Two exact algorithms for the distance‐constrained vehicle routing problem

Laporte, Gilbert; Desrochers, Martin; Nobert, Yves

doi:10.1002/net.3230140113

Cited by 91 publications

(28 citation statements)

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“…This is the Distance Constrained Vehicle Routing Problem (DVRP). It was raised and studied for applications in [7] and [8]. Routing problems like the DVRP can be directly encoded as instances of Minimum Set Cover, and thus often admit logarithmic approximations.…”

Section: Related Workmentioning

confidence: 99%

The School Bus Problem on Trees

Bock

Grant

Könemann

et al. 2011

Algorithms and Computation

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Abstract. The School Bus Problem is an NP-hard vehicle routing problem in which the goal is to route buses that transport children to a school such that for each child, the distance travelled on the bus does not exceed the shortest distance from the child's home to the school by more than a given regret threshold. Subject to this constraint and bus capacity limit, the goal is to minimize the number of buses required. In this paper, we give a polynomial time 4-approximation algorithm when the children and school are located at vertices of a fixed tree. As a byproduct of our analysis, we show that the integrality gap of the natural setcover formulation for this problem is also bounded by 4. We also present a constant approximation for the variant where we have a fixed number of buses to use, and the goal is to minimize the maximum regret.

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Section: Related Workmentioning

confidence: 99%

The School Bus Problem on Trees

Bock

Grant

Könemann

et al. 2011

Algorithms and Computation

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“…The addition of distance constraints to the CVRP yields the Distance-constrained CVRP (DCVRP; see Christofides,Mingozzi,and Toth [31] and Laporte, Desrochers, and Nobert [88]). In the following, we assume that t i j > 0 is the distance between vertex i and vertex j for all (i, j ) ∈ A.…”

Section: Route Lengthmentioning

confidence: 99%

Chapter 1: The Family of Vehicle Routing Problems

Irnich¹,

Toth²,

Vigo³

2014

Vehicle Routing

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A generic verbal definition of the family of vehicle routing problems can be the following:Given: A set of transportation requests and a fleet of vehicles.The problem is then to find a plan for the following:Task: Determine a set of vehicle routes to perform all (or some) transportation requests with the given vehicle fleet at minimum cost; in particular, decide which vehicle handles which requests in which sequence so that all vehicle routes can be feasibly executed.In this type of problem, subsumed under the term Vehicle Routing Problem (VRP), the transportation requests to be served are generally concentrated in specific points of a road network as opposed to the Arc Routing Problems (ARP; see the companion book by Corberán and Laporte [35]), where the requests are dispersed along the arcs, i.e., street segments of the underlying road network. The following sections will shed light on the basic VRP components, which are the transportation requests and how they can be performed, the fleet of vehicles, the related costs and profits (if relevant), and the feasibility of routes.Before going into the details, however, we discuss the economic relevance of computersupported vehicle routing. Indeed, the large number of real-world applications have widely shown that the use of computerized solution methods for the solution of VRP, both at the planning and the operational levels, yields substantial savings in the global transportation costs. The success of the utilization of optimization techniques is due not only to the power of the current computer systems and to the full integration of the information systems into the operations and commercial processes, but it can also be attributed to the development of rigorous mathematical models, which are able to take into account al-1 Downloaded 12/15/14 to 132.236.27.111. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 2 Chapter 1. The Family of Vehicle Routing Problems most all the characteristics of the VRP arising in real-world applications. Furthermore, the corresponding algorithms and their computer implementations (software tools) play an essential role in finding high-quality feasible solutions for real-world instances within acceptable computing times. Compared to procedures not based on optimization techniques, significant cost savings and a better utilization of the vehicle fleet can be achieved. In addition, by means of such planning software it is possible to improve the automation, standardization, and integration into the organizations' overall planning processes, leading to less time-consuming and more cost-efficient planning processes with respect to manual planning. Moreover, computerized planning allows planners to compare several different planning scenarios, and herewith to choose a best one through a careful and fast evaluation of cost and service-related performance indicators.In the last years, software tools integrating telematics services (electronic data transmission between vehicles and planners) have b...

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“…Interestingly, our algorithm for RVRP yields improved guarantees for (the path-variant of) the classical distance-constrained vehicle-routing problem (DVRP) [26,28,29,30]-find the fewest number of rooted paths of length at most D that cover all the nodes-via a reduction to RVRP. (DVRP usually refers to the version where we seek tours containing the root; [29] shows that the path-and tour-versions are within a factor of 2 in terms of approximability.)…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for regret-bounded vehicle routing and applications to distance-constrained vehicle routing

Friggstad

Swamy

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

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We consider vehicle-routing problems (VRPs) that incorporate the notion of regret of a client, which is a measure of the waiting time of a client relative to its shortest-path distance from the depot. Formally, we consider both the additive and multiplicative versions of, what we call, the regret-bounded vehicle routing problem (RVRP). In these problems, we are given an undirected complete graph G = ({r} ∪ V, E) on n nodes with a distinguished root (depot) node r, edge costs {cuv} that form a metric, and a regret bound R. Given a path P rooted at r and a node v ∈ P , let cP (v) be the distance from r to v along P . The goal is to find the fewest number of paths rooted at r that cover all the nodes so that for every node v covered by (say) path P : (i) its additive regret cP (v) − crv, with respect to P is at most R in additive-RVRP; or (ii) its multiplicative regret, cP (v)/crv, with respect to P is at most R in multiplicative-RVRP.Our main result is the first constant-factor approximation algorithm for additive-RVRP. This is a substantial improvement over the previous-best O(log n)-approximation. Additive-RVRP turns out be a rather central vehicle-routing problem, whose study reveals insights into a variety of other regret-related problems as well as the classical distance-constrained VRP (DVRP), enabling us to obtain guarantees for these various problems by leveraging our algorithm for additive-RVRP and the underlying techniques. We obtain approximation ratios of O log( Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. bound D via reductions to additive-RVRP; the latter improves upon the previous-best approximation for DVRP. A noteworthy aspect of our results is that they are obtained by devising rounding techniques for a natural configuration-style LP. This furthers our understanding of LP-relaxations for VRPs and enriches the toolkit of techniques that have been utilized for configuration LPs.

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Two exact algorithms for the distance‐constrained vehicle routing problem

Cited by 91 publications

References 22 publications

The School Bus Problem on Trees

The School Bus Problem on Trees

Chapter 1: The Family of Vehicle Routing Problems

Approximation algorithms for regret-bounded vehicle routing and applications to distance-constrained vehicle routing

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