Probabilistic analysis for a multiple depot vehicle routing problem

Baltz, Andreas; Dubhashi, Devdatt; Srivastav, Anand; Tansini, Libertad; Werth, Sören

doi:10.1002/rsa.20156

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…For the general case k = λn + o(n), λ ≥ 0, Baltz et al [3] proved that the sum of all tour lengths asymptotically approaches α √ n as n → ∞, where the constant α is equal to the TSP constant α for the case λ = 0 and depends on λ for the case λ > 0. Therefore, we can obtain a direct lower bound according to their results.…”

Section: First We Have the Following Observationmentioning

confidence: 99%

“…Recently, Lim and Wang [14] gave a one-stage approach to MDVRP with the constraint each depot only has a fixed number of vehicles. Baltz et al [2,3] presented a probabilistic analysis of the optimal solution for the problem. Tansini [16] proposed a polynomial-time approximation scheme (PTAS) for the MDVRP similar to Arora's PTAS algorithm for TSP.…”

Section: An Lp-based Load Balancing Heuristicmentioning

confidence: 99%

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Solving min-max multi-depot vehicle routing problem

Carlsson¹,

Ge²,

Subramaniam³

et al. 2009

Lectures on Global Optimization

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The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the sum of all tour lengths, and existing literature handles this problem with a variety of assumptions and constraints. In this paper, we explore the notion of minimizing the maximal length of a tour in MDVRP ("min-max MDVRP"). We present two heuristics in the paper. The first heuristic is a linear programming-based approach with global improvement. The second one, the region partition heuristic, is proved to be asymptotically optimal and is potentially useful for general network applications. A comparison of the computational implementations for different heuristics is presented.

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Section: First We Have the Following Observationmentioning

confidence: 99%

Section: An Lp-based Load Balancing Heuristicmentioning

confidence: 99%

Solving min-max multi-depot vehicle routing problem

Carlsson¹,

Ge²,

Subramaniam³

et al. 2009

Lectures on Global Optimization

View full text Add to dashboard Cite

show abstract

“…In that setting, Rhee [23] and Daganzo [12] analyzed the value of an optimal solution to the CVRP for the case when

k

is fixed. Baltz et al [6] gave an optimal algorithm for the multiple depot vehicle routing problem when both the customers and the depots are i.i.d. random points and assuming unlimited tour capacity.…”

Section: Introductionmentioning

confidence: 99%

Iterated tour partitioning for Euclidean capacitated vehicle routing

Mathieu

Zhou

2022

Random Struct Algorithms

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We give a probabilistic analysis of the unit‐demand Euclidean capacitated vehicle routing problem in the random setting. The objective is to visit all customers using a set of routes of minimum total length, such that each route visits at most k$$ k $$ customers. The best known polynomial‐time approximation is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the solution obtained by the ITP algorithm is arbitrarily close to the optimum when k$$ k $$ is either ofalse(nfalse)$$ o\left(\sqrt{n}\right) $$ or ωfalse(nfalse)$$ \omega \left(\sqrt{n}\right) $$, and they asked whether the ITP algorithm was “also effective in the intermediate range”. In this work, we show that the ITP algorithm is at best a false(1+c0false)$$ \left(1+{c}_0\right) $$‐approximation, for some positive constant c0$$ {c}_0 $$, and is at worst a 1.915‐approximation.

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“…Yao, Jinbao et al [12] proposed a parallel ant colony optimization to work out MDVRP. Baltz [13] adopted probabilistic analysis method to solve MDVRP. Combining GA with ACO algorithm, Calvete, HI [14] proposed evaluative and ACO strategies for solving multi-depot vehicle routing problem ; Chen, S. et al [15] proposed a SA-based heuristic for the multi-depot vehicle routing problem, which a model was proposed to minimize the relative distribution cost incurred in proper delivery routes.…”

Section: Introductionmentioning

confidence: 99%

A tabu search algorithm with variable cluster grouping for multi-depot vehicle routing problem

Miao²,

Xie

et al. 2014

Proceedings of the 2014 IEEE 18th International Conference on Computer Supported Cooperative Work in Design (CSCWD)

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We herein present a tabu search algorithm with variable cluster grouping (TSVCG for short) to deal with Multidepot vehicle routing problem (MDVRP for short). In TSVCG, we firstly adopt variable cluster grouping to convert a complicated MDVRP to typical single depot vehicle routing problem (SDVRP for short). And then we apply a tabu search algorithm to solve each SDVRP. In the grouping process, we discuss how to find a scale factor and minimum geometric semicircle correction factor to improve the customer points' grouping, and thus get the different groups for further problemsolving. The experimental results shown that the proposed variable cluster grouping can reduce grouping blindness and improve the efficiency of grouping and viability of group results. The results also shown that the proposed TSVCG performed well compared with the previous work with the geometric grouping.

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Probabilistic analysis for a multiple depot vehicle routing problem

Cited by 8 publications

References 26 publications

Solving min-max multi-depot vehicle routing problem

Solving min-max multi-depot vehicle routing problem

Iterated tour partitioning for Euclidean capacitated vehicle routing

A tabu search algorithm with variable cluster grouping for multi-depot vehicle routing problem

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