It is well known that the Vehicle Routing Problem (VRP) becomes more difficult to solve as the problem size increases. However little is known about what makes a VRP difficult or easy to solve for problems of the same size. In this paper we investigate the effect of the formulation and data parameters on the efficiency with which we can obtain exact solutions to the VRP with a general IP solver...

Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T , so that no two paths of the same colour use the same arc of T , is equal to the maximum number of paths passing through an arc of T. This result is applied to solve the all-to-all communication ...

A flow on a directed network is said to be confluent if the flow uses at most one outgoing arc at each node. Confluent flows arise naturally from destination-based routing. We study the Maximum Confluent Flow Problem (MaxConf) with a single commodity but multiple sources and sinks. Unlike previous results, we consider heterogeneous arc capacities. The supplies and demands of the sources and sin...

Ad hoc networks have the notable capability of enabling spontaneous networks. These networks are self-initializing, self-configuring, and self-maintaining, even though the underlying topology is often continually changing. Because research has only begun to scratch the surface of the potential applications of this technology, it is important to prepare for the widespread use of these networks. ...

We study the Mixed Capacitated General Routing Problem (MCGRP) in which a fleet of capacitated vehicles has to serve a set of requests by traversing a mixed weighted graph. The requests may be located on nodes, edges, and arcs. The problem has theoretical interest because it is a generalization of the Capacitated Vehicle Routing Problem (CVRP), the Capacitated Arc Routing Problem (CARP), and th...

We introduce a new variant of the Traveling Salesman Problem inspired from applications within maritime transportation. The problem is to find a minimum cost tour of a set of ports, but includes draft limitation of some ports. This problem is henceforth referred to as the Traveling Salesman Problem with Draft Limits (TSPDL) and is an important subproblem in complex routing problems in maritime ...

Appropriate vehicle routing is critical for collecting municipal solid waste (MSW) efficiently. Conventional empirical routing is not easily altered in response to rapidly changing waste management plans and generation. An enhanced model is proposed herein to solve a MSW collection routing problem involving a homogenous fleet. A minimum cost flow method is applied to pre-process the original co...

The Rural Postman Problem (RPP), as an Arc Routing Problem (ARP), consists of determining a minimum cost tour of a specified arc set of a graph (G=(V,A)) but, with the particularity that only a subset R (R ⊆ A) of arcs is required to be traversed at least once. RPPs are applied in a variety of practical contexts, namely the industrial interesting case of path optimization for components cutting...

Motivated by wavelength division multiplexing in all-optical networks, we consider the problem of finding a set of paths from a fixed source to a multiset of destinations, which can be coloured by the fewest number of colours so that paths of the same colour do not share an arc. We prove that this minimum number of colours is equal to the maximum number of paths that share one arc, minimized ov...

We consider two types of path selection problems for arc capacitated network. Given an arc capacitated network and a set of commodities, one problem is to find a subset of commodities to be routed and an assignment of them to the paths so that profit is maximized. The other problem is to route all given commodities in the network so that cost is minimized. Bifurcation of flow is not allowed in ...