Journal of Combinatorial Optimization

, Volume 12, Issue 4, pp 387–394

A note on the complexity of the problem of two-agent scheduling on a single machine

  • C. T. Ng
  • T. C. E. Cheng
  • J. J. Yuan
Article

DOI: 10.1007/s10878-006-9001-0

Cite this article as:
Ng, C.T., Cheng, T.C.E. & Yuan, J.J. J Comb Optim (2006) 12: 387. doi:10.1007/s10878-006-9001-0

Abstract

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agent's objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.

Keywords

Production/schedulingMulti-agent deterministic sequencingGames/group decisionsCooperative sequencing

Copyright information

© Springer Science + Business Media, LCC 2006

Authors and Affiliations

  • C. T. Ng
    • 1
  • T. C. E. Cheng
    • 1
  • J. J. Yuan
    • 2
  1. 1.Department of LogisticsThe Hong Kong Polytechnic University, Hung HomKowloonPeople”s Republic of China
  2. 2.Department of MathematicsZhengzhou UniversityZhengzhouPeople”s Republic of China