We present a column generation algorithm for solving the bi-objective multicommodity minimum cost flow problem. This method is based on the biobjective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using DantzigWolfe decomposition. Then, sim...

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) pr...

We present a unified analytical framework within which power control, routing, and congestion control for wireless networks can be optimized on a node-by-node basis. We consider a multi-commodity flow model for interference-limited wireless networks, and develop distributed scaled gradient projection algorithms which iteratively adjust power control and routing schemes at individual nodes to mi...

We investigate an oblivious routing scheme, amenable to distributed computation and resilient to graph changes, based on electrical flow. Our main technical contribution is a new rounding method which we use to obtain a bound on the `1 → `1 operator norm of the inverse graph Laplacian. We show how this norm reflects both latency and congestion of electric routing.

We develop and implement a model for a profit maximizing firm that provides an intermediation service between commodity producers and commodity end-users distributed over a realistic spatial network. Producers and end-users trade with the firm through contracts for delivery of grain during the marketing season. The firm begins the marketing season with a portfolio of prearranged purchase and sa...

We define a NP-hard clustered variant of the Set Covering Problem where subsets are partitioned into K clusters and a fixed cost is paid for selecting at least one subset in a given cluster. This variant can reformulate as a master problem various multi-commodity flow problems in transportation planning. We show that the problem is approximable within ratio (1+2)(e/e−1)H(q), where q is the maxi...

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are piecewise linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and...

A classical result in undirected edge-capaciated networks is the approximate optimality of routing (flow) for multiple-unicast: the min-cut upper bound is within a logarithmic factor of the number of sources of the max flow [2, 3]. In this paper we focus on extending this result to a more general network model, where there are joint polymatroidal constraints on the rates of the edges that meet ...

This paper defines an incremental version of the maximum flow problem. In this model, the capacities increase over time and the resulting solution is a sequence of flows that build on each other incrementally. Thus far, incremental problems considered in the literature have been built on NP-complete problems. To the best of our knowledge, our results are the first to find a polynomial time prob...

The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a network such that a given demand can be satisfied. There are two objectives. Passengers want to minimize travel times, the transport company wishes to minimize operating costs. We investigate three variants of a multi-co...