• 융합정보논문지
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• 제9권12호
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• pp.124-132
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• 2019

일정계획은 오프라인(offline) 일정계획과 온라인(online) 일정계획으로 구분할 수 있고, 본 논문은 온라인 상황에서 병렬설비의 주기적 일정계획 수립문제를 다룬다. 도착시간(ready time)이 다른 여러 작업들에 대해 makespan을 최소화하기 위한 작업 일정계획 알고리즘 개발이 목적이다. 이를 위해 각 설비에서의 작업처리 순서는 ERD(Earliest Ready Date) 규칙에 따른 순서가 최적임을 밝혔다. 각 설비 별 배정 작업도 결정 해야하는 병렬설비 문제를 위해서는 혼합정수계획모형(MIP)을 이용하는 알고리즘을 제시하였다. 개발한 알고리즘의 유용성과 성능분석을 위해 수치 예를 활용하여 오프라인 일정계획과 비교하였다. 비교분석 결과, 오프라인 일정계획에 비해 매우 빠른 시간에 일정계획을 수립할 수 있음을 보였고, 주기시간의 감소를 통한 makespan의 단축 가능성을 보였다. 본 논문의 주기적 일정계획 방법은 계획수립을 위한 시간이 매우 작으므로, 설비 및 작업의 수가 많은 온라인 환경에서도 활용할 수 있다. 더불어서 스마트공장이나 블록체인 플랫폼에서의 작업일정 수행을 위해 활용될 수 있을 것으로 기대한다.

• Industrial Engineering and Management Systems
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• 제10권2호
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• pp.134-139
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• 2011

The problem of scheduling in permutation flowshops has been extensively investigated by many researchers. Recently, attempts are being made to consider more than one objective simultaneously and develop algorithms to obtain a set of Pareto-optimal solutions. Varadharajan et al. (2005) presented a multi-objective simulated-annealing algorithm (MOSA) for the problem of permutation-flowshop scheduling with the objectives of minimizing the makespan and the total flowtime of jobs. The MOSA uses two initial sequences obtained using heuristics, and seeks to obtain non-dominated solutions through the implementation of a probability function, which probabilistically selects the objective of minimizing either the makespan or the total flowtime of jobs. In this paper, the same problem of heuristically developing non-dominated sequences is considered. We propose an effective heuristics based on simulated annealing (SA), in which the weighted sum of the makespan and the total flowtime is used. The essences of the heuristics are in selecting the initial sequence, setting the weight and generating a solution in the search process. Using a benchmark problem provided by Taillard (1993), which was used in the MOSA, these conditions are extracted in a large-scale experiment. The non-dominated sets obtained from the existing algorithms and the proposed heuristics are compared. It was found that the proposed heuristics drastically improved the performance of finding the non-dominated frontier.

• Management Science and Financial Engineering
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• 제3권2호
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• pp.29-43
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• 1997

Many heuristics have been developed in order to overcome the computational complexity of job shop problems. In this research, we develop a new heuristic by selecting four simple dispatching rules, i.e., SPT, LPT, SR and LR, dynamically as scheduling proceeds. The selection is accomplished by using artificial neural networks. As a result of testing on 50 problems, the makespan obtained by our heuristic is, on the average, 13.0% shorter than the longest makespan, and 0.4% shorter than the shortest makespan obtained by existing dispatching rules.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.825-827
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• 1989

A heuristic model which determines the scheduling of serial flowshops with minimization of the makespan is proposed for an idealized batch chemical plant. It generates an initial sequence by heuristic reasoning and improves it recursively until no improvement is possible. The heuristic reasoning is based on Johnson's Rule which gives the sequence with the minimum makespan for a two-unit flowshop. The evolutionary step searches the neighborhood of the current sequence for sequences with lower makespan. The robustness of this model is also examined by comparing the minimum makespan of literature examples with the theoretical one.

• 산업경영시스템학회지
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• 제30권2호
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• pp.44-50
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• 2007

This paper deals with the problem of scheduling jobs and rate-modifying activities on parallel machines. A rate-modifying activity is an activity that changes the production rate of equipment such as maintenance and readjustment. If a job is scheduled after the rate-modifying activity, then the processing time varies depending on the modifying rate of the activity. In this study, we extend the single machine problem to parallel machines problem and propose algorithms is to schedule the rate-modifying activities and jobs to minimize the makespan on parallel machines which is NP-hard. We propose a branch and bound algorithm with three lower bounds to solve medium size problems optimally. Also we develop three heuristics, Modified Longest Processing Time, Modified MULTIFIT and Modified COMBINE algorithms to solve large size problems. The test results show that branch and bound algorithm finds the optimal solution in a reasonable time for medium size problems (up to 15 jobs and 5 machines). For large size problem, Modified COMBINE and Modified MULTIFIT algorithms outperform Modified LPT algorithm in terms of solution quality.

• 품질경영학회지
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• 제17권2호
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• pp.121-141
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• 1989

This paper is concerned with a development and evaluation of heuristics for the multi-stage sequence dependent flowshop sequencing. Eighteen heuristics, CAM1, CAM2, and etc., are proposed. The performance measure is a makespan which is to be minimized. The experiment for each algorithm is designed for a 4*3*3 factorial design with 360 observations. The experimental factors are PS(ratio of processing times to setup times), M(number of machines), N(number of jobs). The makespan of the proposed heuristics is compared with the optimal makespan obtained by the complete enumeration of schedules. This yardstick of comparison is called a relative error. The mean relative errors of the eighteen heuristics are from 2.048% to 8.717%. The computational results are analysed using SPSS. The experimental results show that the three factors are statistically significant at 5% level. The simulation for the large size problems is conducted to show having the similar computational results like the small size problems.

• 품질경영학회지
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• 제17권1호
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• pp.35-47
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• 1989

This paper is concerned with a development and evaluation of heuristic algorithms for the n-job, M-stage flowshop with sequence dependent setup times. Three heuristic algorithms, CAIDAN, DANNEN and PETROV, are proposed. The makespan is taken as a performance measure for the algorithms. The experiment for each algorithm is designed for a $4{\times}3{\times}3$ factorial design with 360 observations. The experimental factors are PS (ratio of processing times to setup times), M (number of machines), and N (number of jobs). The makespan of the proposed heuristic algorithms is compared with the optimal makespan obtained by the complete enumeration method. The result of comparision of performance measure is called a relative error. The mean relative errors of CAIDAN, DANNEN and PETROV algorithms are 4.488%. 6.712% and 7.282%, respectively. The computational results are analysed using SPSS. The experimental results show that the three factors are statistically signiticant at 5% level.

• 한국산학기술학회논문지
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• 제5권2호
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• pp.137-140
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• 2004

다중 프로세서 시스템이 개발됨에 따라, 새로운 일정계획문제, 하나의 작업이 하나이상의 기계에 의해 동시에 처리되어야 하는 문제가 대두되었다. 이 연구에서는 선행관계를 가진 이러한 다중 프로세서 일정계획문제에 대해 다루어 보았다. 이 연구의 목적은 makespan을 최소화하는 일정계획을 찾는 것이다. 일반적으로 Branch and Bound 기법을 이용하여 선행관계를 가진 다중 프로세서 일정계획문제의 최적해를 찾았는데, 해의 탐색시간이 너무 오래 걸린다는 단점이 있었다. 본 연구에서는 짧은 시간 내에 최적해와 가까운 근사해를 simulated annealing(SA)방법을 이용하여 구해보았다. SA의 성능을 측정하기 위하여, SA의 CPU 처리시간과 구한 근사해를 40개의 예제문제를 통하여 Kramer의 방법의 CPU 처리시간과 최적해와 비교해 보았다.

• 대한산업공학회지
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• 제13권2호
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• pp.35-46
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• 1987

To minimize makespan for preemptive sequence dependent job scheduling with parallel identical processors, fundamental results, as the basis of new algorithm to be presented, such as McNauton's algorithm for independent jobs, Hu's characterization for dependent jobs, and Muntz-Coffman's algorithm, were first introduced. Then a huristic procedure was presented applying those concepts of zoning of assembly line balancing and of resource leveling on CPM network scheduling with two or more of parallel machines in general. New procedure has eliminated presumative machine assignment using ${\rho}$, rate of resource capability (${\rho}$ < 1), for practical scheduling.

• 산업경영시스템학회지
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• 제22권52호
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• pp.297-309
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• 1999

Resource Constrained Dynamic Multi-Projects Scheduling(RCDMPS) is intended to minimize the total processing time(makespan) of two or more projects sequentially arriving at the shop under restricted resources. The aim of this paper is to develop the new Tabu Search heuristic for RCDMPS to minimize makespan. We propose the insertion method to generate the neighborhood solutions in applying the Tabu Search for the RCDMPS and the diversification strategy to search the solution space diversely. The proposed diversification strategy apply the dynamic tabu list that the tabu list size is generated and renewed at each iteration by the complexity of the project, and change the proposed tabu attribute. In this paper, We use the dynamic tabu list for the diversification strategy and intensification strategy in the tabu search, and compare with other dispatching heuristic method to verify that the new heuristic method minimize the makespan of the problem.