In this study, we have concerned with a hierarchical logistic network design problem from two aspects that have been scarcely considered previously though they are very common in real-world. That is, to cope with a multi-commodity problem and a problem with stair-wised discount cost of transportation effectively as well as practically, we have developed the extended hybrid tabu search method fo...

Combinatorial optimization problems are by nature very difficult to solve, and the Capacitated Minimum Spanning Tree problem is one such problem. Much work has been done in the management sciences to develop heuristic solution procedures that suboptimally solve large instances of the Capacitated Minimum Spanning Tree problem in a reasonable amount of time. The Capacitated Minimum Spanning Tree ...

Given a network with a set of nodes and a set of potential edges, we must decide what edges will be included in the design to satisfy demands between pairs of nodes. Each edge has associated a finite capacity, a fixed cost and routing costs. Uncertainty will be considered in important input parameters such as demands and routing costs and will be modeled through scenarios. The objective is to f...

We address the one-to-one multi-commodity pickup and delivery traveling salesman problem (m-PDTSP) which is a generalization of the TSP and arises in several transportation and logistics applications. The objective is to find a minimum-cost directed Hamiltonian path which starts and ends at given depot nodes and such that the demand of each given commodity is transported from the associated sou...

6. Lecture notes on flows and cuts 6.1 Maximum Flows Network flows deals with modelling the flow of a commodity (water, electricity, packets, gas, cars, trains, money, or any abstract object) in a network. The links in the network are capacitated and the commodity does not vanish in the network except at specified locations where we can either inject or extract some amount of commodity. The mai...

The primary purpose of this paper is to identify recent major accomplishments and prophesy (suggest) future trends in the solution, modeling, and human engineering aspects of network and network-related problems. In particular, the suggested future trends consist of an integrated sequence of modeling, theoretical and computational developments which may allow mathematical programming to attain ...

In this article we study capacitated network design problems. We unify and extend poly-hedral results for directed, bidirected and undirected link capacity models. Based on validinequalities for a network cut we show that regardless of the link capacity model, facets of thepolyhedra associated with such a cut translate to facets of the original network design polyhedraif the...