Optimal Path Problems with Second-Order Stochastic Dominance Constraints
This paper studies optimal path problems integrated with the concept of second order stochastic dominance. These problems arise from applications where travelers are concerned with the trade off between the risks associated with random travel time and other travel costs. Risk-averse behavior is embedded by requiring the random travel times on the optimal paths to stochastically dominate that on a benchmark path in the second order. A general linear operating cost is introduced to combine link- and path-based costs. The latter, which is the focus of the paper, is employed to address schedule costs pertinent to late and early arrival. An equivalent integer program to the problem is constructed by transforming the stochastic dominance constraint into a finite number of linear constraints. The problem is solved using both off-the-shelf solvers and specialized algorithms based on dynamic programming (DP). Although neither approach ensures satisfactory performance for general large-scale problems, the numerical experiments indicate that the DP-based approach provides a computationally feasible option to solve medium-size instances (networks with several thousand links) when correlations among random link travel times can be ignored. Copyright Springer Science+Business Media, LLC 2012
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
- Carraway, Robert L. & Morin, Thomas L. & Moskowitz, Herbert, 1990. "Generalized dynamic programming for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 44(1), pages 95-104, January.
- Miller-Hooks, Elise & Mahmassani, Hani, 2003. "Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 146(1), pages 67-82, April.
- Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Current, J. R. & Re Velle, C. S. & Cohon, J. L., 1985. "The maximum covering/shortest path problem: A multiobjective network design and routing formulation," European Journal of Operational Research, Elsevier, vol. 21(2), pages 189-199, August.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:12:y:2012:i:4:p:561-587. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.