• Title/Summary/Keyword: Two-Agent Single-Machine Scheduling

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Two-Agent Single-Machine Scheduling with Linear Job-Dependent Position-Based Learning Effects (작업 종속 및 위치기반 선형학습효과를 갖는 2-에이전트 단일기계 스케줄링)

  • Choi, Jin Young
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.38 no.3
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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.

Two-Agent Scheduling with Sequence-Dependent Exponential Learning Effects Consideration (처리순서기반 지수함수 학습효과를 고려한 2-에이전트 스케줄링)

  • Choi, Jin Young
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.36 no.4
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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.

Just-in-time Scheduling with Multiple Competing Agents (다수의 경쟁이 존재하는 환경에서 적시 스케줄링에 관한 연구)

  • Chung, Dae-Young;Choi, Byung-Cheon
    • Journal of the Korean Operations Research and Management Science Society
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    • v.37 no.1
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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.

Simulated Annealing for Two-Agent Scheduling Problem with Exponential Job-Dependent Position-Based Learning Effects (작업별 위치기반 지수학습 효과를 갖는 2-에이전트 스케줄링 문제를 위한 시뮬레이티드 어닐링)

  • Choi, Jin Young
    • Journal of the Korea Society for Simulation
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    • v.24 no.4
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    • pp.77-88
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    • 2015
  • In this paper, we consider a two-agent single-machine scheduling problem with exponential job-dependent position-based learning effects. The objective is to minimize the total weighted completion time of one agent with the restriction that the makespan of the other agent cannot exceed an upper bound. First, we propose a branch-and-bound algorithm by developing some dominance /feasibility properties and a lower bound to find an optimal solution. Second, we design an efficient simulated annealing (SA) algorithm to search a near optimal solution by considering six different SAs to generate initial solutions. We show the performance superiority of the suggested SA using a numerical experiment. Specifically, we verify that there is no significant difference in the performance of %errors between different considered SAs using the paired t-test. Furthermore, we testify that random generation method is better than the others for agent A, whereas the initial solution method for agent B did not affect the performance of %errors.