A survey of scheduling with deterministic machine availability constraints

Minimizing Total Completion Time in Flowshop with Availability Constraint on the First Machine

“…Almost all research papers about flow shop scheduling with availability constraint are with respect to makespan criterion ( [20]). Lee ([17]) showed that if there is only one unavailable interval, either on the first machine or on the second machine,the problem is NP-hard in the ordinary sense.…”

“…Furthermore, for the former case, Johnson's rule gives a 2-approximation regardless of the number of unavailable intervals; On the other hand, for the latter case, there is no polynomial time constant approximation for any constant even if there are only two unavailable intervals on the second machine and the first machine is always available. Many heuristics, meta-heuristics and exact methods are developed for the general problem, see the surveys [18], [21], [22], [20] and the references therein for more details.…”

“…While some of the problems can still be easily solved, many of them become more complicated and new optimal algorithms/heuristics need to be designed. Many papers have been devoted to various scheduling problems with machine availability constraint, see the survey papers by Lee, Lei and Pinedo ( [18]), Sanlaville and Schmidt ([21]), Schmidt ([22]), Ma, Chu and Zuo ( [20]), etc.…”

“…For flowshop scheduling with availability constraint, most research is done for two-stage flowshop problems( [20]): there are two machines, machine 1 and machine 2. Each machine may have one or more unavailable intervals; There are n jobs, 1, 2, .…”

An integrated model of production scheduling and maintenance planning under imperfect preventive maintenance

“…And many works have been published on this issue. Among the existing works, most of them focus on a single machine [24,4,8]. Because the single machine problems could be interpreted as fundamental basis for more complex problems [10,23].…”