불확실한 환경 하에서 중간 평가가 있는 시간-비용 프로젝트 문제

We consider a project time-cost tradeoff problem with two milestones, where one of the jobs has an uncertain processing time, Unless each milestone is completed on time, some penalty cost may be imposed, However, the penalty costs can be avoided by compressing the processing times of some jabs, which requires additional resources or costs. The objective is to minimize the expected total costs subject to the constraint on the expected project completion time, We show that the problem can be solved in polynomial time if the precedence graph of a project is a chain.