Intra-cell manpower transfers and cell loading in labor-intensive manufacturing cells

Labor-intensive manufacturing cells consist of simple machines and equipment that require continuous operator attendance and involvement. Operators are often re-assigned to different machines when a new product is released to the cell. The main reason for this re-assignment is to maximize the output rate of the cell by balancing the flow of products through several machines with varying capacities. In this paper, first a product-sequencing problem with the objective of minimizing the total intra-cell manpower transfers is introduced. A three-phase hierarchical methodology is proposed to solve the problem optimally. Next, manpower transfer matrix values are modified considering the distances traveled among machines. In the second part of the paper, a machine-level-based similarity coefficient that uses the number of machines as a similarity measure is discussed. Later, these coefficients are used during the cell loading process to minimize makespan and also machine and space requirements. Manpower allocation decisions are made along with scheduling decisions that are critical in most labor-intensive manufacturing cells and both approaches are illustrated with an example problem.     

Minimizing makespan and flowtime in a parallel multi-stage cellular manufacturing company

This study proposes a 3-phase solution approach for a multi-product parallel multi-stage cellular manufacturing company. The study focuses on a case study involving a shoe manufacturing plant in which products are produced according to their due dates. The investigated manufacturing process has three stages, namely lasting cells, rotary injection molding cells, finishing-packaging cells. System performance is measured based on total flowtime and makespan. We propose a 3-phase solution approach to tackle the problem; 1) the first phase of the proposed approach allocates manpower to operations in the lasting cells and finishing-packaging cells, independently. The objective is to maximize the production rates in these cells. 2) The second phase includes cell loading to determine product families based on a similarity coefficient using mathematical modeling and genetic algorithms (GA). The proposed GA algorithm for cell loading performs mutation prior to crossover, breaking from traditional genetic algorithm flow. The performance measures flow time and makespan are considered in this phase. 3) Flow shop scheduling is then performed to determine the product sequence in each (lasting, rotary injection molding, finishing-packaging) cell group. This 3-phase solution approached is repeated with alternative manpower level allocation to lasting and finishing-packaging cells where the total manpower level remains the same.     

Characterization of the iterative application of makespan heuristics on non-makespan machines in a heterogeneous parallel and distributed environment

Heterogeneous computing (HC) is the coordinated use of different types of machines, and networks to process a diverse workload in a manner that will maximize the combined performance and/or cost effectiveness of the system. Heuristics for allocating resources in an HC system are based on some optimization criterion. A common optimization criterion is to minimize the completion time of the machine that finishes last (makespan). In this study, we consider an iterative approach that repeatedly runs a mapping heuristic to minimize the makespan of the considered machines and tasks. For each successive iteration, the makespan machine of the previous iteration and the tasks assigned to it are removed from the set of considered machines and tasks. This study focuses on understanding the different mathematical characteristics of resource allocation heuristics that cause them to behave differently when combined with this iterative approach. This paper has three main contributions. The first contribution is the study of an iterative technique used in conjunction with resource allocation heuristics. The second contribution is the definition and mathematical characterization of “iteration invariant” heuristics. The third contribution is to determine the characteristics of a heuristic that will cause the mapping to change across iterations.     

A computer simulation model for job shop scheduling problems minimizing makespan

One of the basic and significant problems, that a shop or a factory manager is encountered, is a suitable scheduling and sequencing of jobs on machines. One type of scheduling problem is job shop scheduling. There are different machines in a shop of which a job may require some or all these machines in some specific sequence. For solving this problem, the objective may be to minimize the makespan. After optimizing the makespan, the jobs sequencing must be carried out for each machine. The above problem can be solved by a number of different methods such as branch and bound, cutting plane, heuristic methods, etc. In recent years, researches have used genetic algorithms, simulated annealing, and machine learning methods for solving such problems. In this paper, a simulation model is presented to work out job shop scheduling problems with the objective of minimizing makespan. The model has been coded by Visual SLAM which is a special simulation language. The structure of this language is based on the network modeling. After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented and compared with other results reported in the literature. Finally, the model output is analyzed.     

Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure

A batch processing machine can simultaneously process several jobs forming a batch. This paper considers the problem of scheduling jobs with non-identical capacity requirements, on a single-batch processing machine of a given capacity, to minimize the makespan. The processing time of a batch is equal to the largest processing time of any job in the batch. We present some dominance properties for a general enumeration scheme and for the makespan criterion, and provide a branch and bound method. For large-scale problems, we use this enumeration scheme as a heuristic method.Scope and purposeUsually in classical scheduling problems, a machine can perform only one job at a time. Although, one can find machines that can process several jobs simultaneously as a batch. All jobs of a same batch have common starting and ending times. Batch processing machines are encountered in many different environments, such as burn-in operations in semiconductor industries or heat treatment operations in metalworking industries. In the first case, the capacity of the machine is defined by the number of jobs it can hold. In the second case, each job has a certain capacity requirement and the total size of a batch cannot exceed the capacity of the machine. Hence, the number of jobs contained in each batch may be different. In this paper, we consider this second case (which is more difficult) and we provide an exact method for the makespan criterion (minimizing the last ending time).     

Scheduling and Lot Streaming in Flowshops with No-Wait in Process

Lot streaming involves splitting a production lot into a number of sublots, in order to allow the overlapping of successive operations, in multi-machine manufacturing systems. In no-wait flowshop scheduling, sublots are necessarily consistent, that is, they remain the same over all machines. The benefits of lot streaming include reductions in lead times and work-in-process, and increases in machine utilization rates. We study the problem of minimizing the makespan in no-wait flowshops producing multiple products with attached setup times, using lot streaming. Our study of the single product problem resolves an open question from the lot streaming literature. The intractable multiple product problem requires finding the optimal number of sublots, sublot sizes, and a product sequence for each machine. We develop a dynamic programming algorithm to generate all the nondominated schedule profiles for each product that are required to formulate the flowshop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and computationally test an efficient heuristic for this problem. Our results indicate that solutions can quickly be found for flowshops with up to 10 machines and 50 products. Moreover, the solutions found by our heuristic provide a substantial improvement over previously published results.     

Scheduling Flexible Flow Shop in Labeling Companies to Minimize the Makespan

In the competitive global marketplace, production scheduling plays a vital role in planning in manufacturing. Scheduling deals directly with the time to output products quickly and with a low production cost. This research examines case study of a Radio-Frequency Identification labeling department at Avery Dennison. The main objective of the company is to have a method that allows for the sequencing and scheduling of a set of jobs so it can be completed on or before the customer’s due date to minimize the number of late orders. This study analyzes the flexible flow shop scheduling problem with a sequence dependent setup by modifying the processing time and setup time to minimize the makespan on multiple machines. Based on the defined mathematical model, this study includes an alternative approach and application of heuristic algorithm with the input being big data. Both optimization programs are used in this study and compared to determine which method can better solve the company’s problems. The proposed algorithm is able to improve machine utilization with large-scale problems.     

不确定环境下项目拆分和带缓冲时间的多项目协同调度研究

针对不确定环境下移动式装配的项目存在项目工期随机延长的问题,首先引用项目拆分思想,将单项目虚拟拆分成多项目;在加入最大鲁棒性约束下,以最小化项目工期为目标建立数学优化模型。并提出了改进的两阶段循环算法求解：项目划分阶段通过子项目拆分算法进行子项目划分;项目调度阶段以布谷鸟算法为框架对划分后的多项目调度进行求解,并将调度结果反馈至上阶段。最后选取PSPLIB算例库中不同规模的算例,分析各种参数在不同规模下对项目计划的影响。实例验证结果表明,所提方法能在不确定环境下提高项目资源利用率并缩短工期。     

A new heuristic for scheduling the two-stage flowshop with additional resources

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines at the first stage and a single machine at the second stage. At the first stage, jobs use some additional resources which are available in limited quantities at any time. The resource requirements are of 0–1 type. The objective is the minimization of makespan. The problem is NP-hard. Heuristic algorithms are proposed which solve to optimality the resource constrained scheduling problem at the first stage of the flowshop, and at the same time, minimize the makespan in the flowshop by selecting appropriate jobs for simultaneous processing. Several rules of job selection are considered. The performance of the proposed heuristic algorithms is analyzed by comparing solutions with the lower bound on the optimal makespan. The extensive computational experiment shows that the proposed heuristic algorithms are able to produce near-optimal solutions in short computational time.     

A note on longest processing time algorithms for the two uniform parallel machine makespan minimization problem

This note considers the longest processing time heuristic for scheduling n independent jobs on two uniform parallel machines to minimize the makespan. A posterior worst-case performance ratio, by depending on the index of the latest job inserted in the machine where the makespan takes place, is developed for this heuristic, and some examples demonstrate that the ratio is tight.     

Heuristic procedures and mathematical models for cell loading and scheduling in a shoe manufacturing company

This paper focuses on cell loading and scheduling issues in a shoe manufacturing company. It involves a three-phase solution methodology where first number of cells is determined, then cells are loaded and finally detailed scheduling is performed. Three different family definitions are used (subfamilies, families and superfamilies) during the cell loading process. Three cell loading heuristic procedures (H1, H2, and H3), a simple cell scheduling heuristic and two-level mathematical models are proposed and then compared with respect to makespan. An important observation is that better post-loading schedules did not lead to better post-scheduling results. As a result, the best schedule can only be known after both cell loading and cell scheduling functions are performed. The results showed that H1 led to the best post-scheduling makespan values and they were on the average within 3% of the optimal solution. The execution time for H1 was less than four seconds for the problems tested in the experimentation and this can be considered negligible for a manufacturing setting.     

超启发式交叉熵算法求解分布式装配柔性作业车间调度问题

本文针对一类新型两阶段分布式装配柔性作业车间调度问题(DAFJSP),建立问题模型,以最小化最大完工时间为优化目标并提出一种超启发式交叉熵算法(HHCEA)进行求解.首先,设计基于工序序列、工厂分配和产品序列的三维向量编码规则和结合贪婪策略的解码规则,同时提出4种启发式方法以提高初始解的质量.然后,设计高低分层结构的HHCEA,高层为提高对搜索方向的引导性,采用交叉熵算法(CEA)学习和积累优质排列的信息,其中各排列由结合问题特点设计的11种启发式操作(即11种有效的邻域操作)构成;低层为增加在解空间中的搜索深度,将高层确定的每个排列中的启发式操作依次重复执行指定次数并在执行过程中加入基于模拟退火的扰动机制,以此作为一种新的启发式方法执行搜索.最后,通过仿真实验与算法对比验证HHCEA可有效求解DAFJSP.     

An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan

This paper considers a two-stage assembly scheduling problem of N products with setup times to minimize the makespan. In this problem, there is a machining machine which produces components in the first stage. When the required components are available, a single assembly machine can assemble these components into products in the second stage. A setup time is needed whenever the machining machine starts processing components, or the item of component is switched on the machine. The problem is formulated as a mixed integer programming model, and several properties for finding optimal solutions are developed. Moreover, an efficient heuristic based on these optimal properties is proposed. A lower bound is derived to evaluate the performance of the proposed heuristic. Computational results show that the proposed heuristic can obtain a near optimal solution in almost zero time and the average percentage deviation is only 0.478.     

Scheduling jobs to consider physiological factors

We studied scheduling jobs and breaks for a single worker. The processing time of jobs increases as the worker tires. In this study, we assume that conventional machine scheduling models do not always work for humans. So, while determining the break time, we consider the workers' physiological factors. The two objectives considered are the total flow time and makespan. An exact mathematical model and heuristic algorithm are developed to solve large problems. Numerical examples are presented for understanding and analyzing the performance of the mathematical model and the heuristic. © 2011 Wiley Periodicals, Inc.     

基于蚁群粒子群算法求解多目标柔性调度问题

通过分析多目标柔性作业车间调度问题中各目标的相互关系,提出一种主、从递阶结构的蚁群粒子群求解算法。算法中,主级为蚁群算法,在选择工件加工路径过程中实现设备总负荷和关键设备负荷最小化的目标;从级为粒子群算法,在主级工艺路径约束下的设备排产中实现工件流通时间最小化的目标。然后,以设备负荷和工序加工时间为启发式信息设计蚂蚁在工序可用设备间转移概率;基于粒子向量优先权值的大小关系设计解码方法实现设备上的工序排产。最后,通过仿真和比较实验,验证了该算法的有效性。     

求解任务可拆分多项目协同调度问题的启发式算法

生产项目计划与调度过程中任务可以被拆分为更小粒度的子任务分批次执行,实现缩短项目总工期的优化目标.针对抢占式任务可拆分多项目调度问题,从协同优化角度探讨任务拆分与重组方式,提出一个长工期任务优先拆分、长工期项目优先拆分和高资源利用率项目优先拆分3种任务拆分优先级判断规则,设计一种求解任务可拆分多项目协同调度问题的启发式算法.最后通过数值实例和仿真分析验证了所提出方法在多项目调度总工期的优化效果和求解效率.     

Effects of different fuzzy operators on fuzzy bi-objective cell loading problem in labor-intensive manufacturing cells

In this study, a fuzzy bi-objective cell loading problem in labor-intensive cellular environments is presented and the effects of different fuzzy operators on the model are investigated. The objective functions of the proposed mathematical model for the problem are minimizing the number of the tardy jobs and the minimizing the total manpower needed. The mathematical model determines the number of cells to open and the cell size for each opened cell and assigns products to cells (cell loading) and also determines the sequence of products in each cell simultaneously. Fuzziness stems from the fuzzy aspiration levels attained to both objective functions. To solve the model, fuzzy mathematical programming approach is used and fuzzy achievement function of the model is defined by six different fuzzy operators which are min, fuzzy and, fuzzy or, minimum bounded sum, add, and product. An example problem is solved to represent the performance of the operators. Experimentation shows that the fuzzy and-operator and product-operator are suitable to reach efficient solutions for the problem on hand.     

Maximizing the number of dual-cycle operations of quay cranes in container terminals

An important objective of all schedules in a port is to minimize turnaround time of vessels. An operation schedule for Quay Cranes (QCs) can significantly affect the turnaround time of a vessel. Recently dual cycling techniques have already been used for reducing the number of operation cycles of QCs in some advanced container terminals. This study attempts to minimize the number of operation cycles of a QC for discharging and loading containers in a ship-bay, which is equivalent to maximizing the number of dual cycle operations. A formulation in QC scheduling problems is proposed as a mixed integer programming model. A hybrid heuristic approach is proposed to solve this model. The algorithm applied in this study takes two types of sequencing into account, i.e. inter-stage sequencing (hatch sequencing) and intra-stage sequencing (stack sequencing in the same hatch). This approach hybridizes a certain reconstructive Johnson’s rule with an effective local search method. Finally, certain data in real cases are used to evaluate the effectiveness of the proposed approach.     

Minimizing makespan on a three-machine flowshop batch scheduling problem with transportation using genetic algorithm

This paper studies the minimization of makespan in a three-machine flowshop scheduling problem in which a batch processing machine is located between two single processing machines on first and third stages. In this study also transportation capacity and transportation among machines times are explicitly considered.We establish a mixed integer programming model and propose a heuristic algorithm based on the basic idea of Johnson's algorithm. Since the problem under study is NP-hard, a genetic algorithm is also proposed to minimize makespan. The effectiveness of our solution procedures is evaluated through computational experiments. The results obtained from the computational study have shown that the genetic algorithm is a viable and effective approach that is capable to produce consistently good results.     

Algorithms for distributed data processing

This paper analyzes a problem that occurs in distributed database systems. The problem is how to minimize the communication cost incurred by inter-site data transfers that are associated with on-line retrieval requests. A mathematical model of the problem is developed and results in an NP-Complete integer linear program. A lower bounding procedure, based on a Lagrangean relaxation and sub-gradient optimization, is devised and heuristic procedures are proposed. The results of computational experiments reveal good performance of the heuristic procedures.