Optimally rescheduling jobs with a Last-In-First-Out buffer

This paper considers single-machine scheduling problems in which a given solution, i.e., an ordered set of jobs, has to be improved as much as possible by re-sequencing the jobs. The need for rescheduling may arise in different contexts, e.g., due to changes in the job data or because of the local objective in a stage of a supply chain that is not aligned with the given sequence. A common production setting entails the movement of jobs (or parts) on a conveyor. This is reflected in our model by facilitating the re-sequencing of jobs via a buffer of limited capacity accessible by a LIFO policy. We consider the classical objective functions of total weighted completion time, maximum lateness and (weighted) number of late jobs and study their complexity. For three of these problems, we present strictly polynomial-time dynamic programming algorithms, while for the case of minimizing the weighted number of late jobs NP-hardness is proven and a pseudo-polynomial algorithm is given.