We consider in this note the maximum integral two-commodity flow problem in augmented planar graphs, that is with both sourceesink edges added. We provide an O(n&) simple algorithm for finding a maximum integral two-commodity flow in augmented planar graphs.

In this paper I improve Gardner's surplus transformation curve framework by assuming that government is able to vary many policy instruments simultaneously instead of only one. I use my framework to find the combination of the currently used instruments which provides the most efficient income redistribution for the Austrian bread grains market. Contrasting the most efficient policy to the actu...

We study taxes in the well-known game theoretic traffic model due to Wardrop. Given a network and a subset of edges, on which we can impose taxes, the problem is to find taxes inducing an equilibrium flow of minimal networkwide latency cost. If all edges are taxable, then marginal cost pricing is known to induce the socially optimal flow for arbitrary multi-commodity networks. In contrast, if o...

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1 − ǫ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical p...

This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell...

We study a cement transportation problem with asset-management (equipment selection) for strategic planning scenarios involving multiple forms of transportation and network expansion. A deterministic mixed integer programming approach is difficult due to the underlying capacitated multi-commodity network flow model and the need to consider a time-space network to ensure operational feasibility....

The fixed-charge Capacitated Multi-commodity Network Design (CMND) is a well-known problem of both practical and theoretical significance. Network design models represent a wide variety of planning and operation management issues in transportation telecommunication, logistics, production and distribution. In this paper, Ant Colony Optimization (ACO) based neighborhoods are proposed for CMND pro...

With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most commonly used intra-domain Interne...

We present a branch-and-cut algorithm to solve the single commodity uncapacitated fixed charge network flow problem, which includes the Steiner tree problem, uncapacitated lot-sizing problems, and the fixed charge transportation problem as special cases. The cuts used are simple dicut inequalities and their variants. A crucial problem when separating these inequalities is to find the right cut ...

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1 − ǫ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical p...