Bicriterion parallel-machine scheduling of equal-length jobs to minimize total tardiness and number of tardy jobs

Jing Zhang (), Rubing Chen (), Jinjiang Yuan (), C. T. Ng () and T. C. E. Cheng ()
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Jing Zhang: Zhengzhou University
Rubing Chen: Zhengzhou University
Jinjiang Yuan: Zhengzhou University
C. T. Ng: The Hong Kong Polytechnic University
T. C. E. Cheng: The Hong Kong Polytechnic University

Journal of Combinatorial Optimization, 2025, vol. 50, issue 3, No 2, 15 pages

Abstract: Abstract We consider bicriterion scheduling of equal-length jobs on uniform parallel machines to minimize total tardiness and number of tardy jobs. The Pareto-scheduling problem is studied in this paper, which includes the hierarchical-scheduling problem as a subversion. By using the single-machine scheduling with generated completion times model introduced by Zhao and Yuan (J Comb Optim 39:637–661, 2020), we present an $$O(n^2)$$ -time algorithm to solve the Pareto-scheduling problem, and two $$O(n\log n)$$ -time algorithms to solve two hierarchical-scheduling problems, respectively. Our $$O(n\log n)$$ -time algorithms improve the $$O(n^2\log n)$$ -time algorithms given by Sarin and Prakash (J Comb Optim 8:227–240, 2004) to solve two hierarchical-scheduling problems on identical parallel machines.

Keywords: Bicriterion scheduling; Equal-length jobs; Uniform parallel machines; Total tardiness; Number of tardy jobs. (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01353-9

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