Search results for: Machine scheduling

Authors: Jian Zheng, Yoshiyasu Takahashi, Yuichi Kobayashi, Tatsuhiro Sato

Abstract:

In the study, we present a conceptual framework for developing a scheduling system that can generate self-explanatory and easy-understanding schedules. To this end, a user interface is conceived to help planners record factors that are considered crucial in scheduling, as well as internal and external sources relating to such factors. A hybrid approach combining machine learning and constraint programming is developed to generate schedules and the corresponding factors, and accordingly display them on the user interface. Effects of the proposed system on scheduling are discussed, and it is expected that scheduling efficiency and system understandability will be improved, compared with previous scheduling systems.

Keywords: Constraint programming, Factors considered in scheduling, machine learning, scheduling system.

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Authors: Keqin Li

Abstract:

Given a parallel program to be executed on a heterogeneous computing system, the overall execution time of the program is determined by a schedule. In this paper, we analyze the worst-case performance of the list scheduling algorithm for scheduling tasks of a parallel program in a mixed-machine heterogeneous computing system such that the total execution time of the program is minimized. We prove tight lower and upper bounds for the worst-case performance ratio of the list scheduling algorithm. We also examine the average-case performance of the list scheduling algorithm. Our experimental data reveal that the average-case performance of the list scheduling algorithm is much better than the worst-case performance and is very close to optimal, except for large systems with large heterogeneity. Thus, the list scheduling algorithm is very useful in real applications.

Keywords: Average-case performance, list scheduling algorithm, mixed-machine heterogeneous computing system, worst-case performance.

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Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

Abstract:

There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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Authors: Farhad Kolahan, Vahid Kayvanfar

Abstract:

In this paper we address a multi-objective scheduling problem for unrelated parallel machines. In unrelated parallel systems, the processing cost/time of a given job on different machines may vary. The objective of scheduling is to simultaneously determine the job-machine assignment and job sequencing on each machine. In such a way the total cost of the schedule is minimized. The cost function consists of three components, namely; machining cost, earliness/tardiness penalties and makespan related cost. Such scheduling problem is combinatorial in nature. Therefore, a Simulated Annealing approach is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.

Keywords: Makespan, Parallel machines, Scheduling, Simulated Annealing

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Authors: Saleem Z. Ramadan, Gürsel A. Süer

Abstract:

In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper is concerned with minimization of mean tardiness and flow time in a real single machine production scheduling problem. Two variants of genetic algorithm as metaheuristic are combined with hyper-heuristic approach are proposed to solve this problem. These methods are used to solve instances generated with real world data from a company. Encouraging results are reported.

Keywords: Hyper-heuristics, evolutionary algorithms, production scheduling.

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Authors: H.-H. Doh, J.-M. Yu, Y.-J. Kwon, J.-H. Shin, H.-W. Kim, S.-H. Nam, D.-H. Lee

Abstract:

This paper suggests a decision tree based approach for flexible job shop scheduling with multiple process plans, i.e. each job can be processed through alternative operations, each of which can be processed on alternative machines. The main decision variables are: (a) selecting operation/machine pair; and (b) sequencing the jobs assigned to each machine. As an extension of the priority scheduling approach that selects the best priority rule combination after many simulation runs, this study suggests a decision tree based approach in which a decision tree is used to select a priority rule combination adequate for a specific system state and hence the burdens required for developing simulation models and carrying out simulation runs can be eliminated. The decision tree based scheduling approach consists of construction and scheduling modules. In the construction module, a decision tree is constructed using a four-stage algorithm, and in the scheduling module, a priority rule combination is selected using the decision tree. To show the performance of the decision tree based approach suggested in this study, a case study was done on a flexible job shop with reconfigurable manufacturing cells and a conventional job shop, and the results are reported by comparing it with individual priority rule combinations for the objectives of minimizing total flow time and total tardiness.

Keywords: Flexible job shop scheduling, Decision tree, Priority rules, Case study.

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

Abstract:

As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling. The research proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling. The paper concludes the challenges and improvement directions for Deep Reinforcement Learning-based resource scheduling algorithms.

Keywords: Resource scheduling, deep reinforcement learning, distributed system, artificial intelligence.

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Authors: M. Duran Toksarı, B. Uçarkuş

Abstract:

In this paper, we propose two algorithms to optimally solve makespan and total completion time scheduling problems with learning effect and job dependent delivery times in a single machine environment. The delivery time is the extra time to eliminate adverse effect between the main processing and delivery to the customer. In this paper, we introduce the job dependent delivery times for some single machine scheduling problems with position dependent learning effect, which are makespan are total completion. The results with respect to two algorithms proposed for solving of the each problem are compared with LINGO solutions for 50-jobs, 100-jobs and 150- jobs problems. The proposed algorithms can find the same results in shorter time.

Keywords: Delivery times, learning effect, makespan, scheduling, total completion time.

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Authors: D. Sumathi, P. Poongodi

Abstract:

Cloud Computing refers to applications delivered as services over the internet, and the datacenters that provide those services with hardware and systems software. These were earlier referred to as Software as a Service (SaaS). Scheduling is justified by job components (called tasks), lack of information. In fact, in a large fraction of jobs from machine learning, bio-computing, and image processing domains, it is possible to estimate the maximum time required for a task in the job. This study focuses on Trust based scheduling to improve cloud security by modifying Heterogeneous Earliest Finish Time (HEFT) algorithm. It also proposes TR-HEFT (Trust Reputation HEFT) which is then compared to Dynamic Load Scheduling.

Keywords: Software as a Service (SaaS), Trust, Heterogeneous Earliest Finish Time (HEFT) algorithm, Dynamic Load Scheduling.

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Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.

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Authors: Raksha Sharma, Vishnu Kant Soni, Manoj Kumar Mishra, Prachet Bhuyan

Abstract:

Grid computing is a form of distributed computing that involves coordinating and sharing computational power, data storage and network resources across dynamic and geographically dispersed organizations. Scheduling onto the Grid is NP-complete, so there is no best scheduling algorithm for all grid computing systems. An alternative is to select an appropriate scheduling algorithm to use in a given grid environment because of the characteristics of the tasks, machines and network connectivity. Job and resource scheduling is one of the key research area in grid computing. The goal of scheduling is to achieve highest possible system throughput and to match the application need with the available computing resources. Motivation of the survey is to encourage the amateur researcher in the field of grid computing, so that they can understand easily the concept of scheduling and can contribute in developing more efficient scheduling algorithm. This will benefit interested researchers to carry out further work in this thrust area of research.

Keywords: Grid Computing, Job Scheduling, ResourceScheduling.

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

Abstract:

The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: Flow-shop scheduling problem, makespan, Petri nets, state equation.

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Authors: Mohammad Mirabi

Abstract:

Flow-shop scheduling problem (FSP) deals with the scheduling of a set of jobs that visit a set of machines in the same order. The FSP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To meet the requirements on time and to minimize the make-span performance of large permutation flow-shop scheduling problems in which there are sequence dependent setup times on each machine, this paper develops one hybrid genetic algorithms (HGA). Proposed HGA apply a modified approach to generate population of initial chromosomes and also use an improved heuristic called the iterated swap procedure to improve initial solutions. Also the author uses three genetic operators to make good new offspring. The results are compared to some recently developed heuristics and computational experimental results show that the proposed HGA performs very competitively with respect to accuracy and efficiency of solution.

Keywords: Hybrid genetic algorithm, Scheduling, Permutationflow-shop, Sequence dependent

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Authors: Bita Tadayon, Nasser Salmasi

Abstract:

This research deals with a flexible flowshop scheduling problem with arrival and delivery of jobs in groups and processing them individually. Due to the special characteristics of each job, only a subset of machines in each stage is eligible to process that job. The objective function deals with minimization of sum of the completion time of groups on one hand and minimization of sum of the differences between completion time of jobs and delivery time of the group containing that job (waiting period) on the other hand. The problem can be stated as FFc / rj , Mj / irreg which has many applications in production and service industries. A mathematical model is proposed, the problem is proved to be NPcomplete, and an effective heuristic method is presented to schedule the jobs efficiently. This algorithm can then be used within the body of any metaheuristic algorithm for solving the problem.

Keywords: flexible flowshop scheduling, group processing, machine eligibility constraint, mathematical modeling.

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Authors: Anis Gharbi

Abstract:

This paper considers the problem of scheduling maintenance actions for identical aircraft gas turbine engines. Each one of the turbines consists of parts which frequently require replacement. A finite inventory of spare parts is available and all parts are ready for replacement at any time. The inventory consists of both new and refurbished parts. Hence, these parts have different field lives. The goal is to find a replacement part sequencing that maximizes the time that the aircraft will keep functioning before the inventory is replenished. The problem is formulated as an identical parallel machine scheduling problem where the minimum completion time has to be maximized. Two models have been developed. The first one is an optimization model which is based on a 0-1 linear programming formulation, while the second one is an approximate procedure which consists in decomposing the problem into several two-machine subproblems. Each subproblem is optimally solved using the first model. Both models have been implemented using Lingo and have been tested on two sets of randomly generated data with up to 150 parts and 10 turbines. Experimental results show that the optimization model is able to solve only instances with no more than 4 turbines, while the decomposition procedure often provides near-optimal solutions within a maximum CPU time of 3 seconds.

Keywords: Aircraft turbines, Scheduling, Identical parallel machines, 0-1 linear programming, Heuristic.

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Authors: M. Haddadzade, M. R. Razfar, M. Farahnakian

Abstract:

Integration of process planning and scheduling functions is necessary to achieve superior overall system performance. This paper proposes a methodology for integration of process planning and scheduling for prismatic component that can be implemented in a company with existing departments. The developed model considers technological constraints whereas available time for machining in shop floor is the limiting factor to produce multiple process plan (MPP). It takes advantage of MPP while guarantied the fulfillment of the due dates via using overtime. This study has been proposed to determinate machining parameters, tools, machine and amount of over time within the minimum cost objective while overtime is considered for this. At last the illustration shows that the system performance is improved by as measured by cost and compatible with due date.

Keywords: Due date, Integration, Multiple process plan, Process planning, Scheduling.

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Authors: R. Santhosh, T. Ravichandran

Abstract:

This paper evaluates the accrual based scheduling for cloud in single and multi-resource system. Numerous organizations benefit from Cloud computing by hosting their applications. The cloud model provides needed access to computing with potentially unlimited resources. Scheduling is tasks and resources mapping to a certain optimal goal principle. Scheduling, schedules tasks to virtual machines in accordance with adaptable time, in sequence under transaction logic constraints. A good scheduling algorithm improves CPU use, turnaround time, and throughput. In this paper, three realtime cloud services scheduling algorithm for single resources and multiple resources are investigated. Experimental results show Resource matching algorithm performance to be superior for both single and multi-resource scheduling when compared to benefit first scheduling, Migration, Checkpoint algorithms.

Keywords: Cloud computing, Scheduling, Migration, Checkpoint, Resource Matching.

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Authors: J. Kaabi, Y. Harrath

Abstract:

This paper studied the flow shop scheduling problem under machine availability constraints. The machines are subject to flexible preventive maintenance activities. The nonresumable scenario for the jobs was considered. That is, when a job is interrupted by an unavailability period of a machine it should be restarted from the beginning. The objective is to minimize the total tardiness time for the jobs and the advance/tardiness for the maintenance activities. To solve the problem, a genetic algorithm was developed and successfully tested and validated on many problem instances. The computational results showed that the new genetic algorithm outperforms another earlier proposed algorithm. 

Keywords: Flow shop scheduling, maintenance, genetic algorithm, priority rules.

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Authors: Farzad Abtahi, Sahar Khanmohamadi, Bahram Sadeghi Bigham

Abstract:

Wireless channels are characterized by more serious bursty and location-dependent errors. Many packet scheduling algorithms have been proposed for wireless networks to guarantee fairness and delay bounds. However, most existing schemes do not consider the difference of traffic natures among packet flows. This will cause the delay-weight coupling problem. In particular, serious queuing delays may be incurred for real-time flows. In this paper, it is proposed a scheduling algorithm that takes traffic types of flows into consideration when scheduling packets and also it is provided scheduling flexibility by trading off video quality to meet the playback deadline.

Keywords: Data communication, Real-time, Scheduling, Video transport.

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Authors: Samia Dardouri, Ridha Bouallegue

Abstract:

Scheduling is the process of dynamically allocating physical resources to User Equipment (UE) based on scheduling algorithms implemented at the LTE base station. Various algorithms have been proposed by network researchers as the implementation of scheduling algorithm which represents an open issue in Long Term Evolution (LTE) standard. This paper makes an attempt to study and compare the performance of PF, MLWDF and EXP/PF scheduling algorithms. The evaluation is considered for a single cell with interference scenario for different flows such as Best effort, Video and VoIP in a pedestrian and vehicular environment using the LTE-Sim network simulator. The comparative study is conducted in terms of system throughput, fairness index, delay, packet loss ratio (PLR) and total cell spectral efficiency.

Keywords: LTE, Multimedia flows, Scheduling algorithms.

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Authors: Yi Zhang, Quan Zhou, Jun Li, Yanlang Hu

Abstract:

Scheduling algorithm is a key technology in satellite switching system with input-buffer. In this paper, a new scheduling algorithm and its realization are proposed. Based on Crossbar switching fabric, the algorithm adopts serial scheduling strategy and adjusts the output port arbitrating strategy for the better equity of every port. Consequently, it increases the matching probability. The algorithm can greatly reduce the scheduling delay and cell loss rate. The analysis and simulation results by OPNET show that the proposed algorithm has the better performance than others in average delay and cell loss rate, and has the equivalent complexity. On the basis of these results, the hardware realization and simulation based on FPGA are completed, which validate the feasibility of the new scheduling algorithm.

Keywords: Scheduling algorithm, input-buffer, serial scheduling, hardware design.

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Authors: Sangsuree Vasupongayya

Abstract:

Fair share is one of the scheduling objectives supported on many production systems. However, fair share has been shown to cause performance problems for some users, especially the users with difficult jobs. This work is focusing on extending goaloriented parallel computer job scheduling policies to cover the fair share objective. Goal-oriented parallel computer job scheduling policies have been shown to achieve good scheduling performances when conflicting objectives are required. Goal-oriented policies achieve such good performance by using anytime combinatorial search techniques to find a good compromised schedule within a time limit. The experimental results show that the proposed goal-oriented parallel computer job scheduling policy (namely Tradeofffs( Tw:avgX)) achieves good scheduling performances and also provides good fair share performance.

Keywords: goal-oriented parallel job scheduling policies, fairshare.

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Authors: Sahar Sohrabi

Abstract:

The emergence of Cloud data centers has revolutionized the IT industry. Private Clouds in specific provide Cloud services for certain group of customers/businesses. In a real-time private Cloud each task that is given to the system has a deadline that desirably should not be violated. Scheduling tasks in a real-time private CLoud determine the way available resources in the system are shared among incoming tasks. The aim of the scheduling policy is to optimize the system outcome which for a real-time private Cloud can include: energy consumption, deadline violation, execution time and the number of host switches. Different scheduling policies can be used for scheduling. Each lead to a sub-optimal outcome in a certain settings of the system. A Bayesian Scheduling strategy is proposed for scheduling to further improve the system outcome. The Bayesian strategy showed to outperform all selected policies. It also has the flexibility in dealing with complex pattern of incoming task and has the ability to adapt.

Keywords: Bayesian, cloud computing, real-time private cloud, scheduling.

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Authors: Shinpei Kato, Nobuyuki Yamasaki

Abstract:

This paper proposes a scheduling scheme using feedback control to reduce the response time of aperiodic tasks with soft real-time constraints. We design an algorithm based on the proposed scheduling scheme and Total Bandwidth Server (TBS) that is a conventional server technique for scheduling aperiodic tasks. We then describe the feedback controller of the algorithm and give the control parameter tuning methods. The simulation study demonstrates that the algorithm can reduce the mean response time up to 26% compared to TBS in exchange for slight deadline misses.

Keywords: Real-Time Systems, Aperiodic Task Scheduling, Feedback-Control Scheduling, Total Bandwidth Server.

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Authors: Seyed Habib A. Rahmati

Abstract:

During last decades, developing multi-objective evolutionary algorithms for optimization problems has found considerable attention. Flexible job shop scheduling problem, as an important scheduling optimization problem, has found this attention too. However, most of the multi-objective algorithms that are developed for this problem use nonprofessional approaches. In another words, most of them combine their objectives and then solve multi-objective problem through single objective approaches. Of course, except some scarce researches that uses Pareto-based algorithms. Therefore, in this paper, a new Pareto-based algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our considered objectives are makespan, critical machine work load, and total work load of machines. The proposed algorithm is also compared with one the best Pareto-based algorithms of the literature on some multi-objective criteria, statistically.

Keywords: Scheduling, Flexible job shop scheduling problem, controlled elitism non-dominated sorting genetic algorithm

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Authors: Rajeswari Raju, Saiful Nizam Warris, Hazlifah Mohd Rusli

Abstract:

Developing a university course schedule is difficult. This is due to the limitations in the resources available. The process is made even harder with different faculties or departments having different ways of stating their schedule requirements. The person in charge of taking the schedule requirements and turning them into a proper course schedule is not only burden with the task of allocating the appropriate classes and time to lecturers and students, they also need to understand the schedule requirements. Therefore a scheduling support system named SATA is developed to assist ICRESS in the course scheduling process. SATA has been put to use for several semesters and the results have been encouraging. It won a bronze medal in the 2008 Invention, Innovation and Design competition (IID-08) and has been submitted to be patented in October 2008

Keywords: Course Scheduling, Scheduling Tool Aid.

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Authors: Yongxian Jin, Jingzhou Huang

Abstract:

In an open real-time system environment, the coexistence of different kinds of real-time and non real-time applications makes the system scheduling mechanism face new requirements and challenges. One two-level scheduling scheme of the open real-time systems is introduced, and points out that hard and soft real-time applications are scheduled non-distinctively as the same type real-time applications, the Quality of Service (QoS) cannot be guaranteed. It has two flaws: The first, it can not differentiate scheduling priorities of hard and soft real-time applications, that is to say, it neglects characteristic differences between hard real-time applications and soft ones, so it does not suit a more complex real-time environment. The second, the worst case execution time of soft real-time applications cannot be predicted exactly, so it is not worth while to cost much spending in order to assure all soft real-time applications not to miss their deadlines, and doing that may cause resource wasting. In order to solve this problem, a novel two-level real-time scheduling mechanism (including scheduling profile and scheduling algorithm) which adds the process of dealing with soft real-time applications is proposed. Finally, we verify real-time scheduling mechanism from two aspects of theory and experiment. The results indicate that our scheduling mechanism can achieve the following objectives. (1) It can reflect the difference of priority when scheduling hard and soft real-time applications. (2) It can ensure schedulability of hard real-time applications, that is, their rate of missing deadline is 0. (3) The overall rate of missing deadline of soft real-time applications can be less than 1. (4) The deadline of a non-real-time application is not set, whereas the scheduling algorithm that server 0 S uses can avoid the “starvation" of jobs and increase QOS. By doing that, our scheduling mechanism is more compatible with different types of applications and it will be applied more widely.

Keywords: Hard real-time, two-level scheduling profile, open real-time system, non-distinctive schedule, soft real-time

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Authors: Oscar Fernandez-Flores, Tony Speer, Rodney Day

Abstract:

This paper identifies five key design characteristics of production scheduling software systems in printed circuit board (PCB) manufacturing. The authors consider that, in addition to an effective scheduling engine, a scheduling system should be able to process a preventative maintenance calendar, to give the user the flexibility to handle data using a variety of electronic sources, to run simulations to support decision-making, and to have simple and customisable graphical user interfaces. These design considerations were the result of a review of academic literature, the evaluation of commercial applications and a compilation of requirements of a PCB manufacturer. It was found that, from those systems that were evaluated, those that effectively addressed all five characteristics outlined in this paper were the most robust of all and could be used in PCB manufacturing.

Keywords: Decision-making, ERP, PCB, scheduling.

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Authors: Khalid Abd, Kazem Abhary, Romeo Marian

Abstract:

Multiple criteria decision making (MCDM) is an approach to ranking the solutions and finding the best one when two or more solutions are provided. In this study, MCDM approach is proposed to select the most suitable scheduling rule of robotic flexible assembly cells (RFACs). Two MCDM approaches, Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are proposed for solving the scheduling rule selection problem. The AHP method is employed to determine the weights of the evaluation criteria, while the TOPSIS method is employed to obtain final ranking order of scheduling rules. Four criteria are used to evaluate the scheduling rules. Also, four scheduling policies of RFAC are examined to choose the most appropriate one for this purpose. A numerical example illustrates applications of the suggested methodology. The results show that the methodology is practical and works in RFAC settings.

Keywords: AHP, TOPSIS, Scheduling rules selection

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