraints

In this paper, a more general version of the flow shop scheduling problem with the objective of minimizing the total flow time is investigated. In order to get closer to the actual conditions of the problem, some realistic assumptions including non-permutation scheduling, learning effect, multiple availability constraints, and release times are considered. It is assumed that the real processing time of each job on a machine depends on the position of that job in the sequence, and after processing a specified number of jobs at each machine, an unavailability period is occurring because of maintenance activities. Moreover, it is supposed that each job may not be ready for processing at time zero and may have a release time. According to these assumptions, a new mixed integer linear programming (MILP) model is proposed to formulate the problem. Due to the high complexity of the problem, a heuristic method and a simulated annealing algorithm are presented to find the nearly optimal solutions for medium- and large-sized problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution methods.     

A conflict-based priority dispatching rule and operation-based approaches to job shops

Job shop scheduling (JSS) problems consist of a set of machines and a collection of jobs to be scheduled. Each job consists of several operations with a specified processing order. In this paper, a job shop model problem is scheduled with the help of the Giffler and Thompson algorithm using a priority dispatching rule (PDR). A conflict based PDR is used to schedule the job shop model by using Genetic Algorithms (GAs). An iterative method is applied to the job model to find the optimal conflict-based PDR order and the operation sequence. The same job shop model is also scheduled based on an operation using simulated annealing (SA) and hybrid simulated annealing (HSA). A makespan of the job model is used as an objective. These four methods are considered as different solutions for each problem. A two-way analysis of variance (ANOVA) is applied to test its significance.     

A rolling horizon job shop rescheduling strategy in the dynamic environment

In this paper, the job shop scheduling problem in a dynamic environment is studied. Jobs arrive continuously, machines breakdown, machines are repaired and due dates of jobs may change during processing. Inspired by the rolling horizon optimisation method from predictive control technology, a periodic and event-driven rolling horizon scheduling strategy is presented and adapted to continuous processing in a changing environment. The scheduling algorithm is a hybrid of genetic algorithms and dispatching rules for solving the job shop scheduling problem with sequence-dependent set-up time and due date constraints. Simulation results show that the proposed strategy is more suitable for a dynamic job shop environment than the static scheduling strategy.     

A Genetic Algorithm Approach to the Scheduling of FMSs with Multiple Routes

Usually, most of the typical job shop scheduling approaches deal with the processing sequence of parts in a fixed routing condition. In this paper, we suggest a genetic algorithm (GA) to solve the job-sequencing problem for a production shop that is characterized by flexible routing and flexible machines. This means that all parts, of all part types, can be processed through alternative routings. Also, there can be several machines for each machine type. To solve these general scheduling problems, a genetic algorithm approach is proposed and the concepts of virtual and real operations are introduced. Chromosome coding and genetic operators of GAs are defined during the problem solving. A minimum weighted tardiness objective function is used to define code fitness, which is used for selecting species and producing a new generation of codes. Finally, several experimental results are given.     

An improved mixed integer linear formulation and lower bounds for minimizing makespan on a flow shop with batch processing machines

This paper considers a flow shop scheduling problem with batch processing machines. Each batch processing machine has a limited capacity and can process a group of jobs, each of them having a different known capacity requirement, simultaneously. Job processing time on each machine is known and arbitrary. The processing time of a batch on each machine is the longest processing time of all jobs in the batch. We improve the only existing mixed integer linear formulation (MILF) of the problem through significant reduction in size complexity of the model. Results justify that the improved MILF is clearly more efficient in reducing the required time for obtaining optimal makespan of small-size problems, in comparison with the existing MILF. Motivated by relaxing variety of the problem assumptions, several valid lower bounds on the optimal makespan are also proposed that can furtheraccelerate obtaining optimal solution through proposed MILF. Robustness evaluation of each bound under the different problem settings is reported through computations.     

Bottleneck identification procedures for the job shop scheduling problem with applications to genetic algorithms

Two bottleneck identification algorithms (one for bottleneck machines and the other for bottleneck jobs) are presented for the job shop scheduling problem in which the total weighted tardiness must be minimized. The scheduling policies on bottleneck machines can have significant impact on the final scheduling performance, and therefore, they need to be optimized with more computational effort. Meanwhile, bottleneck jobs that can cause considerable deterioration to the solution quality also need to be considered with higher priority. In order to describe the characteristic information concerning such bottleneck machines and bottleneck jobs, a statistical approach is devised to obtain the bottleneck characteristic values for each machine, and, in addition, a fuzzy inference system is employed to transform human knowledge into the bottleneck characteristic values for each job. These bottleneck characteristic values reflect the features of both the objective function and the current optimization stage. Finally, the effectiveness of the two procedures is verified by specifically designed genetic algorithms.     

可变机器约束的模糊作业车间调度问题研究

在车间实际加工中，工件的加工时间和交货期是一个模糊数，而且工件的某道工序有多台机器可供选择。针对这类作业的车间调度，提出了以极大化最小客户满意度为指标的可变机器约束的模糊作业车间调度模型，并给出了算法设计。应用遗传算法在适应度函数处理中引入模糊数处理方法，解决作业车间模糊调度问题，实现调度优化。仿真实验结果表明了该调度方法的有效性，为可变机器约束的模糊作业车间调度提供了一种实现途径。     

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.     

Bi-objective hybrid flow shop scheduling: a new local search

In this paper, we have considered the bi-objective hybrid flow shop scheduling problem with the objectives of minimizing makespan and minimizing total tardiness. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally, and hence, heuristics are used to obtain good solutions in a reasonable time. On the other hand, local search is a method for solving computationally hard optimization problems. Hence, we introduce a novel bi-objective local search algorithm (BOLS) to solve the problem efficiently. This local search can perform an effective search in three phases. In the initial phase, the assigned job set of a machine is moved to other machines. In the second phase, the order of jobs is changed for a machine. Finally, in phase 3, a process is done to change the assigned job set of a machine and order of jobs for a machine simultaneously. A measure of performance in literature namely free disposal hull approach and a new technique proposed by authors called “triangle method” have been used to evaluate the quality of the obtained solutions. The experimental results of the comparison between the proposed algorithm and several effective algorithms show that the BOLS is attractive for solving the bi-objective scheduling problem.     

A hybrid metaheuristic for concurrent layout and scheduling problem in a job shop environment

In order to obtain efficiency and flexibility, assignment of machines’ layout and determination of jobs’ schedule on each machine are among the most important decisions. These decisions are interrelated and may impact each other but they are often treated separately or as a sequential decision in prior researches. In this paper, we propose a new approach to concurrently make the layout and scheduling decisions in a job shop environment. In other words, we consider an extension of the well-known job shop scheduling problem with transportation delay in which in addition to decisions made in the classic problem, the locations of machines have to be selected among possible sites. The only goal of the problem is the minimization of the makespan. A hybrid metaheuristic approach based on the scatter search algorithm is developed to tackle this problem. Using 43 randomly generated benchmark instances, the performance of the scatter search and its components are evaluated. We also applied our procedure to the classic job shop scheduling problems. Computational results show that our procedure is efficient.     

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 genetic algorithm and particle swarm optimization for no-wait flow shop problem with separable setup times and makespan criterion

This paper considers the problem of no-wait flow shop scheduling, in which a number of jobs are available for processing on a number of machines in a flow shop context with the added constraint that there should be no waiting time between consecutive operations of a job. Each operation has a separable setup time, meaning that the setup time of an operation is independent on the previous operations; and the machine can be prepared for a specific operation and remain idle before the operation actually starts. The considered objective function in this paper is the makespan. The problem is proven to be NP-hard. In this paper, two frameworks based on genetic algorithm and particle swarm optimization are developed to deal with the problem. For the case of no-wait flow shop problem without setup times, the developed algorithms are applied to a large number of benchmark problems from the literature. Computational results confirm that the proposed algorithms outperform other methods by improving many of the best-known solutions for the test problems. For the problems with setup time, the algorithms are compared against the famous 2-Opt algorithm. Such comparison reveals the efficiency of the proposed method in solving the problem when separable setup times are considered.     

基于过程集成的闭环动态工艺规划系统

描述了一个在过程上实现工艺规划与车间规划集成的闭环动态工艺规划系统,建立了实用化CAPP系统的新模型,丰富了动态CAPP的概念。它能根据车间环境的状态,充分利用制造工艺和车间环境的柔性产生优化的工艺方案。系统在车间环境约束下采用专家系统技术进行非线性工艺规划,产生可选工艺路线和工序可选设备。在一个由工艺路线选择、设备动态优化选择和车间优化规划构成的闭环系统中,以高生产效率为目标,根据推广的关键路线分析的结果和一系列启发式知识动态地选择工艺路线和设备,最后获得有较高实践意义的结果。     

具有柔性加工路径的作业车间批量调度优化研究

古典作业车间调度问题已经被研究了几十年并证明为 NP- hard问题。柔性作业车间调度是古典作业车间调度问题的扩展 ,它允许工序可以由一个机床集合中的多台机床完成加工 ,调度的目的是将工序分配给各机床 ,并对各机床上的工序进行排序以使完成所有工序的时间最小化。本文采用遗传算法进行柔性作业车间调度研究 ,针对柔性作业车间问题提出了一种新颖直观的基因编码方法以适用于批量调度 ,并分析了几种批量调度方案 ,最后给出了这些调度的仿真结果 ,证明单件最佳调度不适合扩展成批量最佳调度