Scheduling under linear constraints

Kameng Nip, Zhenbo Wang, Zizhuo Wang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with no more than two linear constraints, or both the number of machines and the number of linear constraints are fixed constants, then the problem is polynomial-time solvable via solving a series of linear programming problems. If both the number of machines and the number of constraints are inputs of the problem instance, then the problem is NP-Hard. We further propose several approximation algorithms for the latter case.

Original languageEnglish (US)
Pages (from-to)290-297
Number of pages8
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Sep 1 2016

Bibliographical note

Funding Information:
Zhenbo Wangs research has been supported by NSFC no. 11371216 .

Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.


  • Approximation algorithm
  • Computational complexity
  • Linear programming
  • Parallel machine scheduling


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