Skip to main content
Log in

Abstract

Recently, the theory of sortability of partition property has been shown to be an effective tool to prove the existence of an optimal partition with that property. In this paper, we extend the theory to multi-partition where the partition is on t types of components. We apply our results to settle an optimal assignment problem whose proof was incomplete as given in the literature.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Chakravarty, A.K., Orlin, J.B. and Rothlbum, U.G. (1982), A partitioning problem with additive objective with an application to optimal inventory grouping for joint replenishment, Oper. Res. 30: 1018–1022.

    Google Scholar 

  2. Chang G.J. et al. (1999), Sortabilities of partition properties, J. Combin. Opt. 2: 413–427.

    Google Scholar 

  3. Derman, C., Lieberman, G.J. and Ross, S.M. (1972), On optimal assembly of systems, Naval Res. Logist. Quart. 19: 564–574.

    Google Scholar 

  4. Du, D.Z., When is a monotonic grouping optimal? in: Osalei, S. and Cas, J. (eds), Reliability Theory and Applications, World Scientific, New Jersey, pp. 66–76.

  5. Du, D.Z. and Hwang, F.K. (1990), Optimal assembly of an s-stage k-out-of-n system, SIAM J. Disc. Math. 3: 349–354.

    Google Scholar 

  6. Hollander, M., Proschan, F. and Sethuraman, J. (1977), Functions decreasing in transportation and their applications in ranking problems, Ann. Statist. 5: 722–733. 472 F.K. HWANG ET AL.

    Google Scholar 

  7. Hwang, F.K. (1981), Optimal partitions, J. Opt. Thy. and Appl. 34: 1–10.

    Google Scholar 

  8. Hwang, F.K. and Mallows, C.L. (1995), Enumerating consecutive and nested partitions, J. Combin. Thys., Series A 70: 1–23.

    Google Scholar 

  9. Hwang, F.K. and Rothblum, U.G. (1994), Optimality of monotone assemblies for coherent systems composed of series modules, Oper. Res. 42: 709–720.

    Google Scholar 

  10. Hwang, F.K., Rothblum, U.G. and Yao, Y.C. (1996), Localizing combinatorial properties of partitions, Disc. Math. 160: 1–23.

    Google Scholar 

  11. El-Neweihi, E., Proschan, F. and Setheraman, J. (1987), Optimal assembly of systems using Schur functions and majorization, Naval Res. logist. Quart. 34: 705–712.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hwang, F., Wang, Y. & Lee, J. Sortability of Multi-partitions. Journal of Global Optimization 24, 463–472 (2002). https://doi.org/10.1023/A:1021216024210

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021216024210

Keywords

Navigation