The single‐machine absolute‐deviation early‐tardy problem with random completion times
研究了机器故障导致随机完工时间下，单机调度中最小化预期加权惩罚（包括交货期、完工时间、早到和迟到）的问题，并证明了V形序列的最优性。
We consider sequencing n jobs on a single machine subject to job completion times arising from either machine breakdowns or other causes. The objective is to minimize an expected weighted combination of due dates, completion times, earliness, and tardiness penalties. The determination of optimal distinct due dates or optimal common due dates for a given schedule is investigated. The scheduling problem for a fixed common due date is considered when random completion times arise from machine breakdowns. The optimality of a V-shaped about (a point) T sequence is established when the number of machine breakdowns follows either a Poisson or a geometric distribution and the duration of a breakdown has an exponential distribution. © 1996 John Wiley & Sons, Inc.