The capacitated minimum spanning tree (CMST) problem is to 3nd a minimum cost spanning tree in a network where nodes have speci3ed demands, with an additional capacity constraints on the subtrees incident to a given source node s. The capacitated minimum spanning tree problem arises as an important subproblem in many telecommunication network design problems. In a recent paper, Ahuja et al. (Ma...

We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer programs. After distinguishing the general case, which is NP–hard, from a polynomially solvable case, we anal...

The authors also gratefully acknowledge the detailed comments of two anonymous referees regarding relationships with lot-sizing problems. ii Abstract This paper studies the polyhedral structure of dynamic fixed-charge problems that have nested relationships constraining the flow or activity variables. Constraints of this type might typically arise in hierarchical or multi-period models, but mig...

In this paper, we present a state-of-the-art branch-and-cut (B&C) algorithm for the multicommodity capacitated fixed charge network design problem (MCND). This algorithm combines bounding and branching procedures inspired by the latest developments in mixed-integer programming (MIP) software tools. Several filtering methods that exploit the structure of the MCND are also developed and embedded ...

This paper presents a comprehensive survey of models and algorithms for multicommodity capacitated network design problems, which are mostly encountered in telecommunications and transportation network planning. These problems are important not only due to the major relevance of their applications, but also because they pose considerable modeling and algorithmic challenges. We present a general...