Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles

In 1991, D. J. Bertsimas and G. van Ryzin introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a Euclidean region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. This paper extends our analysis in several directions. First, we analyze the problem of m identical vehicles with unlimited capacity and show that in heavy traffic the system time is reduced by a factor of 1/m2 over the single-server case. One of these policies improves by a factor of two on the best known system time for the single-server case. We then consider the case in which each vehicle can serve at most q customers before returning to a depot. We show that the stability condition in this case depends strongly on the geometry of the region. Several pol...

[1]  Richard M. Karp,et al.  Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane , 1977, Math. Oper. Res..

[2]  Patrick Jaillet,et al.  A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers Are Visited , 1988, Oper. Res..

[3]  Dimitris Bertsimas,et al.  A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane , 1991, Oper. Res..

[4]  Warren B. Powell,et al.  THE DYNAMIC VEHICLE ALLOCATION PROBLEM WITH UNCERTAIN DEMANDS , 1987 .

[5]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  Patrick Jaillet,et al.  A Priori Optimization , 1990, Oper. Res..

[8]  Michael J. Ferguson,et al.  Exact Results for Nonsymmetric Token Ring Systems , 1985, IEEE Trans. Commun..

[9]  N. Biggs.  THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

[10]  D. Bertsimas.  Probabilistic combinatorial optimization problems , 1988 .

[11]  D. Bertsimas,et al.  Stochastic and dynamic vehicle routing with general demand and interarrival time distributions , 1993, Advances in Applied Probability.

[12]  Kathryn E. Stecke,et al.  REVIEW OF OPERATOR/MACHINE INTERFERENCE MODELS. , 1985 .

[13]  Gerald G. Brown,et al.  Real-Time Dispatch of Petroleum Tank Trucks , 1981 .

[14]  D. Iglehart,et al.  Multiple channel queues in heavy traffic. I , 1970, Advances in Applied Probability.

[15]  Amedeo R. Odoni,et al.  A single-server priority queueing-location model , 1988, Networks.

[16]  Paul M. Thompson,et al.  Analysis and solution algorithms of sealift routing and scheduling problems : final report , 1985 .

[17]  Dimitris Bertsimas,et al.  A Vehicle Routing Problem with Stochastic Demand , 1992, Oper. Res..

[18]  J. Steele.  Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability , 1981 .

[19]  高木 英明,et al.  Analysis of polling systems , 1986 .

[20]  Alexander H. G. Rinnooy Kan,et al.  Bounds and Heuristics for Capacitated Routing Problems , 1985, Math. Oper. Res..

[21]  U. Yechiali,et al.  Dynamic priority rules for cyclic-type queues , 1989, Advances in Applied Probability.

[22]  Thomas L. Magnanti,et al.  Extremum Properties of Hexagonal Partitioning and the Uniform Distribution in Euclidean Location , 1988, SIAM J. Discret. Math..

[23]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[24]  Izhak Rubin,et al.  Polling with a General-Service Order Table , 1987, IEEE Trans. Commun..

[25]  Saligrama R. Agnihothri.  A Mean Value Analysis of the Travelling Repairman Problem , 1988 .