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

Bertazzi, Luca; Golden, Bruce L.; Wang, Xingyin

doi:10.1016/j.ejor.2014.07.025

Cited by 40 publications

(20 citation statements)

References 19 publications

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“…Finally, we agree with the closing remark in Bertazzi et al. () that multiobjective vehicle routing problems with MinMax and MinSum objectives is a promising research area. We intend to consider such combinations of objectives in our continued research.…”

Section: Conclusion and Future Researchsupporting

confidence: 92%

A matheuristic for the MinMax capacitated open vehicle routing problem

Lysgaard

López-Sánchez

Hernández-Díaz

2018

Int Trans Operational Res

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In this paper, the MinMax‐COVRP (where COVRP is capacitated open vehicle routing problem) is considered as a variation of the COVRP where the objective is to minimize the duration of the longest route. For the purpose of producing high‐quality solutions, elements from the fields of mathematical programming and metaheuristics are combined, resulting in a matheuristic for solving the MinMax‐COVRP. The matheuristic benefits from the diversification produced by a metaheuristic and the intensification from mixed‐integer linear programming (MILP). The initial solution provided by a multistart heuristic is used to seed and accelerate the MILP in which a local branching framework and the separation of k‐path inequalities are suitably combined. Computational experience shows promising results not only improving the initial solution provided by the multistart algorithm, but also ensuring optimality for most of the small‐ and medium‐sized instances.

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Section: Conclusion and Future Researchsupporting

confidence: 92%

A matheuristic for the MinMax capacitated open vehicle routing problem

Lysgaard

López-Sánchez

Hernández-Díaz

2018

Int Trans Operational Res

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“…For example, the min-max tree cover that we study is an NP-hard problem (even for k = 2) whereas finding k trees such that their total length is minimized can be done in polynomial time (using the greedy algorithm for finding a minimum cost basis of a matroid). A comparison between min-max vehicle routing models and min-sum vehicle routing models was done by Bertazzi et al [10]. This comparison also motivates by practical applications the study of the min-max versions.…”

Section: Introductionmentioning

confidence: 97%

“…This comparison also motivates by practical applications the study of the min-max versions. We refer to [10] for details. In this paper, we consider k to be a parameter.…”

Section: Introductionmentioning

confidence: 99%

Min–max cover of a graph with a small number of parts

Farbstein

Levin

2015

Discrete Optimization

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a b s t r a c tWe consider a variety of vehicle routing problems. The input consists of an undirected graph and edge lengths. Customers located at the nodes have to be visited by a set of vehicles. Two important parameters are k the number of vehicles, and the longest distance traveled by a vehicle denoted by λ. Here, we consider k to be a given bound on the maximum number of vehicles, and thus the decision maker cannot increase its value. Therefore, the goal will be to minimize λ. We study different variations of this problem, where for instance instead of servicing the customers using paths, we can serve them using spanning trees or cycles. For all these variations, we present new approximation algorithms with FPT time (where k is the parameter) which improve the known approximation guarantees for these problems.

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“…Insights from Bertazzi et al (2015) show that also the objective of minimizing t L may have significantly higher total travel distance than the minimizing total travel distance solution. In fact, the authors prove that in the worst case the ratio of the two solutions total travel distance tends to infinity.…”

Section: Inmentioning

confidence: 99%

“…The best route balance solution will be that each vehicle service one customer in each cluster. Total travel distances for each of the best solutions are then: Bertazzi et al (2015) show that also when the balance objective is to minimize t L the worst case is T s ∆ /T s T → Q. However, unless Q = 1, this ratio will never reach Q.…”

Section: Inmentioning

confidence: 99%

The bi-objective mixed capacitated general routing problem with different route balance criteria

Halvorsen-Weare

2016

European Journal of Operational Research

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The mixed capacitated general routing problem consists of determining routes for vehicles that are to service segments of a mixed network consisting of vertices, edges and arcs. In this study we present a bi-objective version of this problem. In addition to the traditional minimize total route cost objective we introduce several ways of considering route balance as a second objective. Insights on route balance and which effects variants of this objective have on the solutions are given. An exact solution method is used to generate exact Pareto fronts for a number of small benchmark instances. We illustrate the effects on the solutions for four suggestions for route balance objectives.

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

Cited by 40 publications

References 19 publications

A matheuristic for the MinMax capacitated open vehicle routing problem

A matheuristic for the MinMax capacitated open vehicle routing problem

Min–max cover of a graph with a small number of parts

The bi-objective mixed capacitated general routing problem with different route balance criteria

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