We study a capacity expansion problem that arises in telecommunication network design. Given a capacitated network and a traac demand matrix, the objective is to add capacity to the edges, in modularityes of various modularities, and route traac, so that the overall cost is minimized. We study the polyhedral structure of a mixed-integer formulation of the problem and develop a cutting-plane alg...

the existing works considering the flow-based discount factor in the hub and spoke problems, assume that increasing the amount of flow passing through each edge of network continuously decreases the unit flow transportation cost. although a higher volume of flow allows for using wider links and consequently cheaper transportation, but the unit of flow enjoys more discounts, quite like replacing...

Let G = (V, E) be a graph with a source node s and a sink node t, |V | = n, |E| = m. For a given number k, the Maximum k–Splittable Flow Problem (MkSF) is to find an s, t–flow of maximum value with a flow decomposition using at most k paths. In the multicommodity case this problem generalizes disjoint paths problems and unsplittable flow problems. We provide a comprehensive overview of the comp...

Each day, railroads face the problem of allocating power to trains. Often, power requirements for each train are not known with certainty, and the fleet of locomotives may not be homogeneous. To deal with both of these complications, we formulate a multicommodity flow problem with convex objective function on a timespace network. The convex objective allows us to minimize expected cost under un...

We describe an upper-bound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for set-covering problems.

This work deals with a multi-period capacitated location problem inspired by telecommunication access network planning problems, where demands and costs vary from one period to another. On each concentrator site, several capacitated concentrators can be installed at each period. Similarly, several capacitated modules can be installed at each period between each terminal and concentrator sites. ...

Distribution network design as a strategic decision has long-term effect on tactical and operational supply chain management. In this research, a supply chain design problem based on a two level capacity location allocation problem (TLCLAP) is presented. A product must be transported from a set of seaport to meet stores demands, passing out by intermediate warehouses. The objective is to locate...

Two special and important network flow problems are the maximal flow problem and the shortest path problem. Both of these problems can be solved by either the network simplex method of Chapter 9 or the out-of-kilter algorithm of Chapter 11. However, their frequent occurrence in practice and the specialized, more efficient procedures that can be developed for handling these two problems provide ...

Abstract We derive an analytical expression for the mean load at each node of arbitrary undirected graph non-uniform multicommodity flow problem under weighted random routing. show node, net its demand and normalized by (weighted) degree, is a constant equal to trace product two matrices: Laplacian matrix generalized inverse Laplacian. For case uniform demand, this reduces sum inverses non-zero...

The methodology used for the prediction of trips through the allocation of these according to the origin-destination (OD) survey, constitutes a traditional methodology to cover the demand of existing transport between the zones of analysis. When the transportation system fulfills the characteristics of a network (topology, routed arcs, nodes with commodity supply and demand, etc.) in addition, ...