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The scheduling problem of PCBs for multiple non-identical parallel machines

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第3期158卷 577-594页

作者： Van Hop, N Nagarur, NN SUNY Binghamton Thomas Watson Sch Engn & Appl Sci Dept Syst Sci & Ind Engn Binghamton NY 13902 USA Thammasat Univ Sirindhorn Int Inst Technol Ind Engn Program Klongluang 12121 Pathumthani Thailand

The scheduling problem of n printed circuit boards (PCBs) for m non-identical parallel machines is considered in this paper. The problem has to deal with three issues: (i) classifying the PCBs into m groups corresponding to m machines, (ii) sequencing the boards for each machine, and (iii) component switching (component unloading/loading) from the machine magazine. A general objective is to minimize the total makespan, which is shown here to be the same as minimizing the maximum of number of component switches. The complete problem is complex, and is usually dealt in stages, which may not yield a good solution. We model the problem in an integrated manner using weighted multiple objectives to deal with grouping of the boards, load balancing at each machine, board sequencing and component switching at a machine. A composite genetic algorithm is developed to solve this multi-objective problem. The integrated solution is encoded as a string of pair values for each group of boards. The first number indicates the board membership in a group, and the second one represents the sequencing position of a board in that group. A new population of solutions is generated by using both binary genetic operators for grouping and genetic operators for board sequencing. A fitness function evaluates workload balancing, board similarities and total setup time simultaneously. Experiments are designed and run to test the proposed methodology, and the results show that the solutions are efficient, and are obtained within a reasonable amount of time. (C) 2003 Elsevier B.V. All rights reserved.

关键词： scheduling genetic algorithms PCB assembly non-identical parallel machines multiple criteria

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Optimizing multiple qualifications of products on non-identical parallel machines

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COMPUTERS & OPERATIONS RESEARCH 2022年 144卷 1页

作者： Perraudat, Antoine Dauzere-Peres, Stephane Vialletelle, Philippe Univ Clermont Auvergne Dept Mfg Sci & Logist CMP CNRSMines St EtienneUMR 6158 LIMOS 880 Route Mimet F-13120 Gardanne France STMicroelect Crolles 850 Rue Jean Monnet F-38920 Crolles France BI Norwegian Business Sch Dept Accounting & Operat Management N-0484 Oslo Norway

In some manufacturing contexts, such as semiconductor manufacturing, machines must be qualified, or eligible, to process a product, and machines cannot be qualified for all products. This paper investigates the problem of optimizing a given number of new qualifications of products to machines to maximize a flexibility measure that evaluates the balance of the qualification configuration of a work center in terms of utilization rate of machines on a set of non-identical parallel machines. Motivated by empirical observations, new solution approaches, notably inspired by heuristics for discrete location problems and based on the analysis of dual variables, are proposed and compared on industrial data from a semiconductor manufacturing facility and on randomly instances. The use of dual variables leads to heuristics that are effective both in terms of solution quality and computational time. The best proposed approach is currently used in the decision support system of a semiconductor manufacturing facility.

关键词： Flexible manufacturing systems Qualification management non-identical parallel machines Optimization Heuristics

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Optimal allocation and processing time decisions on non-identical parallel CNC machines:: ε-constraint approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期183卷 591-607页

作者： Gurel, Sinan Akturk, M. Selim Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey

When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. In this paper, we deal with making optimal machine-job assignments and processing time decisions so as to minimize total manufacturing cost while the makespan being upper bounded by a known value, denoted as E-constraint approach for a bicriteria problem. We then give optimality properties for the resulting single criterion problem. We provide alternative methods to compute cost lower bounds for partial schedules, which are used in developing an exact (branch and bound) algorithm. For the cases where the exact algorithm is not efficient in terms of computation time, we present a recovering beam search algorithm equipped with an improvement search procedure. In order to find improving search directions, the improvement search algorithm uses the proposed cost bounding properties. Computational results show that our lower bounding methods in branch and bound algorithm achieve a significant reduction in the search tree size that we need to traverse. Also, our recovering beam search and improvement search heuristics achieve solutions within 1% of the optimum on the average while they spent much less computational effort than the exact algorithm. (c) 2006 Elsevier B.V. All rights reserved.

关键词： scheduling controllable processing times manufacturing cost makespan non-identical parallel machines

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Scheduling non-identical parallel batch processing machines to minimize total weighted tardiness using particle swarm optimization

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COMPUTERS & INDUSTRIAL ENGINEERING 2017年 113卷 425-436页

作者： Hulett, Maria Damodaran, Purushothaman Amouie, Mahbod Univ Miami Dept Management Sci Miami FL 33124 USA Northern Illinois Univ Dept Ind & Syst Engn De Kalb IL 60115 USA Norfolk Southern Corp Norfolk VA 23510 USA

This research aims at scheduling a set of Batch Processing machines (BPMs) used to test printed circuit boards in an electronics manufacturing facility. The facility assembles and tests printed circuit boards (or jobs) of different sizes. The BPMs can process a batch of jobs as long as the total size of all the jobs in a batch does not exceed the machine's capacity. The objective is to minimize the total weighted tardiness, thereby minimize the total penalty incurred by the company for late deliveries. The problem under study is known to be NP-hard. Consequently, a Particle Swarm Optimization (PSO) algorithm has been proposed. Likewise, a heuristic is proposed to simultaneously group the jobs into batches and schedule them on a machine. The effectiveness of the PSO algorithm is examined using random instances and the results were compared to a differential evolution algorithm and a commercial solver used to solve a mixed-integer linear program. Experimental results indicate that the PSO algorithm is very competitive on smaller problem instances and reports better quality solutions in a short time on larger problem instances.

关键词： Batch processing machines non-identical parallel machines Total weighted tardiness Particle Swarm Optimization

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A Benders decomposition approach for order acceptance and scheduling problem: a robust optimization approach

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COMPUTATIONAL & APPLIED MATHEMATICS 2017年第4期36卷 1471-1515页

作者： Emami, Saeed Moslehi, Ghasem Sabbagh, Mohammad Isfahan Univ Technol Dept Ind & Syst Engn Esfahan *** Iran

In this paper, we consider a simultaneous order acceptance and scheduling problem in a non-identical parallel machines environment. The orders are defined by their due dates, revenues, tardiness penalties, different processing times on the machines, and sequence-dependent setup times. We present an MILP formulation to maximize the profit. Furthermore, we assume that the revenue from an accepted order and the processing times are uncertain and accordingly, develop the robust counterpart of the proposed MILP model. The problem is computationally intractable;therefore, we develop a Benders decomposition approach to solve it. We introduce some valid cuts to accelerate the convergence of the classical Benders algorithm and a heuristic method to obtain the feasible solutions. Through numerical experiments on randomly generated large instances with up to 40 orders and 6 machines, we demonstrate that the proposed Benders decomposition approach outperforms the MILP model.

关键词： Order acceptance and scheduling non-identical parallel machines Robust optimization Benders decomposition algorithm

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non-identical parallel machine scheduling using genetic algorithm

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第6期38卷 6814-6821页

作者： Balin, Savas Yildiz Tech Univ Dept Ind Engn TR-34349 Istanbul Turkey

Most of the scheduling problems are NP-hard. In the literature, several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems and genetic algorithm (GA) ranks among the most preferred ones in view of its characteristics such as high adaptability, near optimization and easy realization. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this paper, the authors propose a new "crossover operator" and a new "optimality criterion" in order to adapt the GA to non-identical parallel machine scheduling problem. New algorithm is tested on a numerical example by implementing it in a simulation software and computational results are compared to those obtained with LPT (Longest Processing Time) dispatching rule;results were promising. Findings show that, in addition to its high computational speed for larger scale problem, the GA proposed here fits the non-identical parallel machine scheduling problem of minimizing the maximum completion time (makespan). (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Job scheduling non-identical parallel machines Heuristics Simulation Genetic algorithm (GA) LPT

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A Lagrangian relaxation algorithm for order acceptance and scheduling problem: a globalised robust optimisation approach

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INTERNATIONAL JOURNAL OF COMPUTER INTEGRATED MANUFACTURING 2016年第5期29卷 535-560页

作者： Emami, Saeed Sabbagh, Mohammad Moslehi, Ghasem Isfahan Univ Technol Dept Ind & Syst Engn Esfahan Iran

In this paper, a simultaneous order acceptance and scheduling problem in a non-identical parallel machines environment is considered. The order is defined by their due date, revenue, tardiness penalty, different processing times on the machines, and sequence-dependent set-up times. A mixed-integer linear programming (MILP) formulation is presented to maximise profit. Furthermore, it is assumed that the revenue from an accepted order and the processing times are uncertain;the globalized robust counterpart (GRC) of the proposed MILP model is presented such that the normal range of the perturbation is the intersection of a box and a polyhedral. The problem is computationally intractable. Therefore, the Lagrangian relaxation algorithm is developed to solve it. A cutting plane method is used to update the Lagrangian multipliers and a heuristic method is presented to obtain feasible solutions. Through numerical experiments on randomly generated large instances with up to 40 orders and six machines, the authors demonstrate that the proposed Lagrangian algorithm outperforms the monolithic MILP model. Furthermore, a simulation study demonstrates that, on average, the GRC of the MILP model provides slightly better results in comparison with its conventional robust counterpart.

关键词： order acceptance and scheduling non-identical parallel machines globalised robust counterpart Lagrangian relaxation algorithm

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A genetic algorithm application using fuzzy processing times in non-identical parallel machine scheduling problem

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ADVANCES IN ENGINEERING SOFTWARE 2012年第1期45卷 272-280页

作者： Alcan, Pelin Basligil, Huseyin Yildiz Tekn Univ Makine Fak Endustri Muh Bolumu Istanbul Turkey

There are many scheduling problems which are NP-hard in the literature. Several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problems in view of its characteristic that has high efficiency and that is fit for practical application [1]. Two different scale numerical examples demonstrate the genetic algorithm proposed is efficient and fit for larger scale identical parallel machine scheduling problem for minimizing the makespan. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this article, a kind of genetic algorithm based on machine code for minimizing the processing times in non-identical machine scheduling problem is presented. Also triangular fuzzy processing times are used in order to adapt the GA to non-identical parallel machine scheduling problem in the paper. Fuzzy systems are excellent tools for representing heuristic, commonsense rules. That is why we try to use fuzzy systems in this study. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Job scheduling non-identical parallel machines Heuristics Fuzzy logic Genetic algorithm (GA) Fuzzy processing times

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The integrated production-distribution scheduling in parallel machine environment by using improved genetic algorithms

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2021年第3期38卷 157-170页

作者： Kazemi, Hamed Mahdavi Mazdeh, Mohammad Rostami, Mohammad Heydari, Mahdi Laval Univ Dept Mech Engn Quebec City PQ Canada Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Shahrood Univ Technol Dept Ind Engn & Management Shahrood Iran

This study investigates the integrated production-distribution scheduling in a workshop which utilizes the non-identical parallel machines in production line. The objective is to schedule the jobs on machines and forming them into the batches so as to minimize the sum of tardiness and delivery costs. First, a mixed integer linear programming model is proposed which can solve the small-size instances in a reasonable time. To deal with large-size instances, a genetic algorithm (GA) and the improved genetic algorithm (IGA) equipped with optimal properties mechanism is developed. Areal life instance in bedroom furniture manufacturing is also presented that indicates the algorithm can reach the optimal solution for this problem. In order to evaluate the performance of the algorithms, 150 small size instances and more than 800 large size instances are generated which is conducted from benchmarks. The results indicate that IGA outperforms GA with respect to relative percentage deviations.

关键词： Production-distribution scheduling non-identical parallel machines mixed integer programming model improved genetic algorithm

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Improving a Production-Inventory Model in the Multi-Machine, Hybrid MTO-MTS Chemical Industry

Improving a Production-Inventory Model in the Multi-Machine,...

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作者： T. M. P. Vranken Eindhoven University of Technology

学位级别：硕士

In this research, a redesign is proposed for a production-inventory model in the hybrid MTO-MTS chemical industry. The project, conducted at SABIC, converges from a higher decision making level to a lower decision making level, i. e. from the tactical level to the operational level. First, a general MTO- MTS decision framework is adapted from literature to fit to the problem context at hand. Thereafter, inventory control systems are evaluated and an applicable design for the context is presented. At last, a production planning model integrating a block planning approach is presented for a non-identical parallel machine production environment. The proposed MILP formulation extents current literature on block planning by introducing different types, timings and lengths of blocks, allowing for backorders, and introducing service level constraints. In a case study, the products are partitioned based on the proposed MTO-MTS decision framework and inventory policy parameters are determined for MTS items. A simulation study validated that the new design generated significant cost reductions and increased performance on service levels. Moreover, the planning model is able to decrease the production costs significantly by allocating production orders cost optimal to the different machines.

关键词： make-to-order make-to-stock MTO-MTS partitioning sequence-dependent setups block planning production planning mixed-integer linear programming non-identical parallel machines

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