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212 Deolinda M. L. D. Rasteiro and António J. B. AnjoFigure 4. Running times (seconds) for acyclic networkswithout initialization.Figure 5. Running times (seconds) for acyclic networkswith initialization.Figure 6. Running times (seconds) for cyclic networkswithout initialization.Figure 7. Running times (seconds) for cyclic networkswith initialization.References[1] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network flows theory, algorithms, and applications, Uper SaddleRiver, Prentice-Hall, 1993.[2] J. F. Bard and J. E. Bennett, Arc reduction and path preference in stochastic acyclic networks, Management Science31/7 (1991), 198–215.[3] R. Bellman, On a routing problem, Quarterly of Applied Mathematics 16 (1958), 88–90.[4] R. K. Cheung and B. Muralidharan, Dynamic routing of priority shipments on a less-thantruckload service network,Tech. report, Department of Industrial and Manufacturing Systems Engineering, Iowa State University, 1995.[5] P. C Fishburn, Utility theory for decision making, Wiley, New York, 1970.[6] H. Frank, Shortest paths in probabilistic graphs, Operations Research 17 (1969), 583–599.[7] R. D. Luce and H. Raiffa, Games and decisions, Wiley, New York, 1957.[8] J. W. Pratt, H. Raiffa, and R. O. Schlaifer, Introduction to statistical decision theory, McGraw-Hill, New York,1965.[9] L. J. Savage, The foundations of statistics, Wiley, New York, 1954.[10] J. von Neumann and O. Mogenstern, Theory of games and economic behavior, Princeton University Press,Princeton, N.J., 1947.[11] Rasteiro, D.M.L.D. and Anjo, A.J.B., Optimal Paths in Probabilistic Networks , Journal of Mathematical Sciences120/1 (2004), 974–987.