Abstract
In this paper we provide an overview and modeling details regarding vehicle routing in situations in which customer demand is revealed only when the vehicle arrives at the customer’s location. Given a fixed capacity vehicle, this setting gives rise to the possibility that the vehicle on arrival does not have sufficient inventory to completely supply a given customer’s demand. Such an occurrence is called a route failure and it requires additional vehicle trips to fully replenish such a customer. Given a set of customers, the objective is to design vehicle routes and response policies which minimize the expected delivery cost by a fleet of fixed capacity vehicles. We survey the different problem statements and formulations. In addition, we describe a number of the algorithmic developments for constructing routing solutions. Primarily we focus on stochastic programming models with different recourse options. We also present a Markov decision approach for this problem and conclude with a cha llenging conjecture regarding finite sums of random variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Applegate, D., R. Bixby, V. Chvatal, and W. Cook. (1998). “On the solution of traveling salesman problem”, Documenta Mathemaitica, extra volume ICM 1998; III, 645–656.
Bertsimas, D.J. (1992). “A vehicle routing problem with stochastic demand”, Operations Research 40, 574–585.
Bertsimas, D.J., P. Chevi, and M. Peterson. (1995). “Computational approaches to stochastic vehicle routing problems”, Transportation Science 29,342–352.
Birge, J.R. (1985). “decomposition and partition methods for multistage stochastic linear programs”, Operations Research 33, 989–1007.
Clarke, C. and J.W. Wright. (1964). “Scheduling of vehicles from a central depot to a number of delivery points”, Operations Research 12, 568–581.
Dror, M. (1983). The Inventory Routing Problem, Ph.D. Thesis, University of Maryland. College Park, Maryland, USA.
Dror, M. (1993). “Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution”, European J. of Operational Research 64, 532–441.
Dror, M. and P. Trudeau. (1986). “Stochastic vehicle routing with modified savings algorithm”, European Journal of Operations Research 23, 228–235.
Dror, M, M.O. Ball, and B.L. Golden. (1985). “Computational comparison of algorithms for inventory routing”, Annals of Operations Research 4, 3–23.
Dror, M., G. Laporte, and P. Trudeau. (1989). “Vehicle routing with stochastic demands: Properties and solution framework”, Transportation Science 23, 166–176.
Dror, M., G. Laporte, and V.F. Louveaux. (1993). “Vehicle routing with stochastic demands and restricted failures”, ZOR-Zeitschrift fur Operations Research 37, 273–283.
Eilon, S, C.D.T. Watson-Gandy, N. Christofides. (1971). Distribution Management: Mathematical Modelling and Practical Analysis, Griffin, London.
Jailet, P. (1985). “Probabilistic traveling salesman problem”, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Kreimer J. and M. Dror. (1990). “The monotonicity of the threshold detection probability in stochastic accumulation process”, Computers & Operations Research 17, 63–71.
Laipala, T. (1978). “On the solutions of the stochastic traveling salesman problems”, European J. of Operational Research 2, 291–297.
Laporte, G. and F.V. Louveaux. (1993). “The integer L-shaped method for stochastic integer programs with complete recourse”, Operations Research Letters 13, 133–142.
Laporte, G., F.V. Louveaux, and L. Van hamme. (2001). “An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands”, Operations Research (forthcoming).
Larson, R.C. (1988). “Transportation of sludge to the 106-mile site: An inventory routing algorithm for fleet sizing and logistical system design”, Transportation Science 22, 186–198.
Noon, C.E. and J.C. Bean. (1991). “A Lagrnagian based approach to the asymmetric Generalized Traveling Salesman Problem”, Operations Research 39, 623–632.
Noon, C.E. and J.C. Bean. (1993). “An efficient transformation of the Generalized Traveling Salesman Problem”, IN FOR 31, 39–44.
Secomandi, N. (1998). “Exact and Heuristic Dynamic Programming Algorithms for the Vehicle Routing Problem with Stcochastic Demands”, Doctoral Dissertation, University of Houston, USA.
Secomandi, N. (2000). “Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands”, Computers & Operations Research 27, 1201–1225.
Stewart, W.R., Jr. and B.L. Golden. (1983). “Stochastic vehicle routing: A comprehensive approach”, European Journal of Operational Research 14, 371–385.
Stewart, W.R., Jr., B.L. Golden, and F. Gheysens. (1983). “A survey of stochastic vehicle routing”, Working Paper MS/S, College of Business and Management, University of Maryland at College Park.
Trudeau, P. and M. Dror. (1992). “Stochastic inventory routing: Stockouts and route failure”, Transportation Science 26,172–184.
Yang, W.-H. (1996). “Stochastic Vehicle Routing with Optimal Restocking”, Ph.D. Thesis, Case Western Reserve University, Cleveland, OH.
Yang, W.-H., K. Mathur, and R.H. Ballou. (2000). “Stochastic vehicle routing problem with restocking”, Transportation Science 34, 99–112.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science + Business Media, Inc.
About this chapter
Cite this chapter
Dror, M. (2002). Vehicle Routing with Stochastic Demands: Models & Computational Methods. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, New York, NY. https://doi.org/10.1007/0-306-48102-2_25
Download citation
DOI: https://doi.org/10.1007/0-306-48102-2_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-7923-7463-3
Online ISBN: 978-0-306-48102-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)