Minimax regret makespan scheduling with interval release dates on unrelated machines

Mirosław Ławrynowicz () and Jerzy Józefczyk
Additional contact information
Mirosław Ławrynowicz: Wrocław University of Science and Technology
Jerzy Józefczyk: Wrocław University of Science and Technology

Journal of Heuristics, 2025, vol. 31, issue 4, No 3, 37 pages

Abstract: Abstract In this paper, we present a study of the robust (non-deterministic) job scheduling problem with interval release dates on unrelated machines. Robust optimization is a tractable alternative to stochastic optimization suited for problems in which parameter distributions are undetermined due to insufficient data. Our problem formulation involves minimizing the maximum regret, defined as the worst-case deviation from an optimal makespan, with the assumption that each release date belongs to a well-defined interval. Mathematical analysis is accomplished to investigate the properties of the robust scheduling problem examining the inapproximability, determination of the upper bound of a regret function, and selection of feasible scenarios. In order to solve the robust scheduling problem, we propose an algorithm that implements a greedy strategy and schedules jobs using only the deterministic criterion (the makespan) instead of assessing the worst-case regret value. We compare the quality of our schedules with the solutions obtained by the properly adapted and tuned simulated annealing algorithm. Additionally, the applicability of our robust approach (robust framework) in the Scheduling-Location problem (deterministic problem in which the parameters are precisely defined), which combines the facility location problem and job scheduling problem, is demonstrated. The numerical evaluation shows that including the uncertainty and regret-averse (the minimax regret criterion) can allow, in certain cases, to achieve optimal solutions for incomplete dataset.

Keywords: Job scheduling; Robust optimization; Minimax regret; Makespan; Unrelated machines; Scheduling-Location (ScheLoc) problem (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10732-025-09571-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:joheur:v:31:y:2025:i:4:d:10.1007_s10732-025-09571-4

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10732

DOI: 10.1007/s10732-025-09571-4

Access Statistics for this article

Journal of Heuristics is currently edited by Manuel Laguna

More articles in Journal of Heuristics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().