Workload vs scheduling policies in a dual-resource constrained job shop

The purpose of this paper is to report on research conducted to examine the effectiveness of different scheduling policies in a dual-constrained job shop under various workload conditions. The standard assumption in most job shop scheduling research has been that a 90% utilization of the shop is achieved. However, since shop utilization levels vary widely, it was hypothesized that scheduling policies that are optimum under one load condition might not be as effective under other load conditions. The model for this simulation experiment represented a job shop constrained by both labor and machines. The shop contains four machine centers with random routing of jobs through the shop. Shop workload was defined at three levels: 70, 85 and 99% utilization. Four machine scheduling rules and three labor assignment rules were tested for each of the shop workload levels, with mean job flow time as. the performance criterion. The results of the 3 × 4 × 3 factorial experiment showed that the advantage of the SPT (shortest processing time) machine scheduling rule over other rules is diminished dramatically when shop utilization is reduced from 99 to 85% or below. This same observation holds for other rules considered. The LNQ (longest queue length) labor assignment rule outperformed other rules at the 99% utilization level, but yielded no significant difference in performance at the 85% and below workload levels.     

A simulation study comparing GT vs. job shop manufacturing systems

Two discrete simulation models were developed, one representing a typical job shop (JS) manufacturing system (process layout) and the other representing group technology (GT) manufacturing system (cellular layout). Hypothetical data generated by FORTRAN program and MICRO-CRAFT layout package were used to validate the two models. Simulations were performed using SLAM II. The two layouts were compared with one another under controlled experimental conditions using various combinations of four operating variables: batch size, demand rate, ratio of setup time to process time, and transporter speed. Six indicators of systems performance were used in the study. These were: average time in system, products completed, jobs in process, average machine utilization, average queue length, and average waiting time.

The study found that for environment as set for the models, GT system outperformed JS system as expected. However, using large batch size (more than 75) in Experiment 1 (changing batch size) allowed JS system to perform as well as GT system. Certain specific changes in batch size also allowed to establish optimum results in both systems. No individual change of demand rate (Experiment 2), ratio of setup time to process time (Experiment 3), or transporter speed (Experiment 4) allowed JS system to outperform GT system.     

An integrated scheduler for manufacturing planning and control (INSCH)

The most basic problem in a manufacturing process is to create valid scheduling system which determines the sequence of jobs to be processed at each of the series of machine centers. An integrated scheduler (INSCH) is developed for small job shop manufacturing systems while considering high machine utilization, low work-in-process, and reduced job lateness.

As an and to understand the interaction of live jobs with the shop, sequence scheduler is developed to complement production scheduler such as Gantt bar chart. INSCH can achieve better performance than simple static models as shown in an example. It is desirable for INSCH to be applied to small job shop manufacturing companies using micro personal computer with relevant modifications discussed.     

Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.     

Two machine flow shop scheduling problem with weighted WIP costs

This paper considers two new machine flow shop scheduling problems where the objective is to minimize the total WIP (work-in-process) cost. In this type of problems, the unit time WIP cost increases or decreases as a job passes through a series of stages in the production process.     

Scheduling jobs under decreasing linear deterioration

This paper considers the scheduling problems under decreasing linear deterioration. Deterioration of a job means that its processing time is a function of its execution start time. Optimal algorithms are presented respectively for single machine scheduling of minimizing the makespan, maximum lateness, maximum cost and number of late jobs. For two-machine flow shop scheduling problem to minimize the makespan, it is proved that the optimal schedule can be obtained by Johnson's rule. If the processing times of operations are equal for each job, flow shop scheduling problems can be transformed into single machine scheduling problems.     

Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10?min.     

Improving the delivery efficiency of the customer order scheduling problem in a job shop

The focus of this paper is customer order scheduling (COS) problem, where each order consists of a set of jobs that must be shipped as one batch at the same time. In COS each job is part of a customer order and the make-up of the jobs in the order are pre-specified. Most of the existing research deals with COS in a single machine or in a parallel machine shop for developing an optimal solution. COS is common in a normal job shop, and the more complex the shop, the more complex the scheduling. Most existing research has focused on trying to reduce the completion time of the batch. That is, the focus is only on the point in time the last job is finished, while ignoring the actual duration of the jobs within the same order. The longer it takes to complete all the jobs within an order the more it increases the stock of finished goods and the more it deteriorates the efficiency of the logistics and the supply chain management.A new dispatching rule, referred to as Minimum Flow Time Variation (MFV), has been proposed for COS in a normal job shop, in order to reduce the total time it takes to complete all jobs within the same order. That is, the individual completion times of all jobs for the same customer order will be controlled in order to improve the shipping performance. In the simulation test and statistical analysis, the level of work in process (WIP) under the MFV rule in the finished goods warehouse is reduced by more than 70% compared to any other method. The MFV method will efficiently reduce the stock level of finished goods, and controls the waiting time required before they can be shipped. Depending on the environmental factors, the performance of our proposed method will become increasingly significant the more complex the system.     

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.     

A hybrid scheduling approach for a two-stage flexible flow shop with batch processing machines

In this paper, we discuss a flexible flow shop scheduling problem with batch processing machines at each stage and with jobs that have unequal ready times. Scheduling problems of this type can be found in semiconductor wafer fabrication facilities (wafer fabs). We are interested in minimizing the total weighted tardiness of the jobs. We present a mixed integer programming formulation. The batch scheduling problem is NP-hard. Therefore, an iterative stage-based decomposition approach is proposed that is hybridized with neighborhood search techniques. The decomposition scheme provides internal due dates and ready times for the jobs on the first and second stage, respectively. Each of the resulting parallel machine batch scheduling problems is solved by variable neighborhood search in each iteration. Based on the schedules of the subproblems, the internal due dates and ready times are updated. We present the results of designed computational experiments that also consider the number of machines assigned to each stage as a design factor. It turns out that the proposed hybrid approach outperforms an iterative decomposition scheme where a fairly simple heuristic based on time window decomposition and the apparent tardiness cost dispatching rule is used to solve the subproblems. Recommendations for the design of the two stages with respect to the number of parallel machines on each stage are given.     

Production sequencing problem with reentrant work flows and sequence dependent setup times

This paper addresses a shop scheduling problem for the side frame press shop in a truck manufacturing company. In the problem, a set of n jobs to be scheduled on two machines. All the jobs require processing by the first machine more than once in their operation sequences with reentrant work flows. An unusual aspect of the problem is that the setup times required for a job in the first machine depend not on the immediately preceding job but on the job which is two steps prior to it. Redefining the job elements, the problem is formulated into a general two machine flow shop problem which has a set of job-element precedence constraints. The problem is solved with a modified dynamic programming with the objective of the minimum makespan. An optimal schedule is found utilizing the sequence dominance condition and a decision-delay scheme. A numerical example is presented for the illustration purpose.     

Ant colony optimization for multi-objective flow shop scheduling problem

Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared.     

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.Scope and purposeShop scheduling problems, widely used in the modeling of industrial production processes, are receiving an increasing amount of attention from researchers. To model practical production processes more closely, additional processing restrictions can be introduced, e.g., the resource constraints, the no-wait in process requirement, the precedence constraints, etc. This paper considers the total completion time open shop scheduling problem with a given sequence of jobs on one machine. This model belongs to a new class of shop scheduling problems under machine-dependent precedence constraints. This problem is NP-hard in the strong sense. A heuristic is proposed to efficiently solve large-scaled problems and a branch-and-bound algorithm is presented to optimally solve small-scaled problems. Computational experience is also reported.     

A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates

Flexible job shop scheduling problem (FJSSP) is generalization of job shop scheduling problem (JSSP), in which an operation may be processed on more than one machine each of which has the same function. Most previous researches on FJSSP assumed that all jobs to be processed are available at the beginning of scheduling horizon. The assumption, however, is always violated in practical industries because jobs usually arrive over time and can not be predicted before their arrivals. In the paper, dynamic flexible job shop scheduling problem (DFJSSP) with job release dates is studied. A heuristic is proposed to implement reactive scheduling for the dynamic scheduling problem. An approach based on gene expression programming (GEP) is also proposed which automatically constructs reactive scheduling policies for the dynamic scheduling. In order to evaluate the performance of the reactive scheduling policies constructed by the proposed GEP-based approach under a variety of processing conditions three factors, such as the shop utilization, due date tightness, problem flexibility, are considered in the simulation experiments. The scheduling performance measure considered in the simulation is the minimization of makespan, mean flowtime and mean tardiness, respectively. The results show that GEP-based approach can construct more efficient reactive scheduling policies for DFJSSP with job release dates under a big range of processing conditions and performance measures in the comparison with previous approaches.     

周期性和事件驱动的JobShop滚动调度策略

为了适应加工的连续性及环境的变化，借用了预测控制中的滚动优化思想提出了周期性和事件驱动的滚动调度策略。调度算法将遗传算法和分派规则相结合，以此来处理与操作序列有关的工件安装时 间和工件到期时间约束的复杂调度问题。     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

Mean value analysis of re-entrant line with batch machines and multi-class jobs

We propose an approximate approach for estimating the performance measures of the re-entrant line with single-job machines and batch machines based on the mean value analysis (MVA) technique. Multi-class jobs are assumed to be processed in predetermined routings, in which some processes may utilize the same machines in the re-entrant fashion. The performance measures of interest are the steady-state averages of the cycle time of each job class, the queue length of each buffer, and the throughput of the system. The system may not be modeled by a product form queueing network due to the inclusion of the batch machines and the multi-class jobs with different processing times. Thus, we present a methodology for approximately analyzing such a re-entrant line using the iterative procedures based upon the MVA and some heuristic adjustments. Numerical experiments show that the relative errors of the proposed method are within 5% as compared against the simulation results.Scope and purposeWe consider a re-entrant shop with multi-class jobs, in which jobs may visit some machines more than once at different stages of processing, as observed in the wafer fabrication process of semiconductor manufacturing. The re-entrant line also consists of both the single-job machine and the batch machine. The former refers to the ordinary machine processing one job at a time, and the latter means the machine processing several jobs together as a batch at a time. In this paper, we propose an approximation method based on the mean value analysis for estimating the mean cycle time of each class of jobs, the mean queue length of each buffer, and the throughput of the system.     

Study of stochastic sequence-dependent flexible flow shop via developing a dispatching rule and a hybrid GA

A flexible flow shop is a generalized flow shop with multiple machines in some stages. This system is fairly common in flexible manufacturing and in process industry. In most practical environments, scheduling is an ongoing reactive process where the presence of real time information continually forces reconsideration of pre-established schedules. This paper studies a flexible flow shop system considering non-deterministic and dynamic arrival of jobs and also sequence dependent setup times. The problem objective is to determine a schedule that minimizes average tardiness of jobs. Since the problem class is NP-hard, a novel dispatching rule and hybrid genetic algorithm have been developed to solve the problem approximately. Moreover, a discrete event simulation model of the problem is developed for the purpose of experimentation. The most commonly used dispatching rules from the literature and two new methods presented in this paper are incorporated in the simulation model. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop utilization, setup time level and number of stages. The results indicate that methods proposed in this study are much better than the traditional dispatching rules.     

On the Complexity of Non-preemptive Shop Scheduling with Two Jobs

In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice. Received July 28, 2001; revised May 15, 2002 Published online: July 26, 2002     

A polynomial-time approximation scheme for the two-machine flow shop scheduling problem with an availability constraint

We study the problem of scheduling n preemptable jobs in a two-machine flow shop where the first machine is not available for processing during a given time interval. The objective is to minimize the makespan. We propose a polynomial-time approximation scheme for this problem. The approach is extended to solve the problem in which the second machine is not continuously available.