Parallel Machine System Research Articles

Synchronisation of operations and maintenance in distributed unrelated parallel machine systems: a hierarchical optimisation framework

ABSTRACT Synchronisation of operations and maintenance means that production and maintenance departments work together effectively to achieve integrated optimisation of production scheduling and maintenance activities. This paper addresses such an integrated optimisation problem towards distributed unrelated parallel machine systems, where deteriorating processing time and machine failures are considered. For the trade-off between production and maintenance to obtain a minimal makespan in the worst-case scenario, a hierarchical optimisation framework with reinforcement learning-based encoder and knowledge-based intelligent optimiser (HOFRK) is developed. Experimental results show that HOFRK can be treated as an excellent optimiser for enterprise information systems to solve the proposed problem.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. Furthermore, we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it. In this approach, the multi-verse optimization is adopted to find favorable solutions from the huge solution domain, while the stochastic simulation method is employed to assess them. By conducting comparison experiments on test problems, it can be verified that the developed approach has better performance in coping with the considered problem, compared to two classic multi-objective evolutionary algorithms.

작업자 1명이 셋업을 수행하는 이종병렬기계에서 조기 및 지연 완료를 최소화하는 생산일정계획

Purpose This research deals with a scheduling problem that minimizes weighted sum of earliness and tardiness penalties in a single setup-operator and non-identical parallel machine system. Methods We first present a mixed integer linear programming formulation for the problem, and then, show the optimal solutions for relatively small problems can be easily found with the model and a commercial optimization software. However, since the problem is NP-hard and the size of a real problem can be large, we propose three heuristic algorithms including genetic algorithm to solve the practical big-size problems in a reasonable computational time. Results Through the computational experiments we found the heuristic algorithms show very good performances for the practical big-size problems. Conclusion The heuristic procedures proposed in this study can easily be used in the real situations.

Two-stage parallel speed-scaling machine scheduling under time-of-use tariffs

As one of the demand-side programs, time-of-use (TOU) tariffs brings opportunities of maintaining power grid stability for electricity providers and chances of energy conservation for manufacturers, but it also brings challenge for enterprises to optimize scheduling schemes. This paper studies a two-stage parallel machine scheduling problem under TOU to minimize total electricity costs. The two-stage parallel machine system is composed of identical parallel speed-scaling machines at stage 1 and unrelated parallel machines at stage 2. The key issues lie in assigning a group of jobs to a set of parallel machines at each stage and choosing the appropriate processing speed for all jobs at stage 1, and then determining the interval of processing time for jobs on each selected machine. To solve this problem, a new continuous-time mixed-integer linear programming model is formulated. According to the characteristics of this model, a tabu search-greedy insertion hybrid (TS-GIH) algorithm is designed, which realizes job-machine assignment based on load balancing principle, job insertion with greedy mechanism as well as movement and speed adjustment strategies to find more suitable positions for jobs. The effectiveness of the proposed TS-GIH is demonstrated by comparing with CLPEX and improved genetic algorithm (IGA) through real-life and randomly generated instances. The results show that TS-GIH can realize the trade-off between computation time and solution quality. Compared with CLPEX, the computation time of TS-GIH is significantly less, and the solution quality is much better than IGA.

A meta-heuristic algorithm for integrated optimization of dynamic resource allocation planning and production scheduling in parallel machine system

With the wide application of advanced information technology and intelligent equipment in the manufacturing system, the decisions of design and operation have become more interdependent and their integration optimization has gained great concerns from the community of operational research recently. This article investigates an optimization problem of integrating dynamic resource allocation and production schedule in a parallel machine environment. A meta-heuristic algorithm, in which heuristic-based partition, genetic-based sampling, promising index calculation, and backtracking strategies are employed, is proposed for solving the investigated integration problem in order to minimize the makespan of the manufacturing system. The experimental results on a set of random-generated test instances indicate that the presented model is effective and the proposed algorithm exhibits the satisfactory performance that outperforms two state-of-the-art algorithms from literature.

작업자 1명이 내부 및 외부 셋업을 수행하는 이종병렬기계의 일정계획

This research deals with a scheduling problem that minimizes makespan in a single setup-operator and non-identical parallel machine system, in which the machine dependent setup time of each job is divided into internal and external setup times. The internal setup refers to those setup actions that inevitably require that the machine be stopped, and the external setup refers to actions that can be taken while the machine is operating. We first present a mixed integer linear programming formulation for the problem, and using this formulation, the optimal solutions for relatively small problems can be easily found. However, since the problem is NP-hard and the size of a real problem can be large, we propose a genetic algorithm based heuristic to solve the practical big-size problems in a reasonable computational time. To assess the performance of the algorithm, we conduct a computational experiment, from which we found the heuristic algorithm shows very good performances.

Better Algorithm for Order On-Line Scheduling on Uniform Machines

In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.

Job scheduling and resource allocation in parallel‐machine system via a hybrid nested partition method

Scheduling problems with resource allocation have received much attention in the academic and industrial communities in recent years. This study addresses a parallel‐machine scheduling problem with resource allocation under the objective of minimizing the makespan, where jobs need an additional resource that is allocated to machines in advance. The processing time of jobs is a function of the amount of allocated resources on their corresponding machines. In order to deal with this problem, three decisions must be made, i.e. resource allocation among machines, job assignment on machines, and job sequence on each machine. To solve this problem efficiently, a constructive heuristic approach and a hybrid nested partition method are designed to make these three decisions. Simulation experiments are carried out on a set of instances, and two existing algorithms are chosen to be compared with the proposed algorithms. Experimental results show that the proposed algorithms are promising in coping with this problem. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Integrated production and maintenance planning for parallel machine system considering cost of rejection

Production scheduling and maintenance planning have interdependencies but been often considered and optimized independently in practice and in the literature. Furthermore, product quality has direct relationship with maintenance planning. This paper proposes an integrated approach for production scheduling and maintenance planning for parallel machine system considering the effect of cost of rejection. The approach aims to determine optimal production schedule and maintenance plan such that overall operations cost is minimized. A simulation-based optimization approach is used to solve the problem. A numerical investigation is performed to illustrate the approach. The integrated approach shows between 0.6 and 35.8% improvement in term of overall operations cost over independent approach for various scenarios. The results indicate that simultaneous consideration of production scheduling and maintenance planning results into better system performance.

Total tardiness minimization in a parallel machine system with flexible periodic maintenance

This paper addresses the total tardiness minimization problem in a manufacturing environment made by m uniform parallel processors subjected to regular maintenance activities. According to the so-called flexible periodic maintenance strategy, the time between two consecutive maintenance periods on each machine must be lower than or equal to a certain time value. In order to cope with such scheduling issue, a hybrid metaheuristic procedure integrating features from genetic algorithm and local search is proposed. The devised optimization algorithm is compared against two alternative metaheuristics on the basis of two separate benchmarks of test cases, involving small- and large-sized instances, respectively. For small-sized examples, optimal solutions provided by a specifically developed mixed integer linear programming model are taken as reference. Numerical results, also supported by a non-parametric statistical analysis, demonstrate the superiority of the proposed optimization algorithm in solving the investigated scheduling problem.

On-Line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

Minimizing the total completion time on a parallel machine system with tool changes

In this paper, the identical parallel machine scheduling problem with periodic tool changes due to wear is addressed under the total completion time minimization objective. Due to machine availability restrictions induced by tool replacement operations, the problem is NP-hard in the strong sense. A mixed integer linear programming (MILP) model has been developed with the aim to provide the global optimum for small-sized test cases. Furthermore, a hybrid metaheuristic procedure based on genetic algorithms has been specifically designed to cope with larger instances. A comprehensive experimental analysis supported by a non-parametric statistical test has been fulfilled to select the best metaheuristic configuration in terms of decoding strategy and parameters driving the search mechanism as well. Then, the proposed optimization procedure has been compared with three alternative methods arising from the relevant literature on the basis of a wide benchmark of test cases. The obtained results, also supported by a proper statistical analysis, demonstrate the effectiveness of the proposed approach for solving the tool change scheduling problem at hand.

작업순서 의존형 준비시간을 갖는 이종병렬기계의 휴리스틱 일정계획

This research deals with a problem that minimizes makespan in a non-identical parallel machine system with sequence and machine dependent setup times and machine dependent processing times. We first present a new mixed integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is large, we propose four heuristic algorithms including genetic algorithm based heuristics to solve the practical big-size problems in a reasonable computational time. To assess the performance of the algorithms, we conduct a computational experiment, from which we found the heuristic algorithms show different performances as the problem characteristics are changed and the simple heuristics show better performances than genetic algorithm based heuristics for the case when the numbers of jobs and/or machines are large.

Scheduling parallel machines with single vehicle delivery

We investigate the integrated production and distribution scheduling problem in a supply chain. The manufacturer's production environment is modeled as a parallel machine system. A single capacitated vehicle is employed to deliver products in batches to multiple customers. The scheduling problem can also be viewed as either parallel machines with delivery considerations or a flexible flowshop. Different inventory holding costs, job sizes (volume or storage space required in the transportation unit), and job priorities are taken into account. Efficient mathematical modeling and near-optimal heuristic approaches are presented for minimizing total weighted completion time.

Online scheduling for jobs with nondecreasing release times and similar lengths on parallel machines

In this paper, we consider semi-online scheduling problems on parallel identical machine system which result from the online scheduling problem for jobs with arbitrary release times by knowing part information of the release times or processing sizes. The conditions are informed that the release times are nondecreasing sequence and the processing lengths are similar in with . An upper bound of the competitive ratio of List Scheduling (LS) algorithm is given and it is proved that the LS schedule is optimal when for any . Furthermore, for we present a tight bound when . We also show that the competitive ratio of the LS algorithm is improved when additional information is known by letting each job have release time zero. However, if the processing lengths are arbitrary, then no impact on the competitive ratio of the LS algorithm occurs after imposing the additional information.

A hybrid flowshop scheduling model considering dedicated machines and lot-splitting for the solar cell industry

This paper studies a solar cell industry scheduling problem, which is similar to traditional hybrid flowshop scheduling (HFS). In a typical HFS problem, the allocation of machine resources for each order should be scheduled in advance. However, the challenge in solar cell manufacturing is the number of machines that can be adjusted dynamically to complete the job. An optimal production scheduling model is developed to explore these issues, considering the practical characteristics, such as hybrid flowshop, parallel machine system, dedicated machines, sequence independent job setup times and sequence dependent job setup times. The objective of this model is to minimise the makespan and to decide the processing sequence of the orders/lots in each stage, lot-splitting decisions for the orders and the number of machines used to satisfy the demands in each stage. From the experimental results, lot-splitting has significant effect on shortening the makespan, and the improvement effect is influenced by the processing time and the setup time of orders. Therefore, the threshold point to improve the makespan can be identified. In addition, the model also indicates that more lot-splitting approaches, that is, the flexibility of allocating orders/lots to machines is larger, will result in a better scheduling performance.

Scheduling with an outsourcing option on both manufacturer and subcontractors

This paper addresses a single-stage scheduling problem with outsourcing allowed where each job can be either scheduled for in-house production or outsourced to one of the outside subcontractors available. The manufacturer has an unrelated parallel machine system, and each subcontractor has its own single machine. Subcontractors are capable to process all the jobs. Unlike most of past research, our study considers the joint scheduling of both in-house and outsourced jobs simultaneously. The objective is to minimize sum of the total weighted completion time and total outsourcing cost. An integer programming formulation is presented and then improved through an optimality property on job orders. A heuristic algorithm is also introduced to decompose the problem into smaller and easier subproblems and solve them to optimality.

Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

The problem of state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system is considered, based on the limited signal availability (only the moving platform displacement measurements are assumed available). Unknown velocity signals are estimated via a nonlinear robust observer that is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and that guarantees global exponential stability of the observation error. A proportional-derivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotical stability according to the Lyapunov analysis method and LaSalle's invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM. Modifications to the nonlinear observer and control law are discussed, that assure convergence of the position error and state observation error to zero when the upper bounds on the model uncertainties/disturbances are not known a priori.

Exact Analysis of a Two Stage Production Line with Parallel Unreliable Machines

This paper proposes a new analytical model of manufacturing system with two parallel machine workstations. The machines in the system are non-identical unreliable machines, and the processing times, failure times and repair times of the machines are assumed to be exponentially distributed. In this paper we for the first time give an exact model of two workstation parallel machine system. Case studies show the accuracy of the proposed model.

Comparing Lagrangian-based distributed algorithms for parallel machine scheduling problems

In this paper Lagrangian-based distributed algorithms for scheduling jobs on unrelated parallel machines are presented. In these algorithms, the scheduling process is the result of a cooperation process among several Decision Makers (DMs). DMs have a local knowledge of the system, and the possibility to decide which type of information to exchange each other. Our focus is to investigate the performance of different algorithms based on different knowledge degrees of the parallel machine system. The implementation issues and the effectiveness of the algorithms are analysed via simulation, in which problem instances with job dynamic arrivals are also considered.