Stochastic Vehicle Routing with Random Travel Times

References

  • Ahuja R. K., Magnanti T. L., Orlin J. B.Network Flows (1993) (Prentice Hall, Upper Saddle River, NJ) Google Scholar
  • Bastian C., Rinnooy Kan A. H. G. The stochastic vehicle routing problem revisited. Eur. J. Oper. Res. (1972) 56:407–412CrossrefGoogle Scholar
  • Berman O., Simchi-Levi D. The traveling salesman location problem on stochastic networks. Transportation Sci. (1989) 23:54–57LinkGoogle Scholar
  • Bertsimas D. J. A vehicle routing problem with stochastic demand. Oper. Res. (1992) 40:574–585LinkGoogle Scholar
  • Bertsimas D. J., Howell L. H. Further results on the probabilistic traveling salesman problem. Eur. J. Oper. Res. (1993) 65:68–95CrossrefGoogle Scholar
  • Bertsimas D. J., Jaillet P., Odoni A. R. A priori optimization. Oper. Res. (1990) 38:1019–1033LinkGoogle Scholar
  • Birge J. R. The value of the stochastic solution in stochastic linear programs with fixed recourse. Math. Programming (1982) 24:314–325CrossrefGoogle Scholar
  • Birge J. R., Louveaux F.Introduction to Stochastic Programming (1997) (Springer-Verlag, New York) Google Scholar
  • Carraway R. L., Morin T. L., Moskowitz H. Generalized dynamic programming for stochastic combinatorial optimization. Oper. Res. (1989) 37:819–829LinkGoogle Scholar
  • Clarke G., Wright J. W. Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. (1964) 12:568–581LinkGoogle Scholar
  • CPLEXCPLEX Manual, Version 6.0: Usingthe CPLEX Callable Library Including the CPLEX Base System with CPLEX Barrier and Mixed Integer Solver Options (1997) (CPLEX Division, ILOG, Inc., Incline Village, NV) Google Scholar
  • Crowder H., Johnson E. L., Padberg M. Solving large-scale zero-one linear programming problems. Oper. Res. (1983) 31:803–834LinkGoogle Scholar
  • Dantzig G. B., Fulkerson D. R., Johnson S. M. Solution of a large-scale traveling-salesman problem. Oper. Res. (1954) 2:393–410LinkGoogle Scholar
  • Dror M. Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution. Eur. J. Oper. Res. (1993) 64:432–441CrossrefGoogle Scholar
  • Dror M., Trudeau P. Stochastic vehicle routing with modified savings algorithm. Eur. J. Oper. Res. (1986) 23:228–235CrossrefGoogle Scholar
  • Dror M., Trudeau G. Laporte P. Vehicle routing with stochastic demands: Properties and solution frameworks. Transportation Sci. (1989) 23:166–176LinkGoogle Scholar
  • Edirisinghe N. C. P., Ziemba W. T. Tight bounds for stochastic convex programs. Oper. Res. (1992) 40:660–677LinkGoogle Scholar
  • Edmundson H. P. Bounds on the expectation of a convex function of a random variable. (1956) . Technical Report, The Rand Corporation Paper 982, Santa Monica, CAGoogle Scholar
  • Geoffrion A. M. Computer-based modeling environment. Eur. J. Oper. Res. (1989) 41:33–43CrossrefGoogle Scholar
  • Henig M. I. Risk criteria in a stochastic knapsack problem. Oper. Res. (1990) 38:820–825LinkGoogle Scholar
  • Hoffman K. L., Padberg M. Improving LP-representations of zero-one linear programs for branch-and-cut. ORSA J. Comput. (1991) 3:121–134LinkGoogle Scholar
  • Jaillet P. Probabilistic traveling salesman problems. (1985) . Technical Report No. 185, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
  • Jaillet P. A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Oper. Res. (1988) 36:929–936LinkGoogle Scholar
  • Jensen J. L. Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math. (1906) 30:175–193CrossrefGoogle Scholar
  • Kao E. P. C. A preference order dynamic program for a stochastic traveling salesman problem. Oper. Res. (1978) 26:1033–1045LinkGoogle Scholar
  • Kataoka S. A stochastic programming model. Econometrica (1963) 31:181–196CrossrefGoogle Scholar
  • Kleywegt A. J., Shapiro A., Homem-de-Mello T. The sample average approximation method for stochastic discrete optimization. Stochastic Programming E-Print Series (1999) . Available from: 〈 http://dochost.rz.hu-berlin.de/spepsGoogle Scholar
  • Lambert V., Laporte G., Louveaux F. Designing collection routes through bank branches. Comput. Oper. Res. (1993) 20:783–791CrossrefGoogle Scholar
  • Laporte G., Louveaux F., Gabzewicz J., Richard J.-F., Wolsey L. Formulations and bounds for the stochastic capacitated vehicle routing problem with uncertain supplies. Economic Decision Making: Games, Econometrics and Optimisation (1990) (North-Holland, Amsterdam, The Netherlands)443–455Google Scholar
  • Laporte G., Louveaux F. The integer L-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett. (1993) 13:133–142CrossrefGoogle Scholar
  • Laporte G., Louveaux F., Mercure H. Models and exact solutions for a class of stochastic location-routing problems. Eur. J. Oper. Res. (1989) 39:71–78CrossrefGoogle Scholar
  • Laporte G., Louveaux F., Mercure H. The vehicle routing problem with stochastic travel times. Transportation Sci. (1992) 26:161–170LinkGoogle Scholar
  • Laporte G., Louveaux F., Mercure H. A priori optimization of the probabilistic traveling salesman problem. Oper. Res. (1994) 42:543–549LinkGoogle Scholar
  • Laporte G., Nobert Y., Desrochers M. Optimal routing under capacity and distance restrictions. Oper. Res. (1985) 33:1050–1073LinkGoogle Scholar
  • Leipälä T. On the solutions of stochastic traveling salesman problems. Eur. J. Oper. Res. (1978) 2:291–297CrossrefGoogle Scholar
  • Loéve M.Probability Theory (1963) 3rd ed(D. Van Nostrand Company, Inc., Princeton, NJ) Google Scholar
  • Madansky A. Bounds on the expectation of a convex function of a multivariate random variable. Ann. Math. Statist. (1959) 30:743–746CrossrefGoogle Scholar
  • Mak W. K., Morton D. P., Wood R. K. Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. (1999) 24:47–56CrossrefGoogle Scholar
  • Morton D. P., Wood R. K., Woodruff D. On a stochastic knapsack problem and generalizations. Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research (1998) (Kluwer Academic Publishers, Dordrecht, The Netherlands) 149–168CrossrefGoogle Scholar
  • Padberg M., Rinaldi G. A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. (1991) 33:60–100CrossrefGoogle Scholar
  • Prékopa A. Stochastic Programming. (1995) (Kluwer Academic Publishers, Dordrecht, The Netherlands) CrossrefGoogle Scholar
  • Sniedovich M. Analysis of a preference order traveling salesman problem. Oper. Res. (1981) 29:1234–1237LinkGoogle Scholar
  • Stewart W. R., Golden B. L. Stochastic vehicle routing: A comprehensive approach. Eur. J. Oper. Res. (1983) 14:371–385CrossrefGoogle Scholar
  • Van Slyke R. M., Wets R. J. -B. L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. (1969) 17:638–663CrossrefGoogle Scholar
  • Wollmer R. D. Two-stage linear programming under uncertainty with 0-1 integer first stage variables. Math. Programming (1980) 19:279–288CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.