Workshop scheduling using practical (inaccurate) data Part 2: An investigation of the robustness of scheduling rules in a dynamic and stochastic environment

In research on generating a predictive schedule, the scheduling problem is often viewed as a deterministic problem. However, the real-life job shop environment is stochastic in that information on job attributes and shop floor status is not precisely known in advance. In this situation, in order to increase the effectiveness of a predictive schedule in practice, the focus should be on creating a robust schedule. The purpose of this paper is to investigate the robustness of a number of scheduling rules in a dynamic and stochastic environment using the rolling time horizon approach. A cost-based performance measure is used to evaluate the scheduling rules. The simulation results, under various conditions in a balanced and unbalanced shop, are presented and the effects of the rescheduling interval and operational factors including shop load conditions and a bottleneck on the robustness of the schedule are studied. From the results the key factors that influence the robustness of a scheduling system are identified and, consequently, general guidelines for creating robust schedules are proposed.     

Flexible job-shop scheduling/rescheduling in dynamic environment: a hybrid MAS/ACO approach

In real-world manufacturing, disruptions are often encountered during the execution of a predetermined schedule, leading to the degradation of its optimality and feasibility. This study presents a hybrid approach for flexible job-shop scheduling/rescheduling problems under dynamic environment. The approach, coined as ‘HMA’ is a combination of multi-agent system (MAS) negotiation and ant colony optimisation (ACO). A fully distributed MAS structure has been constructed to support the solution-finding process by negotiation among the agents. The features of ACO are introduced into the negotiation mechanism in order to improve the performance of the schedule. Experimental studies have been carried out to evaluate the performance of the approach for scheduling and rescheduling under different types of disruptions. Different rescheduling policies are compared and discussed. The results have shown that the proposed approach is a competitive method for flexible job-shop scheduling/rescheduling for both schedule optimality and computation efficiency.     

Dynamic job shop scheduling using variable neighbourhood search

In this paper a scheduling method based on variable neighbourhood search (VNS) is introduced to address a dynamic job shop scheduling problem that considers random job arrivals and machine breakdowns. To deal with the dynamic nature of the problem, an event-driven policy is selected. To enhance the efficiency and effectiveness of the scheduling method, an artificial neural network with a back propagation error learning algorithm is used to update parameters of the VNS at any rescheduling point according to the problem condition. The proposed method is compared with some common dispatching rules that have been widely used in the literature for the dynamic job shop scheduling problem. Results illustrate the high efficiency and effectiveness of the proposed method in a variety of shop floor conditions.     

Look-ahead strategies for dynamic pickup and delivery problems

In this paper we consider a dynamic full truckload pickup and delivery problem with time-windows. Jobs arrive over time and are offered in a second-price auction. Individual vehicles bid on these jobs and maintain a schedule of the jobs they have won. We propose a pricing and scheduling strategy based on dynamic programming where not only the direct costs of a job insertion are taken into account, but also the impact on future opportunities. Simulation is used to evaluate the benefits of pricing opportunities compared to simple pricing strategies in various market settings. Numerical results show that the proposed approach provides high quality solutions, in terms of profits, capacity utilization, and delivery reliability.     

蚁群系统结合指派规则求解HFS调度问题

以NP-难的最小化时间表长为目标的混合流水车间调度问题为研究对象。把工件在第1阶段开始加工的排序问题转化为旅行商问题,采用蚁群系统求得初始排序;在第1阶段后各阶段采用工件先到先服务规则选择工件、最先空闲机器优先规则选择机器以构建初始工件的机器指派与排序;充分利用已知的机器布局和工件加工时间特点,确定工件加工瓶颈阶段,并以此为基础对工件的机器指派与排序进行改进。用Carlier和Neron设计的Benchmark算例仿真后与著名的NEH算法比较,表明这种算法是有效的。     

Robust scheduling of a two-stage hybrid flow shop with uncertain interval processing times

This paper studies the makespan minimisation scheduling problem in a two-stage hybrid flow shop. The first stage has one machine and the second stage has m identical parallel machines. Neither the processing time nor probability distribution of the processing time of each job is uncertain. We propose a robust (min–max regret) scheduling model. To solve the robust scheduling problem, which is NP-hard, we first derive some properties of the worst-case scenario for a given schedule. We then propose both exact and heuristic algorithms to solve this problem. In addition, computational experiments are conducted to evaluate the performance of the proposed algorithms.     

Hybrid branch and bound algorithms for the two-stage assembly scheduling problem with separated setup times

This article proposes hybrid branch and bound algorithms to minimise the makespan for the two-stage assembly scheduling problem with separated setup times. In the studied problem, there are multiple machines at the first stage, each of which produces a component of a job. When all components are available, a single assembly machine at the second stage completes the job. Existing algorithms are based on the state space search and hence suffer from the state space explosion problem. In order to reduce the search space, lower and upper bounds for a partial schedule are proposed. Also, a heuristic function and a dominance rule are developed to guide the search process. Moreover, accelerated factors are introduced to increase the speed of the search. Experimental results indicate that our algorithms outperform an existing method, and can find the optimal or near-optimal schedules in a short time for all tested problems with up to ten thousand jobs and nine first-stage machines.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.     

Flow shop scheduling with a batch processor and limited buffer

This paper addresses flow shop scheduling problem with a batch processor followed by a discrete processor. Incompatible job families and limited buffer size are considered, and the objective is to determine a schedule such that the total completion time is minimised. Flexible buffer service policy is designed, and a greedy heuristic together with the worst-case analysis is developed. We also propose a hybrid method involving a Differential Evolution algorithm. Moreover, two tight lower bounds are provided to measure the performances of the proposed algorithms. Numerical results demonstrate that the proposed algorithms are capable of providing high-quality solutions for large-scale problems within a reasonable computational time.     

Minimising makespan on a single batch processing machine with dynamic job arrivals and non-identical job sizes

Batch scheduling is a prevalent policy in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimising makespan on a single batch processing machine in the presence of dynamic job arrivals and non-identical job sizes. The problem under study is NP-hard. Consequently, we develop a number of efficient construction heuristics. The performance of the proposed heuristics is evaluated by comparing their results to two lower bounds, and other solution approaches published in the literature, namely the first-fit longest processing time-earliest release time (FFLPT-ERT) heuristic, hybrid genetic algorithm (HGA), joint genetic algorithm and dynamic programming (GA+DP) approach and ant colony optimisation (ACO) algorithm. The computational experiments demonstrate the superiority of the proposed heuristics with respect to solution quality, especially for the problems with small size jobs. Moreover, the computational costs of the proposed heuristics are very low.     

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.     

Production sequencing problem with re-entrant work flows and sequence dependent setup times

This paper addresses a shop scheduling problem where a set of n jobs needs to be scheduled on two machines for the side frame press shop in a truck manufacturing company. A most 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 can be solved by dynamic programming with the objective of the minimum makespan. An optimal schedule is found utilizing the sequence dominance conditions and the decisiondelay scheme. Since the computational requirements of dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.     

Robust makespan minimisation in identical parallel machine scheduling problem with interval data

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

Centralized Scheduling and Priority Implementation Heuristics for a Dynamic Job Shop Model

The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.     

Hedge against total flow time uncertainty of the uniform parallel machine scheduling problem with interval data

We consider a total flow time minimisation problem of uniform parallel machine scheduling when job processing times are only known to be bounded within certain given intervals. A minmax regret model is proposed to identify a robust schedule that minimises the maximum deviation from the optimal total flow time over all possible realisations of the job processing times. To solve this problem, we first prove that the maximal regret for any schedule can be obtained in polynomial time. Then, we derive a mixed-integer linear programming (MILP) formulation of our problem by exploiting its structural properties. To reduce the computational time, we further transform our problem into a robust single-machine scheduling problem and derive another MILP formulation with fewer variables and constraints. Moreover, we prove that the optimal schedule under the midpoint scenario is a 2-approximation for our minmax regret problem. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

人机协同的生产调度实验平台

生产调度一直以来都是生产管理的难题,同以往单纯采用算法由机器来获得调度最优解的思路不同的是,采用人机协同的思想开展对调度问题的研究,将调度任务进行分派,使凋度员和机器协同完成调度任务,建立了人机协同的生产调度实验平台.实例表明,该实验平台提供了一个训练调度员调度能力的工具,利用该实验平台,调度员和机器可较好地协同得到满意的调度解.     

Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.     

重大水利水电工程施工实时控制关键技术及其工程应用

高心墙堆石坝和高混凝土坝的施工质量与施工进度控制是工程建设的重要技术问题。针对常规人工控制手段难以确保高心墙堆石坝施工质量,以及高强度连续施工下高混凝土坝施工进度难以实时控制等问题,提出了高心墙堆石坝填筑碾压质量实时监控技术、坝料上坝运输过程实时监控技术和施工质量动态信息PDA实时采集技术,实现了大坝填筑碾压全过程的全天候、精细化、在线实时监控;在建立高混凝土坝施工进度实时控制数学模型基础上,提出了施工进度实时预警与动态调整方法,为高混凝土坝施工进度的实时预测、适时预警、动态调整与优化提供了分析手段;提出了网络环境下数字大坝系统集成技术,研制开发了数字大坝系统,为大坝竣工验收、安全鉴定及运行管理提供了支撑平台。成果已应用于10余项重大工程,取得了显著的经济效益和社会效益。     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

A note on resource allocation scheduling with group technology and learning effects on a single machine

In this article, single-machine group scheduling with learning effects and convex resource allocation is studied. The goal is to find the optimal job schedule, the optimal group schedule, and resource allocations of jobs and groups. For the problem of minimizing the makespan subject to limited resource availability, it is proved that the problem can be solved in polynomial time under the condition that the setup times of groups are independent. For the general setup times of groups, a heuristic algorithm and a branch-and-bound algorithm are proposed, respectively. Computational experiments show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions.