Rescheduling to Minimize the Maximum Lateness Under the Sequence Disruptions of Original Jobs

We introduce and study the rescheduling on a single machine to minimize the maximum lateness under the sequence disruptions of original jobs. In the problem, each original job [Formula: see text] has a constraint disruption on its sequence respect to an original optimal schedule [Formula: see text], i.e., [Formula: see text]. That is, if [Formula: see text] is the [Formula: see text]th job in [Formula: see text], then it is required that the position index [Formula: see text] of [Formula: see text] in a schedule for all jobs satisfies [Formula: see text]. By introducing the positive sequence disruption [Formula: see text] and the negative sequence disruption [Formula: see text], three problems are considered in this paper: problem (P1) is [Formula: see text], problem (P2) is [Formula: see text], and problem (P3) is [Formula: see text]. We show that the three problems are equivalent and can be solved in [Formula: see text] time. Then we study an extension of problem (P2): [Formula: see text]. We show that the extended problem can be solved in [Formula: see text] time.