Optimization Letters

, Volume 7, Issue 6, pp 1215–1225 | Cite as

A multi-shift vehicle routing problem with windows and cycle times

  • Shabnam Zangeneh-Khamooshi
  • Zelda B. Zabinsky
  • Joseph A. Heim
Original Paper


In many applications of the vehicle routing problem with time windows (VRPTW), goods must be picked up within desired time frames. In addition, they have some limitations on their arrival time to the central depot. In this paper, we present a new version of VRPTW that minimizes the total cycle time of the goods. In order to meet the time windows and also minimize the cycle time, the courier’s schedule is allowed to vary. An algorithm, named VeRSA, is proposed to solve this problem. VeRSA employs concepts of scheduling theorems and algorithms to determine feasible routes and schedules of the available couriers. We prove a theoretical lower bound that provides a useful bound on the optimality gap. We also conduct a set of numerical experiments. VeRSA obtains a feasible solution faster than solving the MIP. The optimality gap using our proposed lower bound is smaller than the gap found with the standard LP relaxation.


Vehicle routing and scheduling Cycle time Logistics 


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  1. 1.
    Angelelli E., Grazia Speranza M., Savelsbergh M.W.P.: Competitive analysis for dynamic multiperiod uncapacitated routing problems. Networks 49, 308–317 (2007)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Kallehauge, B., Larsen, J., Madsen, O.B.G., Solomon, M.M.: Vehicle routing problem with time windows. Column Gener., 67–98 (2005)Google Scholar
  3. 3.
    Lee Y.H., Pinedo M.: Scheduling jobs on parallel machines with sequence-dependent setup times. Eur. J. Oper. Res. 100, 464–474 (1997)MATHCrossRefGoogle Scholar
  4. 4.
    Pinedo M.: Scheduling: theory, algorithms, and systems. Springer, Berlin (2008)Google Scholar
  5. 5.
    Ren Y., Dessouky M., Ordóñez F.: The multi-shift vehicle routing problem with overtime. Comput. Oper. Res. 37, 1987–1998 (2010)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Toth P., Vigo D.: The vehicle routing problem. Society for Industrial Mathematics, Canada (2002)MATHCrossRefGoogle Scholar
  7. 7.
    Wolsey L.A: Integer programming. Wiley, NY (1998)MATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Shabnam Zangeneh-Khamooshi
    • 1
  • Zelda B. Zabinsky
    • 1
  • Joseph A. Heim
    • 1
  1. 1.Department of Industrial and Systems EngineeringUniversity of WashingtonSeattleUSA

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