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Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis

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  • Bertazzi, Luca
  • Golden, Bruce
  • Wang, Xingyin

Abstract

The classical objective function of the Vehicle Routing Problem (VRP) is to minimize the total distance traveled by all vehicles (Min–Sum). In several situations, such as disaster relief efforts, computer networks, and workload balance, the minimization of the longest route (Min–Max) is a better objective function. In this paper, we compare the optimal solution of several variants of the Min–Sum and the Min–Max VRP, from the worst-case point of view. Our aim is two-fold. First, we seek to motivate the design of heuristic, metaheuristic, and matheuristic algorithms for the Min–Max VRP, as even the optimal solution of the classical Min–Sum VRP can be very poor if used to solve the Min–Max VRP. Second, we aim to show that the Min–Max approach should be adopted only when it is well-justified, because the corresponding total distance can be very large with respect to the one obtained by optimally solving the classical Min–Sum VRP.

Suggested Citation

  • Bertazzi, Luca & Golden, Bruce & Wang, Xingyin, 2015. "Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis," European Journal of Operational Research, Elsevier, vol. 240(2), pages 372-381.
  • Handle: RePEc:eee:ejores:v:240:y:2015:i:2:p:372-381
    DOI: 10.1016/j.ejor.2014.07.025
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    Cited by:

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    3. Halvorsen-Weare, Elin E. & Savelsbergh, Martin W.P., 2016. "The bi-objective mixed capacitated general routing problem with different route balance criteria," European Journal of Operational Research, Elsevier, vol. 251(2), pages 451-465.
    4. P. Matl & R. F. Hartl & T. Vidal, 2018. "Workload Equity in Vehicle Routing Problems: A Survey and Analysis," Transportation Science, INFORMS, vol. 52(2), pages 239-260, March.

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