Workflow balancing strategies in parallel machine scheduling

Workflow balancing on a shop floor helps to remove bottlenecks present in the manufacturing system. Workflow refers to the total time during which the work centres are busy. Idle time is not taken into account when calculating workflow. Earlier researchers have not specified the method for jobs to be executed in parallel in order to balance the workflow to each machine. In many manufacturing environments, multiple processing stations are used in parallel to obtain adequate capacity. In parallel machine scheduling there are m machines to which n jobs are to be assigned based on different priority strategies. The procedure is based on the idea of workload balancing and on balancing the workload among machines. In this paper, workflow and workload are assumed to have the same meaning. A machine with the lowest workflow is selected for assignment of a new job from the list of unfinished jobs. Different priority strategies are followed for the selection of jobs. Three different strategies are considered, namely random (RANDOM), shortest processing time (SPT) and longest processing time (LPT) for the selection of jobs for workflow balancing. The relative percentage of imbalance (RPI) is adopted among the parallel machines to evaluate the performance of these strategies in a standard manufacturing environment. The LPT rule shows better performance for the combination of larger job sizes and higher number of work centres or machines. A computer program was coded for validation in a standard manufacturing environment on an IBM/PC compatible system in the C++ language.     

Machine cell formation for cellular manufacturing systems using an ant colony system approach

The aim of a cellular manufacturing system is to group parts that have similar processing needs into part families and machines that meet these needs into machine cells. This paper addresses the problem of grouping machines with the objective of minimizing the total cell load variation and the total intercellular moves. The parameters considered include demands for number of parts, routing sequences, processing time, machine capacities, and machine workload status. For grouping the machines, an ant colony system (ACS) approach is proposed. The computational procedure of the approach is explained with a numerical illustration. Large problems with up to 40 machines and 100 part types are tested and analyzed. The results of ACS are compared with the results obtained from a genetic algorithm (GA), and it is observed that its performance is better than that of GA.     

Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms

The concept of parallel machines has been widely used in manufacturing. This article proposes a genetic algorithm (GA) approach to minimize total tardiness of a set of tasks for identical parallel machines and worker assignment to machines. A spreadsheet-based GA approach is presented to solve the problem. A domain-independent general purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of minimizing total tardiness for the worker assignment scheduling problem for identical parallel machine models. Two 100 I/P/n/m/W problems taken from Hu (Int J Adv Manuf Technol 23:383–388, 2004, Int J Adv Manuf Technol 29:165–169, 2006) for a similar study are simulated. The performance of GA is superior to SES-A/LMC approach used by Hu and very close to the Exhaustive search procedure. It is shown that the spreadsheet GA implementation makes it very easy to adapt the problem for any set of objective measures without changing the actual model. Empirical analysis has been carried out to study the effect of GA parameters, namely, crossover rate, mutation rate, and the population size.     

以JIT为目标的多阶段非等同并行机调度问题研究

针对多阶段非等同并行机模式下的准时化(Just-in-TimeJ,IT)调度问题,采用由遗传算法和禁忌搜索算法混合的禁忌遗传递阶算法进行求解。禁忌遗传递阶算法用禁忌搜索算法对工件最佳加工次序进行搜索,而相应评价值由遗传算法计算得出。遗传算法采用基于阶段机器号的二维矩阵编码,可有效地避免不可行解的产生,同时采用自适应改进提高遗传算法跳出局部最优的能力。实际算例说明禁忌遗传递阶算法计算结果稳定可靠,适合于解决多阶段非等同并行机的JIT调度问题。     

A genetic algorithm for solving a multi-floor layout design model of a cellular manufacturing system with alternative process routings and flexible configuration

This paper presents a novel integer linear programming model for designing multi-floor layout of cellular manufacturing systems (CMS). Three major and interrelated decisions are involved in the design of a CMS; namely cell formation (CF), group layout (GL), and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions to achieve an optimal design solution in a multi-floor factory. Other compromising aspects are: multi-floor layout to form cells in different floors is considered, multi-rows layout of equal area facilities in each cell is allowed, cells in flexible shapes are configured, and material handling cost based on the distance between the locations assigned to machines are calculated. Such an integrated CMS model with an extensive coverage of important manufacturing features has not been proposed before and this model incorporates several design features including alternative process routings, operation sequence, processing time, production volume of parts, duplicate machines, machine capacity, new machine purchasing, lot splitting, material flow between machines, intra-cell layout, inter-cell layout, multi-floor layout and flexible configuration. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, new machines purchasing and machine processing. Two numerical examples are solved by the Lingo software to verify the performance of the proposed model and illustrate the model features. Sensitive analysis is also implemented on some model parameters. An improved genetic algorithm (GA) is proposed to derive near-optimal solutions for the integrated model because of its NP hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison to a classic simulated annealing algorithm and the Lingo software. The obtained results show the efficiency of proposed GA in terms of objective function value and computational time.     

Controllable processing time policies for job shop manufacturing system

The research presented concerns the policy to manage a job shop in which the machines have controllable processing times. A controllable processing time means that it can be reduced processing time by using additional resources. The model proposed is based on a multi-agent architecture that supports the manufacturing system. The policy proposed concerns the evaluation of the workload of the resources. It is necessary to define the following issues for the controllable time process of a resource: the condition of start and the duration of the process time reduction. Two approaches are proposed to assign the resources to the machines. The first approach concerns the reduction of the processing time one machine at time, while the second approach distributes the additional resources proportionally among the machines. A simulation environment is developed to test the proposed approach in several dynamic conditions. The simulation results show that the control of the processing times proposed allows to improve significantly the performance.     

Workload balance and part-transfer minimization in flexible manufacturing systems

Problems related to the flow management of a flexible manufacturing system (FMS) are here formulated in terms of combinatorial optimization. We consider a system consisting of several multitool automated machines, each one equipped with a possibly different tool set and linked to each other by a transportation system for part moving. The system operates with a given production mix.The focused flow-management problem is that of finding the part routings allowing for an optimal machine workload balancing. The problem is formulated in terms of a particular capacity assignment problem.With the proposed approach, a balanced solution can be achieved by routing parts on a limited number of different paths. Such a balancing routing can be found in polynomial time. We also give polynomial-time and-space algorithms for choosing, among all workload-balancing routings, the ones that minimize the global amount of part transfer among all machines.     

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.     

A new hybrid parallel algorithm for consistent-sized batch splitting job shop scheduling on alternative machines with forbidden intervals

Considering alternative machines for operations, forbidden intervals during which machines cannot be available and a job’s batch size greater than one in the real manufacturing environment, this paper studies the batch splitting scheduling problem on alternative machines with forbidden intervals, based on the objective to minimize the makespan. A scheduling model is established, taking before-arrival set-up, processing, and transfer time into account. And a new hybrid parallel algorithm, based on differential evolution and genetic algorithm, is brought forward to solve both the batch splitting problem and the batch scheduling problem by assuming a common number of sub-batches in advance. A solution consists of the actual optimum number of sub-batches for each job, the optimum batch size for each sub-batch, and the optimum sequence of operations for these sub-batches. Experiments on the performance of the proposed algorithm under different common numbers of sub-batches are carried out. The results of simulations indicate that the algorithm is feasible and efficient.     

Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times

This paper addresses job scheduling problems with parallel machines. To satisfy customers better in a manufacturing company, meeting due dates has been an important performance metric. Besides the numerous other factors affecting due date satisfaction, the splitting of a job through parallel machines can contribute to the reduction of production lead time, resulting in less job tardiness against their due dates. Thus, this paper presents heuristic algorithms for minimizing total tardiness of jobs to meet their due dates in a manufacturing shop with identically functioning machines. The algorithms take into account job splitting and sequence-dependent major/minor setup times. The performance of the proposed heuristics is compared with that of past three algorithms in the literature.     

Evaluation of routing flexibility of a flexible manufacturing system using simulation modelling and analysis

Routing flexibility is a major contributor of the flexibility of a flexible manufacturing system (FMS). The present paper focuses on the evaluation of the routing flexibility of an FMS with the dynamic arrival of part types for processing in the system. A typical FMS configuration is chosen for detailed study and analysis. The system is set at five different levels of routing flexibility. Operations of part types can be processed on alternative machines depending upon the level of routing flexibility present in the system. Two cases have been considered with respect to the processing times of operations on alternative machines. A discrete-event simulation model has been developed to describe the operation of the chosen FMS. The performance of the system under various levels of routing flexibility is analyzed using measures such as mean flow time, mean tardiness, percentage of tardy parts, mean utilisation of machines, mean utilisation of automatic-guided vehicles, and mean queue length at machines. The routing flexibility for producing individual part types has been evaluated in terms of measures such as routing efficiency, routing versatility, routing variety and routing flexibility. The routing flexibility of the system has been evaluated using these measures. The flexibility levels are ranked based on the routing flexibility measure for the system. The ranking thus obtained has been validated with that derived using fuzzy logic approach.     

Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time

This paper addresses a new mathematical model for cellular manufacturing problem integrated with group scheduling in an uncertain space. This model optimizes cell formation and scheduling decisions, concurrently. It is assumed that processing time of parts on machines is stochastic and described by discrete scenarios enhances application of real assumptions in analytical process. This model aims to minimize total expected cost consisting maximum tardiness cost among all parts, cost of subcontracting for exceptional elements and the cost of resource underutilization. Scheduling problem in a cellular manufacturing environment is treated as group scheduling problem, which assumes that all parts in a part family are processed in the same cell and no inter-cellular transfer is needed. Finally, the nonlinear model will be transformed to a linear form in order to solve it for optimality. To solve such a stochastic model, an efficient hybrid method based on new combination of genetic algorithm (GA), simulated annealing (SA) algorithm, and an optimization rule will be proposed where SA and optimization rule are subordinate parts of GA under a self-learning rule criterion. Also, performance and robustness of the algorithm will be verified through some test problems against branch and bound and a heuristic procedure.     

Effectiveness of flexible routing control

Flexibility in part process representation and in highly adaptive routing algorithms are two major sources for improvement in the control of flexible manufacturing systems (FMSs). This article reports the investigation of the impact of these two kinds of flexibilities on the performance of the system. We argue that, when feasible, the choices of operations and sequencing of the part process plans should be deferred until detailed knowledge about the real-time factory state is available.To test our ideas, a flexible routing control simulation system (FRCS) was constructed and a programming language for modeling FMS part process plans, control strategies, and environments of the FMS was designed and implemented. In addition, a scheme for implementing flexible process routing called data flow dispatching rule (DFDR) was derived.The simulation results indicate that flexible processing can reduce mean flow time while increasing system throughput and machine utilization. We observed that this form of flexibility makes automatic load balancing of the machines possible. On the other hand, it also makes the control and scheduling process more complicated and calls for new control algorithms.     

基于节拍平衡的高柔性数控单元调度研究

为提高柔性数控单元生产效率,提出一种基于工序平衡的高柔性数控单元调度方法。第一阶段,根据产品生产工艺和设备生产能力进行工艺路线规划,在考虑生产约束、生产准备时间、工艺柔性和设备产能的基础上,构建产品节拍平衡优化目标,获得其最优加工视图组合;第二阶段,基于工序平衡的结果,在考虑产品换线时间的基础上构建整单调度模型,并采用遗产算法求解。最后,将所提调度方法在某壳体产品高柔性数控生产单元进行应用研究,并与分批量调度模型进行了比较分析。研究表明,所提出的工序平衡的柔性数控单元整批量调度方法可以有效缩短单元的制造周期,提高单元控设备利用率。     

基于扩展随机Petri网的可重组制造系统建模与分析方法

可重组制造系统(Reconfigurable manufacturing system,RMS)可根据市场变化进行组态调整和组元升级,系统的建模与分析方法必须能适应上述特点。提出基于扩展随机Petri网(Extended stochastic Petri nets,ESPN)的模块化建模方法,将RMS不同的加工资源对应于相应的ESPN基本模块,并通过过渡变迁合成ESPN模型,该模型能适应任意分布的制造系统,可更加精确地反映生产过程。在此基础上采用基于行为表达式的分析方法,得到系统性能指标,该分析方法可不必画出可达图而直接得到系统性能关系函数,使分析过程更加直观、简洁。可重组电动机生产线的实例证明了该建模与分析方法的有效性。     

Heuristics to minimize makespan of parallel batch processing machines

Batch-processing machines can process several jobs simultaneously. These machines are commonly used to test Printed Circuit Boards (PCBs). The processing time and the dimensions of the PCB are given. Each batch is formed such that the total size of all the PCBs in the batch does not exceed the machine capacity. The batch processing time is equal to the longest processing time of all the PCBs in the batch. These batch processing machines are expensive and a bottleneck. Scheduling PCBs on these parallel batch processing machines to minimize their makespan is NP-hard. Consequently, we propose several heuristics. The performance of the proposed heuristics is compared to a simulated annealing approach and a commercial solver.     

Loading algorithms for flexible manufacturing systems with partially grouped unrelated machines and additional tooling constraints

This paper considers the loading problem for flexible manufacturing systems with highly flexible partial machine grouping, i.e., machines are tooled differently, but each operation can be assigned to multiple machines. Loading is the problem of allocating operations and their associated cutting tools to machines for a given set of parts. As an extension of the existing studies, we consider unrelated machines, i.e., processing time of an operation depends on the speed of the machine to which it is allocated, and dedicated machines, i.e., certain part types must be processed on a specific machine. Also, we consider the constraints associated with cutting tools: (a) tool life restrictions and (b) number of available tool copies. An integer linear programming model is suggested for the objective of balancing the workloads assigned to machines and then due to the complexity of the problem, we suggest two-stage heuristics in which an initial solution is obtained using modified bin-packing algorithms and then it is improved by a simple search technique. The two-stage heuristics suggested in this study were tested on various test instances, and the results show that they can give reasonable quality solutions within a very short amount of computation time. Also, a sensitivity analysis was done on the tightness of the tooling constraints, and the results are reported.     

A joint GA+DP approach for single burn-in oven scheduling problems with makespan criterion

This research is motivated by the scheduling problem found in the burn-in operation of semiconductor final testing, where jobs are associated with release times, processing times, and sizes. The burn-in ovens are modeled as batch-processing machines which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity, and the processing time of a batch is equal to the longest time among all the jobs in the batch. Moreover, this paper attempts to schedule jobs on a single batch-processing machine to minimize makespan. A joint GA+DP algorithm is proposed involving two stages: (1) the formation of job sequence by genetic algorithm operators, and (2) the formation of batches by a dynamic programming algorithm. Computational experiments are given to examine the performance of the proposed algorithm. The experimental results indicate that the joint GA+DP approach has well improved on all instances with respect to solution quality and runtime.     

基于群智能算法的设备布局离散优化研究

针对单向环形设备布局设计问题,建立了新的数学模型.利用多维实数编码及映射方法,将连续粒子群优化算法应用于求解设备单向环形布局问题,提供了求解离散优化问题的新思路.利用遗传算法中的杂交策略扩展了粒子群优化算法,提高了粒子群优化算法性能.建立了问题的图结构描述,以引入蚁群系统算法搜索优化解.给出了两种方法的求解步骤.通过实例计算和结果比较,说明该算法能有效地解决此类离散优化问题,降低成本,提高效率,所得解质量较高,有很好的实用价值.     

Scheduling optimization of flexible manufacturing system using cuckoo search-based approach

In the present work, a cuckoo search (CS)-based approach has been developed for scheduling optimization of a flexible manufacturing system by minimizing the penalty cost due to delay in manufacturing and maximizing the machine utilization time. To demonstrate the application of cuckoo search (CS)-based scheme to find the optimum job, the proposed scheme has been applied with slight modification in its Levy flight operator because of the discrete nature of the solution on a standard FMS scheduling problem containing 43 jobs and 16 machines taken from literature. The CS scheme has been implemented using Matlab, and results have been compared with other soft computing-based optimization approaches like genetic algorithm (GA) and particle swarm optimization found in the literature. The results shown by CS-based approach have been found to outperform the results of existing heuristic algorithms such as GA for the given problem.