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 ...

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortes...

In the Fixed Cost k-Flow problem, we are given a graph G = (V,E) with edge-capacities {ue | e ∈ E} and edge-costs {ce | e ∈ E}, source-sink pair s, t ∈ V , and an integer k. The goal is to find a minimum cost subgraph H of G such that the minimum capacity of an st-cut in H is at least k. We show that the Group Steiner on Trees problem is a special case of Fixed Cost k-Flow. This implies the fir...

We present the first constant-factor approximation algorithm for network design with multiple commodities andeconomies of scale. We consider the rent-or-buy problem, a type of multicommodity buy-at-bulk network design in which there are two ways to install capacity on any givenedge. Capacity can be rented, with cost incurred on a per-unit of capacity basis, or bought, which allows u...

We consider the design of a multicommodity flow network, in which point-topoint demands are routed across the network subject to link capacity restrictions. Such a design must build enough capacity and diverse routing paths through the network to ensure that feasible multicommodity flows continue to exist, even when components of the network fail. In this paper, we examine several methodologies...

We consider the stochastic variant of the fixed-charge capacitated multicommodity network design (CMND) problem in which demands are stochastic. We propose a two-stage stochastic programming formulation where design decisions make up the first stage, while a series of recourse decisions are made in the second stage to distribute the commodities according to observed demands. The overall objecti...

Facing supply uncertainty of bulky wastes, the capacitated multi-product stochastic network design model for bulky waste recycling is proposed in this paper. The objective of this model is to minimize the first-stage total fixed costs and the expected value of the second-stage variable costs. The possibility of operation costs and transportation costs for bulky waste recycling is considered ...

We propose techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization and nonlinear programming problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in pr...