Scheduling n jobs and preventive maintenance in a single machine subject to breakdowns to minimize the expected total earliness and tardiness costs

This paper focuses on a stochastic scheduling problem in which n immediately available jobs are to be scheduled jointly with the preventive maintenance in a single machine subject to breakdowns. The objective is to minimize expected total earliness and tardiness costs with a common due-date. The problem of scheduling only n jobs to minimize total earliness and tardiness costs in a single machine subject to breakdowns is well known to be NP-hard. We first give a relevant literature review dealing with the single machine to minimize the ET-cost. After we introduce the process of breakdowns considered in this paper. Last we formulate a dynamic programming to solve the problem optimally.