볼록 자원소비함수와 거부 옵션을 갖는 단일공정 스케줄링 문제

Abstract

We consider two single-machine scheduling problems, where each job is accepted or rejected. The processing times of the accepted jobs can be reduced by using some resource, which incurs a resource consumption cost, and their performance is measured by the makespan. For the rejected jobs, the corresponding rejection cost is required. Two objectives are considered, based on the combination of the makespan, the resource consumption cost and the rejection cost. The first objective is to minimize the makespan with a constraint on the sum of the total resource consumption cost and the total rejection cost, and the second one is to minimize the makespan while the total resource consumption and the total rejection costs are less than or equal to their own budgets, respectively. We show that two problems are NP-hard while they are polynomially solvable for the cases with an antithetical property such that the increasing order of jobs’ workloads is identical with the decreasing order of their rejection cost.