Annals of Operations Research

, Volume 129, Issue 1–4, pp 81–106 | Cite as

Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays

  • Peter Brucker
  • Sigrid Knust
  • T.C. Edwin Cheng
  • Natalia V. Shakhlevich


We consider shop problems with transportation delays where not only the jobs on the machines have to be scheduled, but also transportation of the jobs between the machines has to be taken into account. Jobs consisting of a given number of operations have to be processed on machines in such a way that each machine processes at most one operation at a time and a job is not processed by more than one machine simultaneously. Transportation delays occur if a job changes from one machine to another. The objective is to find a feasible schedule which minimizes some objective function. A survey of known complexity results for flow-shop and open-shop environments is given and some new complexity results are derived.

scheduling transportation delays time-lags shop problems complexity results 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Achugbue, J.O. and F.Y. Chin. (1982). “Scheduling the Open Shop to Minimize Mean Flow Time.” SIAM Journal on Computing 11, 709–720.Google Scholar
  2. Brucker, P. (2001). “Scheduling Algorithms.” 3rd ed. Berlin: Springer.Google Scholar
  3. Chretienne, P. and C. Picouleau. (1995). “Scheduling with Communication Delays: A Survey.” In P. Chretiennne, E.G. Coffman, Jr., J.K. Lenstra and Z. Liu (eds.), Scheduling Theory and Its Applications. Chichester: Wiley.Google Scholar
  4. Crama, Y., V. Kats, J. Klundert, and E. van de Levner. (2000). “Cyclic Scheduling in Robotic Flowshops.” Annals of Operations Research 96, 97–124.Google Scholar
  5. Dell'Amico, M. (1996). “Shop Problems with Two Machines and Time Lags.” Operations Research 44, 777–787.Google Scholar
  6. Garey, M.R., D.S. Johnson, and R. Sethi. (1976). “The Complexity of Flowshop and Jobshop Scheduling.” Mathematics of Operations Research 1, 117–129.Google Scholar
  7. Gonzalez, T. and S. Sahni. (1976). “Open Shop Scheduling to Minimize Finish Time.” Journal of the Association for Computing Machinery 23, 665–679.Google Scholar
  8. Graham, R.L., E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. (1979). “Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey.” Annals of Discrete Mathematics 5, 287–326.Google Scholar
  9. Hardy, G.H., J.E. Littlewood, and G. Polya. (1934, 1952). Inequalities, 1st ed., 2nd ed., London/New York: Cambridge Univ. Press.Google Scholar
  10. Johnson, S.M. (1954). “Optimal Two-and Three-Stage Production Schedules with Setup Times Included.” Naval Research Logistics Quarterly 1, 61–68.Google Scholar
  11. Kise, H. (1991). “On an Automated Two-Machine Flowshop Scheduling Problem with Infinite Buffer.” Journal of the Operations Research Society Japan 34, 354–361.Google Scholar
  12. Knust, S. (1999). “Shop-Scheduling Problems with Transportation.” Ph.D. thesis. Fachbereich Mathematik/ Informatik, Universität Osnabrück.Google Scholar
  13. Lawler, E.L., J.K. Lenstra, and A.H.G. Rinnooy Kan. (1981, 1982). “Minimizing Maximum Lateness in a Two-Machine Open Shop.” Mathematics of Operations Research 6, 153–158; Erratum, Mathematics of Operations Research 7, 635.Google Scholar
  14. Lee, C.-Y. and Z.-L. Chen. (2001). “Machine Scheduling with Transportation Considerations.” Journal of Scheduling 4, 3–24.Google Scholar
  15. Lenstra, J.K., A.H.G. Rinnooy Kan, and P. Brucker. (1977). “Complexity of Machine Scheduling Problems.” Annals of Discrete Mathematics 1, 343–362.Google Scholar
  16. Mitten, L.G. (1958). “Sequencing n Jobs on Two Machines with Arbitrary Time Lags.” Management Science 5, 293–298.Google Scholar
  17. Rayward-Smith, V.J. and D. Rebaine. (1992). “Open Shop Scheduling with Delays.” Theoretical Informatics and Applications 26, 439–448.Google Scholar
  18. Rebaine, D. and V.A. Strusevich. (1999). “Two-Machine Open Shop Scheduling with Special Transportation Times.” Journal of the Operational Research Society 50, 756–764.Google Scholar
  19. Strusevich, V.A. (1999). “A Heuristic for the Two-Machine Open-Shop Scheduling with Transportation Times.” Discrete Applied Mathematics 93, 287–304.Google Scholar
  20. Veltmann, B., B. Lageweg, and J.K. Lenstra. (1990). “Multiprocessor Scheduling with Communication Delays.” Parallel Computing 16, 173–182.Google Scholar
  21. Yu, W. (1996). “The Two-Machine Flow Shop Problem with Delays and the One-Machine Total Tardiness Problem.” Ph.D. thesis. Technische Universiteit Eindhoven.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Peter Brucker
    • 1
  • Sigrid Knust
    • 1
  • T.C. Edwin Cheng
    • 2
  • Natalia V. Shakhlevich
    • 3
  1. 1.Fachbereich Mathematik/InformatikUniversität OsnabrückOsnabrückGermany
  2. 2.The Hong Kong Polytechnic UniversityKowloonHong Kong
  3. 3.School of ComputingUniversity of LeedsLeedsUK

Personalised recommendations