• 산업공학
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• 제25권3호
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• pp.357-364
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• 2012

This paper considers a unrelated parallel machine scheduling problem with ready times, due times and sequence and machine-dependent setup times. The objective of this problem is to determine the allocation of jobs and the scheduling of machines to minimize the total tardy time. A mathematical model for optimal solution is derived. An in-depth analysis of the model shows that it is very complicated and difficult to obtain optimal solutions as the problem size becomes large. Therefore, a genetic algorithm using an effective dispatching method is proposed. The performance of the proposed genetic algorithm is evaluated using several randomly generated examples.

• 대한산업공학회지
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• 제40권3호
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• pp.305-312
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• 2014

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.

• Industrial Engineering and Management Systems
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• 제11권1호
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• pp.114-122
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• 2012

This paper considers a non-identical parallel machine scheduling problem with sequence and machine dependent setup times. The objective of this problem is to determine the allocation of jobs and the scheduling of each machine to minimize makespan. A mathematical model for optimal solution is derived. An in-depth analysis of the model shows that it is very complicated and difficult to obtain optimal solutions as the problem size becomes large. Therefore, two meta-heuristics, genetic algorithm (GA) and a new population-based evolutionary meta-heuristic called self-evolution algorithm (SEA), are proposed. The performances of the meta-heuristic algorithms are evaluated through compare with optimal solutions using randomly generated several examples.

• 대한산업공학회지
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• 제27권2호
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• pp.158-168
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• 2001

We present a tabu search (TS) algorithm to minimize maximum lateness on a single machine in the presence of sequence dependent setup times and dynamic job arrivals. The TS algorithm starts with a feasible schedule generated by a modified ATCS (Apparent Tardiness Cost with Setups) rule, then through a series of search steps it improves the initial schedule. Results of extensive computational experiments show that the TS algorithm significantly outperforms a well-known RHP heuristic by Ovacik and Uzsoy, both on the solutions quality and the computation time. The performance advantage is particularly pronounced when there is high competition among jobs for machine capacity.

• Industrial Engineering and Management Systems
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• 제3권2호
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• pp.100-115
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• 2004

The network representation and branch and bound algorithm with efficient lower and upper bounding procedures are developed to determine a global optimal production schedule on a machine that minimizes sequence-dependent setup cost and earliness/tardiness penalties. Lower bounds are obtained based on heuristic and Lagrangian relaxation. Priority dispatching rule with local improvement procedure is used to derive an initial upper bound. Two dominance criteria are incorporated in a branch and bound procedure to reduce the search space and enhance computational efficiency. The computational results indicate that the proposed procedure could optimally solve the problem with up to 40 jobs in a reasonable time using a personal computer.

• 산업경영시스템학회지
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• 제13권21호
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• pp.91-100
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• 1990

This paper is concerned with the development of optimal algorithms for multi-stage flowshop scheduling problems with sequence dependent setup times. In the previous researches the setup time of a job is considered to be able to begin at the earliest opportunity given a particular sequence at the start of operations. In this paper the setup time of a job is considered to be able to begin only at the completion of that job on the previous machine to reflect the effects of the setup time to the performance measure of sequence dependent setup time flowshop scheduling. The results of the study consist of two areas; first, a general integer programming(IP) model is formulated and a nixed integer linear programming(MILP) model is also formulated by introducing a new binary variable. Second a depth-first branch and bound algorithm is developed. To reduce the computational burdens we use the best heuristic schedule developed by Choi(1989) as the first trial. The experiments for developed algorithm are designed for a 4$\times$3$\times$3 factorial design with 360 observations. The experimental factors are PS(ratio of processing time to setup time), M(number of machines), N(number of jobs).

• 대한산업공학회지
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• 제25권3호
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• pp.360-368
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• 1999

We consider the problem of scheduling n jobs with sequence-dependent processing times on a set of parallel-identical machines. The processing time of each job consists of a pure processing time and a sequence-dependent setup time. The objective is to maximize the total remaining machine available time which can be used for other tasks. For the problem, a hybrid genetic algorithm is proposed. The algorithm combines a genetic algorithm for global search and a heuristic for local optimization to improve the speed of evolution convergence. The genetic operators are developed such that parallel machines can be handled in an efficient and effective way. For local optimization, the adjacent pairwise interchange method is used. The proposed hybrid genetic algorithm is compared with two heuristics, the nearest setup time method and the maximum penalty method. Computational results for a series of randomly generated problems demonstrate that the proposed algorithm outperforms the two heuristics.

• 대한산업공학회지
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• 제24권3호
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• pp.431-446
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• 1998

In this paper, we consider the problem of scheduling n jobs with sequence-dependent processing times on a set of parallel-identical machines. The processing time of each job consists of a pure processing time and a sequence-dependent setup time. The objective is to maximize the total remaining machine available time which can be used for other tasks. For the problem, we first propose a dynamic programming(DP) algorithm for sequencing jobs processed on a single machine. The algorithm is then extended to handle jobs on parallel-identical machines. Finally, we developed an improved version of the algorithm which generates optimal solutions using much smaller amount of memory space and computing time. Computational results are provided to illustrate the performance of the DP algorithms.

• Management Science and Financial Engineering
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• 제18권1호
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• pp.1-12
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• 2012

In this paper, we report a case study on the common due-date assignment and scheduling problem in a paper remanufacturing system that produces corrugated cardboards using collected waste papers for a given set of orders under the make-to-order (MTO) environment. Since the system produces corrugated cardboards in an integrated process and has sequence-dependent setups, the problem considered here can be regarded as common due-date assignment and sequencing on a single machine with sequence-dependent setup times. The objective is to minimize the sum of the penalties associated with due-date assignment, earliness, and tardiness. In the study, the earliness and tardiness penalties were obtained from inventory holding and backorder costs, respectively. To solve the problem, we adopted two types of algorithms: (a) branch and bound algorithm that gives the optimal solutions; and (b) heuristic algorithms. Computational experiments were done on the data generated from the case and the results show that both types of algorithms work well for the case data. In particular, the branch and bound algorithm gave the optimal solutions quickly. However, it is recommended to use the heuristic algorithms for large-sized instances, especially when the solution time is very critical.

• 한국컴퓨터정보학회:학술대회논문집
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• 한국컴퓨터정보학회 2023년도 제67차 동계학술대회논문집 31권1호
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• pp.327-329
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• 2023

순서 의존적 준비시간을 갖는 단일기계 생산라인에서 주어진 작업들을 효율적으로 수행하기 위해서는 최대한 동일하거나 유사한 유형의 작업물들을 연속적으로 처리하여 다음 번 작업물의 처리를 시작하기 전에 발생하는 준비시간을 최소화하여야 한다. 따라서, 대기 중인 것들 중 기계에 투입할 작업물을 적절히 선택하는 것이 중요하며, 이를 위해 작업 배정 규칙과 같은 휴리스틱을 사용할 수도 있지만, 이러한 해법들은 일반적으로 다양한 상황을 동적으로 고려하지 못하는 한계점을 갖는다. 따라서, 본 논문에서는 상용 3D 시뮬레이션 소프트웨어인 FlexSim을 사용하여 모형을 구성한 다음, 강화학습을 적용하여 대기 중인 작업물 중 최적의 후보를 선택하기 위한 작업 배정 모형을 개발하고자 한다. 세부적으로는 강화학습의 상태 및 보상을 달리 설정하면서 학습된 모형의 성능을 비교하고자 한다. 실험 결과를 통해 적절한 시뮬레이션 모형 구성과 강화학습의 파라미터 변수들을 적절히 조합하여 적절한 작업 배정 모형의 개발이 가능하다는 점을 알 수 있었다.