Minimizing the number of late jobs and total late work with step-learning

Johnson Phosavanh and Daniel Oron

European Journal of Operational Research, 2025, vol. 321, issue 3, 734-749

Abstract: We study single-machine scheduling problems with step-learning, where an improvement in processing time is experienced if a job is started at, or after, a job-dependent learning-date. We consider minimizing two functions: the number of late jobs and the total late work, and we show that when at least a common due-date or common learning-date is assumed, the problem is NP-hard in the ordinary sense; however, when both are arbitrary, the problem becomes strongly NP-hard. For each of the problems where at least one of the dates is assumed to be common, we analyze the structure of an optimal job schedule with and without idle time and propose pseudo-polynomial time dynamic programming algorithms. We also show that the problem of minimizing the weighted number of late jobs with step-learning can be solved with a minor change to the algorithms for the unweighted case. In addition to this, we show that when a common due-date is assumed and no idle time is allowed, the problem of minimizing the total late work is equivalent to that of minimizing the makespan. Furthermore, we provide a more efficient algorithm to solve the problem of minimizing makespan under the assumption of a common learning-date than the one in the existing literature. Lastly, we show that our analysis can also be applied to the case of step-deterioration, where instead, the processing times of jobs increase at a given date.

Keywords: Scheduling; Single-machine; Step-learning; Dynamic programming (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221724007458
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:321:y:2025:i:3:p:734-749

DOI: 10.1016/j.ejor.2024.09.042

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().