The sample average approximation method applied to stochastic routing problems: A computational study

Computational Optimization and Applications

Volumn 24, Issue 2-3, 2003, Pages 289-333

  Verweij, Bram ^a   Ahmed, Shabbir ^a   Kleywegt, Anton J ^a   Nemhauser, George ^a   Shapiro, Alexander ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Shortest path; Stochastic optimization; Stochastic programming; Stochastic routing; Traveling salesman

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DYNAMIC PROGRAMMING; HEURISTIC METHODS; MONTE CARLO METHODS;

STOCHASTIC ROUTING;

STOCHASTIC PROGRAMMING;

EID: 0037322974     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021814225969     Document Type: Article

References (43)

1. G. Andreatta, "Shortest path models in stochastic networks," in Stochastics in Combinatorial Optimization, G. Andreatta, F. Mason, and P. Serafini (Eds.), CISM Udine, World Scientific Publishing: Singapore, 1987, pp. 178-186.
2. G. Andreatta and L. Romeo, "Stochastic shortest paths with recourse," Networks, vol. 18, pp. 193-204, 1988.
3. D. Applegate, R. Bixby, V. Chvátal, and W. Cook, "On the solution of traveling salesman problems," Documenta Mathematica, extra volume ICM 1998 III, pp. 645-656, 1998.
4. J.B. Birge and F.V. Louveaux, Introduction to Stochastic Programming, Springer-Verlag: Berlin, 1997.
5. Y. Ermoliev and R.J.-B. Wets (Eds.), Numerical Techniques for Stochastic Optimization, Springer-Verlag: Berlin, 1988.
6. M.R. Garey and D.S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness, W.H. Freeman and Company: New York, 1979.
7. S. Garstka and D. Rutenberg, "Computation in discrete stochastic programming with recourse," Operations Research, vol. 21, pp. 112-122, 1973.
8. C.J. Geyer and E.A. Thompson, "Constrained Monte Carlo maximum likelihood for dependent data (with discussion)," Journal of the Royal Statistical Society Series B, vol. 54, pp. 657-699, 1992.
9. R.E. Gomory and T.C. Hu, "Multi-terminal network flows," SIAM Journal on Applied Mathematics, vol. 9, pp. 551-570, 1961.
10. J. Hao and J.B. Orlin, "A faster algorithm for finding the minimum cut in a graph," in Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, 1992, pp. 165-174.
11. J.L. Higle and S. Sen, "Stochastic decomposition: An algorithm for two stage stochastic linear programs with recourse," Mathematics of Operations Research, vol. 16, pp. 650-669, 1991.
12. J.L. Higle and S. Sen, Stochastic Decomposition, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996.
13. ILOG, Inc., CPLEX Division, Incline Village, Nevada, CPLEX, a division of ILOG, 2001.
14. G. Infanger, Planning Under Uncertainty: Solving Large Scale Stochastic Linear Programs, Boyd and Fraser: Derivers, MA, 1994.
15. D.S. Johnson and L.A. McGeoch, "The traveling salesman problem: A case study," in Local Search in Combinatorial Optimization, E. Aarts and J.K. Lenstra (Eds.), John Wiley & Sons: Chichester, 1997, pp. 215-310.
16. A.J. Kleywegt, A. Shapiro, and T. Homem-de-Mello, "The sample average approximation method for stochastic discrete optimization," SIAM Journal on Optimization, vol. 12, pp. 479-502, 2001.
17. G. Laporte and F.V. Lonveaux, "The integer L-shaped method for stochastic integer programs with complete recourse," Operations Research Letters, vol. 13, pp. 133-142, 1993.
18. G. Laporte, F.V. Louveaux, and H. Mercure, "Models and exact solutions for a class of stochastic location-routing problems," European Journal of Operational Research, vol. 39, pp. 71-78, 1989.
19. G. Laporte, F.V. Louveaux, and H. Mercure, "The vehicle routing problem with stochastic travel times," Transportation Science, vol. 26, pp. 161-170, 1992.
20. G. Laporte, F.V. Louveaux, and H. Mercure, "A priori optimization of the probabilistic traveling salesman problem," Operations Research, vol. 42, pp. 543-549, 1994.
21. G. Laporte, F.V. Louveaux, and L. van Hamme, "Exact solution of a stochastic location problem by an integer L-shaped algorithm," Transportation Science, vol. 28, pp. 95-103, 1994.
22. W.K. Mak, D.P. Morton, and R.K. Wood, "Monte Carlo bounding techniques for determining solution quality in stochastic programs," Operations Research Letters, vol. 24, pp. 47-56, 1999.
23. G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley and Sons: New York, 1988.
24. V.I. Norkin, Y.M. Ermoliev, and A. Ruszczyński, "On optimal allocation of indivisibles under uncertainty," Operations Research, vol. 46, pp. 381-395, 1998.
25. V.I. Norkin, G.Ch. Pflug, and A. Ruszczyński, "A branch and bound method for stochastic global optimization," Mathematical Programming, vol. 83, pp. 425-450, 1998.
26. M.W. Padberg and G. Rinaldi, "Facet identification for the symmetric traveling salesman polytope," Mathematical Programming, vol. 47, pp. 219-257, 1990.
27. M.W. Padberg and G. Rinaldi, "A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems," SIAM Review, vol. 33, pp. 60-100, 1991.
28. E.L. Plambeck, B.R. Fu, S.M. Robinson, and R. Suri, "Sample-path optimization of convex stochastic performance functions," Mathematical Programming, vol. 75, pp. 137-176, 1996.
29. G. Reinelt, http://softlib.rice.edu/softlib/tsplib, 1995.
30. R.Y. Rubinstein and A. Shapiro, "Optimization of static simulation models by the score function method," Mathematics and Computers in Simulation, vol. 32, pp. 373-392, 1990.
31. A. Schrijver, Theory of Linear and Integer Programming, John Wiley & Sons: Chichester, 1986.
32. A. Shapiro, "Simulation-based optimization: Convergence analysis and statistical inference," Stochastic Models, vol. 12, pp. 425-454, 1996.
33. A. Shapiro and T. Homem-de-Mello, "A simulation-based approach to two-stage stochastic programming with recourse," Mathematical Programming, vol. 81, pp. 301-325, 1998.
34. A. Shapiro and T. Homem-de-Mello, "On rate of convergence of Monte Carlo approximations of stochastic programs," SIAM Journal on Optimization, vol. 11, pp. 70-86, 2001.
35. A.M. Spaccamela, A.H.G. Rinnooy Kan, and L. Stougie, "Hierarchical vehicle routing problems," Networks, vol. 14, pp. 571-586, 1984.
36. R.M. Van Slyke and R.J.-B. Wets, "L-shaped linear programs with applications to optimal control and stochastic programming," SIAM Journal on Applied Mathematics, vol. 17, pp. 638-663, 1969.
37. A.M. Verweij, "Selected applications of integer programming: A computational study," Ph.D. Thesis, Department of Computer Science, Utrecht University, Utrecht, 2000.
38. S.W. Wallace, "Solving stochastic programs with network recourse," Networks, vol. 16, pp. 295-317, 1986.
39. S.W. Wallace, "Investing in arcs in a network to maximize the expected max flow," Networks, vol. 17, pp. 87-103, 1987.
40. S.W. Wallace, "A two-stage stochastic facility-location problem with time-dependent supply," in Numerical Techniques for Stochastic Optimization, Y. Ermoliev and R.J.-B. Wets, Springer-Verlag: Berlin, 1988, pp. 489-513.
41. R.J-B. Wets, "Solving stochastic programs with simple recourse," Stochastics, vol. 10, pp. 219-242, 1983.
42. R.J.-B. Wets, "Large scale linear programming techniques," in Numerical Techniques for Stochastic Optimization, Y. Ermoliev and R.J.-B Wets, Springer-Verlag: Berlin, 1988, pp. 65-93.
43. L.A. Wolsey, Integer Programming, John Wiley and Sons: New York, 1998.