• Title/Summary/Keyword: Job-Dependent Position-Based Processing Time

Search Result 2, Processing Time 0.021 seconds

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
    • /
    • v.38 no.3
    • /
    • pp.169-180
    • /
    • 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.

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
    • /
    • v.24 no.4
    • /
    • pp.77-88
    • /
    • 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.