The VRP with Time Window Constraints

  • Julien Bramel
  • David Simchi-Levi
Part of the Springer Series in Operations Research book series (ORFE)


In many distribution systems each customer specifies, in addition to the load that has to be delivered to it, a period of time, called a time window, in which this delivery must occur. The objective is to find a set of routes for the vehicles, where each route begins and ends at the depot, serves a subset of the customers without violating the vehicle capacity and time window constraints, while minimizing the total length of the routes. We call this model the Vehicle Routing Problem with Time Windows (VRPTW).


Schedule Problem Vehicle Capacity Vehicle Route Problem With Time Window Assignment Cost Time Window Constraint 
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Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Julien Bramel
    • 1
  • David Simchi-Levi
    • 2
  1. 1.Management Science Division Graduate School of BusinessColumbia UniversityNew YorkUSA
  2. 2.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA

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