Computational Management Science

, Volume 9, Issue 1, pp 139–160 | Cite as

Single source single-commodity stochastic network design

  • Biju K. Thapalia
  • Stein W. Wallace
  • Michal Kaut
  • Teodor Gabriel Crainic
Open Access
Original Paper

Abstract

Stochastics affects the optimal design of a network. This paper examines the single-source single-commodity stochastic network design problem. We characterize the optimal designs under demand uncertainty and compare with the deterministic counterparts to outline the basic structural differences. We do this partly as a basis for developing better algorithms than are available today, partly to simply understand what constitutes robust network designs.

Keywords

Single-commodity network design Stochastic Correlation Robustness 

References

  1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows—theory, algorithms, and applications. Prentice-Hall, Englewood CliffsGoogle Scholar
  2. Aronson JE (1989) A survey of dynamic network flows. Ann oper res 20: 1–66CrossRefGoogle Scholar
  3. Crainic TG, Gendreau M, Farvolden JM (2000) A simplex-based tabu search method for capacitated network design. Inf J Comput 12(3): 223–236. doi:10.1287/ijoc.12.3.223.12638 CrossRefGoogle Scholar
  4. Evans JR (1978) A single-commodity transformation for certain multi-commodity networks. Oper Res 26(4): 673–680CrossRefGoogle Scholar
  5. Gansner ER, North SC (2000) An open graph visualization system and its applications to software engineering. Softw Pract Experience 30(11): 1203–1233. doi:10.1002/1097-024X(200009)30:11<1203::AID-SPE338>3.0.CO;2-N CrossRefGoogle Scholar
  6. Higle JL, Wallace SW (2003) Sensitivity analysis and uncertainty in linear programming. Interfaces 33: 53–60CrossRefGoogle Scholar
  7. Hochbaum DS, Segev A (1989) Analysis of a flow problem with fixed charge. Networks 19: 291–312CrossRefGoogle Scholar
  8. Høyland K, Kaut M, Wallace SW (2003) A heuristic for moment-matching scenario generation. Comp Optim Appl 24(2–3): 169–185CrossRefGoogle Scholar
  9. Kaut M, Wallace SW (2007) Evaluation of scenario-generation methods for stochastic programming. Pacific J Optim 3(2): 257–271Google Scholar
  10. Kuah GK, Perl J (1989) The feeder-bus network-design problem. J Oper Res Soc 40(8): 751–767Google Scholar
  11. Kuan SN, Ong HL, Ng KM (2006) Solving the feeder bus network design problem by genetic algorithms and ant colony optimization. Adv Eng Softw 37(6): 351–359CrossRefGoogle Scholar
  12. Liang LY, Thompson RG, Young DM (2004) Optimising the design of sewer networks using genetic algorithms and tabu search. Eng, Constr Archit Manag 11(2): 101CrossRefGoogle Scholar
  13. Lium A-G, Crainic TG, Wallace SW (2007) Correlations in stochastic programming: a case from stochastic service network design. Asia-Pacific J Oper Res 24((2): 161–179CrossRefGoogle Scholar
  14. Lium A-G, Crainic TG, Wallace SW (2009) A study of demand stochasticity in stochastic network design. Transp Sci 43(2): 144–157CrossRefGoogle Scholar
  15. Orlowski S, Pióro M, Tomaszewski A, Wessäly R (2010) SNDlib 1.0—Survivable network design library. Networks 55(3): 276–286. doi:10.1002/net.20371 Google Scholar
  16. Rothfarb B, Goldstein M (1971) The one-terminal telepak problem. Oper Res 19: 156–169CrossRefGoogle Scholar
  17. Rothfarb B, Frank H, Rosenbaum DM, Steiglitz K, Kleitman DJ (1970) Optimal design of offshore natural-gas pipeline system. Oper Res 18: 992–1020CrossRefGoogle Scholar
  18. Sherali HD, Smith EP (1997) A global optimization approach to a water distribution network design problem. J Glob Optim 11(2): 107–132CrossRefGoogle Scholar
  19. Wallace SW (2000) Decision making under uncertainty: Is sensitivity analysis of any use. Oper Res 48(1): 20–25CrossRefGoogle Scholar
  20. Wallace SW (2010) Stochastic programming and the option of doing it differently. Ann Oper Res 177(1): 3–8CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Biju K. Thapalia
    • 1
  • Stein W. Wallace
    • 2
  • Michal Kaut
    • 3
  • Teodor Gabriel Crainic
    • 4
  1. 1.Molde University CollegeMoldeNorway
  2. 2.Lancaster University Management SchoolLancasterEngland
  3. 3.Norwegian University of Science and TechnologyTrondheimNorway
  4. 4.Université du Québec à Montréal (UQAM)MontrealCanada

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