• 산업경영시스템학회지
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• 제38권3호
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• pp.169-180
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• 2015

Recently, scheduling problems with position-dependent processing times have received considerable attention in the literature, where the processing times of jobs are dependent on the processing sequences. However, they did not consider cases in which each processed job has different learning or aging ratios. This means that the actual processing time for a job can be determined not only by the processing sequence, but also by the learning/aging ratio, which can reflect the degree of processing difficulties in subsequent jobs. Motivated by these remarks, in this paper, we consider a two-agent single-machine scheduling problem with linear job-dependent position-based learning effects, where two agents compete to use a common single machine and each job has a different learning ratio. Specifically, we take into account two different objective functions for two agents: one agent minimizes the total weighted completion time, and the other restricts the makespan to less than an upper bound. After formally defining the problem by developing a mixed integer non-linear programming formulation, we devise a branch-and-bound (B&B) algorithm to give optimal solutions by developing four dominance properties based on a pairwise interchange comparison and four properties regarding the feasibility of a considered sequence. We suggest a lower bound to speed up the search procedure in the B&B algorithm by fathoming any non-prominent nodes. As this problem is at least NP-hard, we suggest efficient genetic algorithms using different methods to generate the initial population and two crossover operations. Computational results show that the proposed algorithms are efficient to obtain near-optimal solutions.

• 산업경영시스템학회지
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• 제36권4호
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• pp.130-137
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• 2013

In this paper, we consider a two-agent scheduling with sequence-dependent exponential learning effects consideration, where two agents A and B have to share a single machine for processing their jobs. The objective function for agent A is to minimize the total completion time of jobs for agent A subject to a given upper bound on the objective function of agent B, representing the makespan of jobs for agent B. By assuming that the learning ratios for all jobs are the same, we suggest an enumeration-based backward allocation scheduling for finding an optimal solution and exemplify it by using a small numerical example. This problem has various applications in production systems as well as in operations management.

• 한국경영과학회지
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• 제37권1호
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• pp.19-28
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• 2012

We consider a multi-agent scheduling problem such that each agent tries to maximize the weighted number of just-in-time jobs. Two objectives are considered : the first is to find the optimal solution for one agent with constraints on the other agents' weight functions, and the second is to find the largest set of efficient schedules of which corresponding objective vectors are different for the case with identical weights. We show that when the number of agents is fixed, the single machine case with the first objective is NP-hard in the ordinary sense, and present the polynomial- time algorithm for the two-machine flow shop case with the second objective and identical weights.

• 한국시뮬레이션학회논문지
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• 제24권4호
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• pp.77-88
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• 2015

본 논문은 작업별 위치기반 지수학습 효과를 갖는 2-에이전트 단일기계 스케줄링 문제를 고려한다. 에이전트 A는 가중 완료 시간의 합을 최소화하며, 에이전트 B는 총소요시간에 대한 상한 값을 만족하는 조건을 갖는다. 본 연구에서는 먼저 우수해/가능해에 대한 특성을 개발하고, 이를 이용하여 최적 해를 찾기 위한 분지한계 알고리즘을 설계한다. 또한 근사 최적 해를 구하기 위해 6가지 다른 초기해 생성 방법을 이용한 시뮬레이티드 어닐링 알고리즘을 제안한다. 수치 실험을 통해 제안된 알고리즘의 우수한 성능을 검증한다. 실험 결과, 다른 초기해 생성 방법들 간에는 %errors 차이가 유의하게 발생하지 않았으며, 에이전트 A의 작업 순서를 무작위로 생성할 때 성능이 좋아짐을 발견하였다. 반면에, 에이전트 B의 초기해 생성 방법은 성능에 영향을 미치지 않았다.