This tutorial is devoted to the notion of Max-Min Fairness (MMF), associated optimization problems, and their applications to multi-commodity flow networks. We first introduce a theoretical background for the MMF problem and discuss its relation to lexicographic optimization. We next present resolution algorithms for the MMF optimization, and then give some applications to telecommunication net...

Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at strategic level, a network design problem under uncertainty. This is defined as stochastic multi-period capacitated location-routing (2E-SM-CLRP). It considers partitioned into two echelons: each echelon involves specific location-assignment-transportation schema that must cope with fut...

In the local access expansion problem we need to expand a given tree network by increasing the capacity of the edges or by installing concentrating devices in some nodes of the network, in order to satisfy the increase in node demands. It was shown in [4] that the problem can be viewed as an extension of the well-known Capacitated Minimum Spanning Tree Problem (CMSTP) and two flowbased models (...

Markovian network equilibrium generalizes the classical Wardrop in games. At a equilibrium, each player of game solves Markov decision process instead shortest path problem. We propose two novel extensions by considering (1) variable demand, which offers players quitting option, and (2) multi-commodity flow, allows to have heterogeneous ending time. further develop dynamic-programming-based ite...

We propose a mathematical programming model of the routing problem in multi-hop wireless networks that takes into account quality of service requirements considering bandwidth constraints. The proposed approach is suitable for Wireless MESH Networks (WMN) where topology is almost fixed and routes can be optimized based on global objectives. We then consider and solve the scheduling problem, ill...

this paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. the objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. a 0-1 mixed intege...

We present a Heuristic Branch&Price&Cut (BPC) approach for a network design problem. This algorithm integrates several original features including: • a multi-commodity multi-capacity network design problem path based model, • a pricing scheme using pools of generators and promising columns, • cutting-planes applied to the path-based formulation to obtain better lower bounds, to make better heur...

CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de...