Novel slack-based robust scheduling rule for a semiconductor manufacturing system with uncertain processing time

The NP-hard scheduling problems of semiconductor manufacturing systems (SMSs) are further complicated by stochastic uncertainties. Reactive scheduling is a common dynamic scheduling approach where the scheduling scheme is refreshed in response to real-time uncertainties. The scheduling scheme is overly sensitive to the emergence of uncertainties because the optimization of performance (such as minimum make-span) and the system robustness cannot be achieved simultaneously by conventional reactive scheduling methods. To improve the robustness of the scheduling scheme, we propose a novel slack-based robust scheduling rule (SR) based on the analysis of robustness measurement for SMS with uncertain processing time. The decision in the SR is made in real time given the robustness. The proposed SR is verified under different scenarios, and the results are compared with the existing heuristic rules. Simulation results show that the proposed SR can effectively improve the robustness of the scheduling scheme with a slight performance loss.     

A two-layer dynamic scheduling method for minimising the earliness and tardiness of a re-entrant production line

This study focuses on the dynamic scheduling problem of a re-entrant production line, in which all of the parts are assumed to have the same processing routes and be processed on every machine. A two-layer dynamic scheduling method is proposed for the dynamic scheduling of the re-entrant line with the objective of minimising total earliness and tardiness. This method consists of two layers. The top layer is to select the appropriate scheduling policy, and the bottom layer is to generate the scheduling by using the policy selected in the top layer. In the top layer, three different rules are constructed for selecting scheduling policies, namely the lateness comparison rule, the lateness variation comparison rule, and the equal interval switching rule. In the bottom layer, three different scheduling policies are proposed to generate the real-time scheduling for manufacturing, namely the FCFS (first come first service) scheduling policy, the PI (proportional-integral) scheduling policy, and the fuzzy PI scheduling policy. Considering that the real-time status of manufacturing changes constantly, it is necessary to switch among different scheduling policies to adapt to this change. Numerical experiments are performed in the situations with and without urgent jobs. The results show that the proposed two-layer dynamic scheduling method outperforms any single scheduling policy (e.g., the FCFS policy, the PI policy and the fuzzy PI policy) for the dynamic scheduling of a re-entrant production line.     

Quality of service supporting downlink scheduling scheme in worldwide interoperability for microwave access wireless access systems

IEEE 802.16 is a standardisation for a broadband wireless access in metropolitan area networks (MAN). Since the IEEE 802.16 standard defines the concrete quality of service (QoS) requirement, a scheduling scheme is necessary to achieve the QoS requirement. Many scheduling schemes are proposed with the purpose of throughput optimisation and fairness enhancement, however, few scheduling schemes support the delay requirement. In this study, the authors propose a new scheduling scheme reflecting the delay requirement. Specifically, the authors add the delay requirement term in the proportional fair scheduling scheme and the scheduling parameters are optimised with respect to the QoS requirement. Therefore the QoS requirement is achieved without the excessive resource consumption.     

A multiple-criteria real-time scheduling approach for multiple-load carriers subject to LIFO loading constraints

This paper studies the problem of scheduling a multiple-load carrier subject to last-in-first-out loading constraints in an automobile assembly line. Two scheduling criteria, the throughput of the assembly line and the material handling distance, are considered in order to maximise the profit of the assembly line. Different from other studies, the product mix and weights of the scheduling criteria are considered to be variable. A scheduling approach is proposed for the problem. At moments when the product mix or weights of the scheduling criteria change, the scheduling approach can select an appropriate rule from a set of given rules. In this study, the proposed approach is compared with other approaches by simulation in order to verify the performance of the proposed approach. The results indicate that, when the product mix and weights of the scheduling criteria are variable, the proposed scheduling approach outperforms other approaches.     

串联生产系统智能维护调度实验平台研究

结合工业工程专业学习需求,设计了考虑有限缓存的串联生产系统维护调度实验平台。实验平台由维护调度计算模块和维护调度演示模块组成。维护调度计算模块基于Matlab,在考虑有限缓存的串联生产系统维护调度模型的基础上,提供3种不同的策略对维护进行调度;维护调度演示模块基于Flexsim。基于该平台,可完成维护调度参数分析、维护调度策略分析、维护调度仿真等实验,并可在此平台基础上建立维护调度相关参数优化模型。     

Emission-constrained optimal generation scheduling incorporating equity principles

An annual emission-constrained generation scheduling model that combines equity principles with cost optimisation is developed. By employing this annual generation scheduling model, an estimation of the daily emission allowance of each generation unit is obtained. A daily emission-constrained generation scheduling model, based on cost optimisation, is proposed. The equity-related issues in the daily scheduling model are discussed. The Shapley value is employed in the daily scheduling problem to allocate the operating cost reduction among the units. Characteristics of the allocation game of operating cost reduction in daily scheduling are discovered, and several methods are proposed to overcome the combinatorial explosion problem in the calculation of the Shapley value. The effectiveness of the proposed models is shown with simulation results on a test power system.     

A logistics scheduling model: scheduling and transshipment for two processing centers

Logistics scheduling refers to problems in which decisions on job scheduling and transportation are integrated into a single framework. A logistics scheduling model for two processing centers that are located in different cities is presented. Each processing center has its own customers. When the demand in one processing center exceeds its processing capacity, it is possible to use part of the capacity of the other processing center subject to a job transshipment delay. Such a coordinated scheduling situation can be modeled as a parallel-machine scheduling problem with transshipment between the machines. We study problems with different objective functions and constraints, and propose various algorithms to solve these problems. Discussions on the benefits and incentives for the coordinated approach are presented.     

Batch versus cyclic scheduling of flexible flow shops by mixed-integer programming

New mixed-integer programming models are proposed for deterministic batch or cyclic scheduling in flow shops with parallel machines and finite in-process buffers. Models for scheduling with all machines continuously available for processing throughout the entire scheduling horizon as well as for scheduling with an arbitrary pattern of machine availability due to pre-scheduled downtime events are provided. Numerical examples modelled after real-world flexible flow shop scheduling in electronics manufacturing are presented, and to compare the batch and cyclic schedules with continuous or with limited machine availability, results of computational experiments are reported.     

FMS Scheduling Simulation Based on an Evolution Algorithm

A FMS（flexible manufacturing system) scheduling algorithm based on an evolution algorithm (EA) is developed by intensively analyzing and researching the scheduling method in this paper.Many factors related to FMS scheduling are considered sufficiently.New explanations for a common kind of the encoding model are given.The rationality of encoding model is ensured by designing a set of new encoding methods,while the simulation experiment is performed.The results show that a FMS scheduling optimum problem with multi-constraint conditions can be effectively solved by a FMS scheduling simulation model based on EA.Comparing this method with others,this algorithm has the advantage of good stability and quick convergence.     

Scheduling manufacturing systems for delayed product differentiation in agile manufacturing

Production of customized products to respond to changing markets in a short time and at a low cost for agile manufacturing can be implemented with delayed product differentiation in a manufacturing system. The successful implementation of delayed product differentiation lies in efficient scheduling of the manufacturing system. Scheduling problems in implementing delayed product differentiation in a general flexible manufacturing system are defined, formulated and solved here. The manufacturing system consists of two stages: machining and assembly. At the machining stage, a single machine is used to produce standard component parts for assembly products. These parts are then assembled at the assembly stage by multiple identical assembly stations to form customized products. The products to be produced in the system are characterized by their assembly sequences represented by digraphs. The scheduling problem is to determine the sequence of products to be produced in the system so that the maximum completion time (makespan) is minimized for any given number of assembly stations at the assembly stage. Based on the representation of assembly sequence of the products, three production modes are defined: production of a single product with a simple assembly sequence ; production of a single product with a complex assembly sequence ; and production of N products . According to the three defined production modes, the associated scheduling problems are defined as G s scheduling problems, G c scheduling problems and N-product scheduling problems, respectively. Optimal and heuristic methods for solving the scheduling problems are developed. The computational experiment shows that the heuristics provide good solutions to the scheduling problems.     

具有工序顺序柔性的车间调度问题研究综述

某些加工车间在生产过程中具有多种柔性,工序顺序柔性就是其中重要的一种。通过对具有工序顺序柔性的车间调度问题的优化求解,能够极大地提高生产效率,节约生产成本。本文对具有工序顺序柔性的车间调度问题的研究现状进行整理分析,主要包括混合车间调度问题(mixed shop scheduling problem, MSP)、分组车间调度问题(group shop scheduling problem, GSP)和部分车间调度问题(partial shop scheduling problem, PSP)。最后,指出了具有工序顺序柔性的车间调度问题的发展前景及发展方向。     

Environmental-impact reduction through simultaneous design, scheduling, and operation

Processing facilities are normally designed with sufficient flexibility to handle nominal variations. When the process features planned changes in feedstock and products, scheduling is often used to optimize process operation. Proper scheduling may be limited to existing design or may entail retrofitting. Traditionally, economic objectives have served as the primary drivers for the design, retrofitting, and scheduling of industrial processes. Once a base design and scheduling plan have been established, environmental issues are addressed in many cases as an afterthought. As a result of this sequential approach, valuable synergisms and tradeoffs of economic and environmental objectives are often missed. The objective of this study is to develop a new approach to design and scheduling with economic and environmental objectives. Specifically, this study introduces a systematic framework and the associated mathematical formulation for simultaneous process design and scheduling while simultaneously addressing economic and environmental objectives. Therefore, this study establishes two types of proper tradeoffs (a) between design and scheduling and (b) between economic and environmental objectives. The environmental issues pertaining to the parameterized process retrofitting, scheduling, and operation strategies are simultaneously considered along with the environmental impact of these changes. An optimization formulation is developed for the case of project schedule while allowing design retrofitting changes that include new environmental units and modification of design and operating conditions in the process (without new process units). Also, a process model with the appropriate level of relevant details is included in the formulation. The projected schedule is discretized to allow for a multiperiod formulation with algebraic equations. The resulting framework identifies opportunities for synergism between the economic and environmental objectives. It also determines points of diminishing return beyond which tradeoffs between economic and environmental objectives are established. The devised procedure is illustrated with a case study on an oil refinery with scheduling of different products and the design of an environmental system that addresses NO _x emission.     

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management. Project scheduling problems depend on precedence relationships and resource constraints, in addition to some other limitations for achieving a subset of goals. Project scheduling problems are dependent on many limitations, including limitations of precedence relationships, resource constraints, and some other limitations for achieving a subset of goals. Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required, which are known and stable during the implementation process. The concept of deterministic project scheduling conflicts with real situations, in which in many cases, some data on the activity' s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations. Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us. We use the multi-mode resource allocation and scheduling model that takes into account the dynamicity features of all parameters, that is, the scheduling process must be flexible to dynamic environment features. In this paper, we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations, in which we apply the proposed heuristic rules (PHR) for scheduling multi-mode resource-constrained projects. Five projects are considered test problems for the PHR. The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems. The results in many cases of the proposed priority rules are very promising, where they achieve better scheduling dates in many test case problems and the same results for the others. The proposed model is based on the dynamic features for project topography.     

Rescheduling parallel machines with stepwise increasing tardiness and machine assignment stability objectives

Nervousness in machine assignments during rescheduling can cause problems for the implementation of a scheduling system. This paper examines rescheduling due to the arrival of new jobs to the system. Parallel machine scheduling problems with stepwise increasing tardiness cost objectives, non-zero machine ready times, constraints that limit machine reassignments, and machine reassignment costs are considered. Simulation experiments and individual scheduling problems indicate that nervousness can be controlled at a low cost in some parallel machine scheduling environments. The rescheduling problems in the simulation are solved with a branch-and-price algorithm. Significant gains in schedule stability can be achieved by selecting the alternative optimal solution with the fewest machine reassignments.     

Block spatial scheduling modelling and application in shipbuilding

With the wide application of module-shipbuilding technology, problems related to block spatial scheduling occur in various working areas, and this restricts the productivity of shipbuilding. To address the problems and to obtain the optimum block sequence and spatial layout, typical block features and work plates were investigated. A heuristic spatial scheduling model was established based on the investigation and proposed strategies with the objective to minimise makespan. With the heuristic algorithm, a block spatial scheduling system was developed and implemented with real data from a large ship. Through the spatial scheduling system, visual results of daily block layouts and progress charts for all blocks can be easily obtained and work orders can also be created for site workers. Several other spatial scheduling methods are described and compared with the above-mentioned heuristic algorithm. The result shows that the heuristic algorithm is better than Cplex and a genetic algorithm in solving large-scale block scheduling, and the heuristic algorithm is better than a grid algorithm and manual scheduling in all aspects such as makespan, utilisation of work plates, runtime of scheduling and on-time delivery. The developed block spatial scheduling system is applied in a block production shop of a modern shipyard and shows good performance.     

Evaluation of the Shortest Processing Time Scheduling Rule with Truncation Process

This paper discusses the development of a scheduling rule and summarizes the results of the evaluation of its performance with respect to some tardiness related criteria. Studies done on job shop scheduling indicated that the simple dispatching rules which mostly perform well with respect to a criterion of performance may have undesirable results with respect to other criteria. In this paper, a scheduling rule with truncation process called SPT-T is introduced and studied. Simulation results showed that the shortcomings of simple dispatching rules are remedied by using the SPT-T scheduling rule.     

采购与多层生产计划问题的协同优化

针对生产与采购这两项企业的重要活动,建立了一种采购计划和多层生产计划的集成优化模型,将采购计划、批量计划以及作业排序这三层计划问题进行综合决策。为求解该问题,设计了一种遗传算法和网络优化方法相结合的协同优化策略,遗传算法中每一个个体同时包含了批量计划和作业排序,并调用网络优化模型得出订购策略。数值仿真实验显示了提出的方法求解该类集成优化问题的良好性能。通过与独立优化方法进行比较,显示了协同优化策略的优越性。     

Production loss functions and subjective assessments of forecast errors: untapped sources for effective master production scheduling

Master production scheduling is complicated by demand uncertainty. The problem from uncertain forecasts is scheduling either too few or too many components relative to actual demand. To cope with this problem, schedulers often form judgments about future forecasts and they adapt production schedules to reflect beliefs and opinions about forecast errors. The research literature on scheduling has largely ignored formal methods for capturing these informal judgments and injecting them explicitly, rather than informally, into the master scheduling process. The current research demonstrates a method for using subjective assessments of forecast accuracy to improve master scheduling. First, a production loss function is derived using performance data from computer simulations of the production environment. Second, subjective assessments of forecasts errors are integrated with the loss function to reveal how forecasts should be adjusted to minimize expected scheduling losses. The procedure enhances intuitive judgmental scheduling; it reveals how managerial beliefs can be formally used to intentionally and optimally bias forecasts. In applying the procedure to 44 simulated MRP configurations, the optimally-biased forecasts are superior to unadjusted forecasts and provide an objective benchmark for using judgmental adjustments. The results demonstrate opportunities for enhancing master schedules by using subjective assessments of forecasts compared with scheduling without subjective assessments.     

Multi-Project Scheduling: Analysis of Project Performance

Application of heuristic solution procedures to the resource-constrained, multi-project scheduling problem is analyzed under equal and unequal penalties. The performance of ten scheduling rules is categorized with respect to four project summary measures, namely, resource-constrainedness, location of the peak requirements, and problem size. It is shown that the choice of a scheduling rule can be based upon the resource-constrainedness, problem size, and penalty. These results are based on scheduling, in detail, over 3000 multi-project scheduling problems, each containing three projects and from 24 to 66 activities.