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

Abstract

We address single machine problems with optional job-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.

Single Machine Vector Scheduling with General Penalties

“…Recently, He et al [10] and Ou et al [11] independently designed an improved approximation algorithm with a running time of O(n log n). More related results can be found in the surveys [12][13][14][15][16][17][18].…”

Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection

“…It follows that when the option of job-rejection is valid, the scheduler may decide to process only a subset of the jobs, and those jobs which are not processed (i.e., totally rejected or outsourced) are penalized. The importance and practicality of job-rejection are demonstrated in the following selection of recently published papers, addressing various machine settings and cost functions: Zou and Miao (2016), Gerstl and Mosheiov (2017), Strusevich (2017), Fiszman and, Huang et al (2018), Mor and Mosheiov (2018), Zhang et al (2018), Dabiri et al (2019, Kovalyov et al (2019), Mor and Shapira (2019), Koulamas, and Kyparisis (2020), , Mor and Shapira (2020a, b), , Mosheiov and Pruwer (2020) and Wang et al (2020).…”