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 KautEmail author
  • Teodor Gabriel Crainic
Open Access
Original Paper


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.


Single-commodity network design Stochastic Correlation Robustness 



This project was supported in part by Grant 171007/V30 from The Research Council of Norway. While working on this project, T.G. Crainic was the NSERC Industrial Research Chair on Logistics Management, ESG UQAM, and Adjunct Professor with the Department of Computer Science and Operations Research, Université de Montréal, and the Department of Economics and Business Administration, Molde University College, Norway. Partial funding for this project has been provided by the Natural Sciences and Engineering Council of Canada (NSERC), through its Industrial Research Chair and Discovery Grants programs.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  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. 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

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Biju K. Thapalia
    • 1
  • Stein W. Wallace
    • 2
  • Michal Kaut
    • 3
    Email author
  • 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

Personalised recommendations