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Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems

Author

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  • Ann Melissa Campbell

    (Department of Management Sciences, Henry B. Tippie College of Business, University of Iowa, Iowa City, Iowa 52242-1000)

  • Martin Savelsbergh

    (Department of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205)

Abstract

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O ( n 3 ). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O ( n 4 ). We demonstrate that with careful implementation it is possible, in most cases, to maintain the O ( n 3 ) complexity or, in a few cases, increase the time complexity to O ( n 3 log n ). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics.

Suggested Citation

  • Ann Melissa Campbell & Martin Savelsbergh, 2004. "Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems," Transportation Science, INFORMS, vol. 38(3), pages 369-378, August.
    • Handle: RePEc:inm:ortrsc:v:38:y:2004:i:3:p:369-378
    DOI: 10.1287/trsc.1030.0046
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    References listed on IDEAS

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