Scheduling with regular performance measures and optional job rejection on a single machine

TL;DR

This paper improves dynamic programming solutions for single machine scheduling problems with optional job rejection, focusing on minimizing various performance measures and providing both theoretical and practical enhancements.

Contribution

Enhanced DP algorithms for scheduling with optional job rejection, improving efficiency for makespan, total completion time, and weighted completion problems.

Findings

Enhanced DP algorithms show improved theoretical bounds.

Numerical studies confirm practical efficiency.

Problems are NP-hard, but solutions are effective in practice.

Abstract

We address single machine problems with optional jobs - rejection, studied recently in Zhang et al. [21] and Cao et al. [2]. In these papers, the authors focus on minimizing regular performance measures, i.e., functions that are non-decreasing in the jobs completion time, subject to the constraint that the total rejection cost cannot exceed a predefined upper bound. They also prove that the considered problems are ordinary NP-hard and provide pseudo-polynomial-time Dynamic Programming (DP) solutions. In this paper, we focus on three of these problems: makespan with release-dates; total completion times; and total weighted completion, and present enhanced DP solutions demonstrating both theoretical and practical improvements. Moreover, we provide extensive numerical studies verifying their efficiency.