2,767 research outputs found
The two-echelon capacitated vehicle routing problem: models and math-based heuristics
Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed
Locating Depots for Capacitated Vehicle Routing
We study a location-routing problem in the context of capacitated vehicle
routing. The input is a set of demand locations in a metric space and a fleet
of k vehicles each of capacity Q. The objective is to locate k depots, one for
each vehicle, and compute routes for the vehicles so that all demands are
satisfied and the total cost is minimized. Our main result is a constant-factor
approximation algorithm for this problem. To achieve this result, we reduce to
the k-median-forest problem, which generalizes both k-median and minimum
spanning tree, and which might be of independent interest. We give a
(3+c)-approximation algorithm for k-median-forest, which leads to a
(12+c)-approximation algorithm for the above location-routing problem, for any
constant c>0. The algorithm for k-median-forest is just t-swap local search,
and we prove that it has locality gap 3+2/t; this generalizes the corresponding
result known for k-median. Finally we consider the "non-uniform"
k-median-forest problem which has different cost functions for the MST and
k-median parts. We show that the locality gap for this problem is unbounded
even under multi-swaps, which contrasts with the uniform case. Nevertheless, we
obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur
On Network Coding Capacity - Matroidal Networks and Network Capacity Regions
One fundamental problem in the field of network coding is to determine the
network coding capacity of networks under various network coding schemes. In
this thesis, we address the problem with two approaches: matroidal networks and
capacity regions.
In our matroidal approach, we prove the converse of the theorem which states
that, if a network is scalar-linearly solvable then it is a matroidal network
associated with a representable matroid over a finite field. As a consequence,
we obtain a correspondence between scalar-linearly solvable networks and
representable matroids over finite fields in the framework of matroidal
networks. We prove a theorem about the scalar-linear solvability of networks
and field characteristics. We provide a method for generating scalar-linearly
solvable networks that are potentially different from the networks that we
already know are scalar-linearly solvable.
In our capacity region approach, we define a multi-dimensional object, called
the network capacity region, associated with networks that is analogous to the
rate regions in information theory. For the network routing capacity region, we
show that the region is a computable rational polytope and provide exact
algorithms and approximation heuristics for computing the region. For the
network linear coding capacity region, we construct a computable rational
polytope, with respect to a given finite field, that inner bounds the linear
coding capacity region and provide exact algorithms and approximation
heuristics for computing the polytope. The exact algorithms and approximation
heuristics we present are not polynomial time schemes and may depend on the
output size.Comment: Master of Engineering Thesis, MIT, September 2010, 70 pages, 10
figure
Computing Bounds on Network Capacity Regions as a Polytope Reconstruction Problem
We define a notion of network capacity region of networks that generalizes
the notion of network capacity defined by Cannons et al. and prove its notable
properties such as closedness, boundedness and convexity when the finite field
is fixed. We show that the network routing capacity region is a computable
rational polytope and provide exact algorithms and approximation heuristics for
computing the region. We define the semi-network linear coding capacity region,
with respect to a fixed finite field, that inner bounds the corresponding
network linear coding capacity region, show that it is a computable rational
polytope, and provide exact algorithms and approximation heuristics. We show
connections between computing these regions and a polytope reconstruction
problem and some combinatorial optimization problems, such as the minimum cost
directed Steiner tree problem. We provide an example to illustrate our results.
The algorithms are not necessarily polynomial-time.Comment: Appeared in the 2011 IEEE International Symposium on Information
Theory, 5 pages, 1 figur
Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation
This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;
Capacitated Vehicle Routing with Non-Uniform Speeds
The capacitated vehicle routing problem (CVRP) involves distributing
(identical) items from a depot to a set of demand locations, using a single
capacitated vehicle. We study a generalization of this problem to the setting
of multiple vehicles having non-uniform speeds (that we call Heterogenous
CVRP), and present a constant-factor approximation algorithm.
The technical heart of our result lies in achieving a constant approximation
to the following TSP variant (called Heterogenous TSP). Given a metric denoting
distances between vertices, a depot r containing k vehicles with possibly
different speeds, the goal is to find a tour for each vehicle (starting and
ending at r), so that every vertex is covered in some tour and the maximum
completion time is minimized. This problem is precisely Heterogenous CVRP when
vehicles are uncapacitated.
The presence of non-uniform speeds introduces difficulties for employing
standard tour-splitting techniques. In order to get a better understanding of
this technique in our context, we appeal to ideas from the 2-approximation for
scheduling in parallel machine of Lenstra et al.. This motivates the
introduction of a new approximate MST construction called Level-Prim, which is
related to Light Approximate Shortest-path Trees. The last component of our
algorithm involves partitioning the Level-Prim tree and matching the resulting
parts to vehicles. This decomposition is more subtle than usual since now we
need to enforce correlation between the size of the parts and their distances
to the depot
A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem
In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.Vehicle routing; branch-and-cut; separation
Minimum Makespan Multi-vehicle Dial-a-Ride
Dial a ride problems consist of a metric space (denoting travel time between
vertices) and a set of m objects represented as source-destination pairs, where
each object requires to be moved from its source to destination vertex. We
consider the multi-vehicle Dial a ride problem, with each vehicle having
capacity k and its own depot-vertex, where the objective is to minimize the
maximum completion time (makespan) of the vehicles. We study the "preemptive"
version of the problem, where an object may be left at intermediate vertices
and transported by more than one vehicle, while being moved from source to
destination. Our main results are an O(log^3 n)-approximation algorithm for
preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation
for its special case when there is no capacity constraint. We also show that
the approximation ratios improve by a log-factor when the underlying metric is
induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200
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