Optimally rescheduling jobs with a LIFO buffer

TL;DR

This paper investigates the problem of re-sequencing jobs on a single machine using a LIFO buffer to optimize various scheduling objectives, providing polynomial algorithms for some cases and proving NP-hardness for others.

Contribution

It introduces a novel model for job re-sequencing with a LIFO buffer and offers efficient algorithms for certain objectives while establishing complexity results for others.

Findings

Polynomial algorithms for total weighted completion time, maximum lateness, and weighted late jobs.

NP-hardness of minimizing the weighted number of late jobs.

Pseudo-polynomial algorithm for the NP-hard case.

Abstract

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 \red{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.