Mathematical Methods of Operations Research

, Volume 80, Issue 1, pp 47–81 | Cite as

A branch-and-bound algorithm for the coupled task problem

  • József Békési
  • Gábor Galambos
  • Michael N. Jung
  • Marcus Oswald
  • Gerhard ReineltEmail author
Original Article


The coupled task problem is to schedule jobs on a single machine where each job consists of two subtasks and where the second subtask has to be started after a given time interval with respect to the first one. The problem has several applications and is NP-hard. In this paper we present a branch-and-bound algorithm for this problem and compare its performance with four integer programming models.


Coupled task problem Branch-and-bound Integer programming 



We would like to thank two anonymous referees for very helpful and extensive comments and suggestions. They improved this paper considerably.


  1. Ageev AA, Baburin AE (2007) Approximation algorithms for UET scheduling problems with exact delays. Oper Res Lett 25:533–540CrossRefMathSciNetGoogle Scholar
  2. Ahr D, Békési J, Galambos G, Oswald M, Reinelt G (2004) An exact algorithm for scheduling identical coupled tasks. Math Methods Oper Res 59:193–203CrossRefzbMATHMathSciNetGoogle Scholar
  3. Blazewicz J, Ecker K, Kis T, Tanas M (2001) A note on the complexity of scheduling coupled tasks on a single processor. J Brazilian Comput Soc 7:23–26CrossRefGoogle Scholar
  4. Elshafei M, Sherali HD, Smith JC (2004) Radar pulse interleaving for multi-target tracking. Nav Res Logist 51(1):72–94CrossRefzbMATHMathSciNetGoogle Scholar
  5. Li H, Zhao H (2007) Scheduling coupled-tasks on a single machine. In: IEEE symposium on computational intelligence in scheduling SCIS ’07, pp 137–142Google Scholar
  6. Orman AJ, Potts CN (1997) On the complexity of coupled-task scheduling. Discret Appl Math 72:141–154CrossRefzbMATHMathSciNetGoogle Scholar
  7. Orman AJ, Potts CN, Shahani AK, Moore AR (1996) Scheduling for a multifunction phased array radar system. Eur J Oper Res 90:13–25CrossRefzbMATHGoogle Scholar
  8. Potts CN, Whitehead JD (2007) Heuristics for a coupled-operation scheduling problem. J Oper Res Soc 58:1375–1388CrossRefzbMATHGoogle Scholar
  9. Sherali HD, Smith JC (2005) Interleaving two-phased jobs on a single machine with application to radar pulse interleaving. Discret Optim 2:348–361CrossRefzbMATHMathSciNetGoogle Scholar
  10. Tanas M, Blazewicz J, Ecker K (2007) Polynomial time algorithm for coupled tasks scheduling problem. In: Blazewicz J, Ecker K, Hammer B (eds) ICOLE 2007. Lessach, Austria. Report IfI-07-03, TU Clausthal, pp 76–69Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • József Békési
    • 1
  • Gábor Galambos
    • 1
  • Michael N. Jung
    • 2
  • Marcus Oswald
    • 2
  • Gerhard Reinelt
    • 2
    Email author
  1. 1.Department of Computer Sciences, Juhász Gyula Teacher Training FacultyUniversity of SzegedSzeged Hungary
  2. 2.Fakultät für Mathematik und Informatik, Institut für InformatikUniversität HeidelbergHeidelbergGermany

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