Skip to main content

Transporting Jobs through a Processing Center with Two Parallel Machines

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6508))

Abstract

In this paper, we consider a processing system that consists of two identical parallel machines such that the jobs are delivered to the system by a single transporter and moved between the machines by the same transporter. The objective is to minimize the length of a schedule, i.e., the time by which the completed jobs are collected together on board the transporter. The jobs can be processed with preemption, provided that the portions of jobs are properly transported to the corresponding machines. We establish properties of feasible schedule, define lower bounds on the optimal length and describe an algorithm that behaves like a fully polynomial-time approximation scheme (FPTAS).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brucker, P., Knust, S., Cheng, T.C.E., Shakhlevich, N.V.: Complexity results for flow-shop and open-shop scheduling problems with transportation delays. Ann. Oper. Res. 129, 81–106 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dell’Amico, M.: Shop problems with two machines and time lags. Oper. Res. 44, 777–787 (1996)

    Article  MATH  Google Scholar 

  3. Hall, L.A.: Approximability of flow shop scheduling. Math. Progr. B 82, 175–190 (1998)

    MathSciNet  MATH  Google Scholar 

  4. Hurink, J., Knust, S.: Makespan minimization for flow-shop problems with transportation times and a single robot. Discrete Appl. Math. 112, 199–216 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kellerer, H., Mansini, R., Pferschy, U., Speranza, M.G.: An efficient fully polynomial approximation scheme for the Subset-Sum Problem. J. Comput. Syst. Sci. 66, 349–370 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  7. Lee, C.-Y., Chen, Z.-L.: Machine scheduling with transportation times. J. Schedul. 4, 3–24 (2001)

    Article  MATH  Google Scholar 

  8. Lee, C.-Y., Strusevich, V.A.: Two-machine shop scheduling with an uncapacitated interstage transporter. IIE Trans. 37, 725–736 (2005)

    Article  Google Scholar 

  9. Lushchakova, I.N., Soper, A.J., Strusevich, V.A.: Transporting jobs through a two-machine open shop. Naval. Res. Log. 56, 1–18 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Qi, X.: A logistic scheduling model: scheduling and transshipment for two processing centers. IIE Trans. 38, 609–618 (2006)

    Article  Google Scholar 

  11. Soper, A.J., Strusevich, V.A.: An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter. Int J. Found. Computer Sci. 18, 565–591 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Strusevich, V.A.: A heuristic for the two-machine open-shop scheduling problem with transportation times. Discrete Appl. Math. 93, 287–304 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yu, W., Hoogeveen, H., Lenstra, J.K.: Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard. J. Schedul. 7, 333–348 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kellerer, H., Soper, A.J., Strusevich, V.A. (2010). Transporting Jobs through a Processing Center with Two Parallel Machines. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17458-2_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17457-5

  • Online ISBN: 978-3-642-17458-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics