Expanding an electrical transmission network requires heavy investments that need to be carefully planned, often at a regional or national level. We study relevant theoretical and practical aspects of transmission expansion planning, set as a bilinear programming problem with mixed 0-1 variables. We show that the problem is NP-hard and that, unlike the so-called Network … Read more
In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay … Read more
The Hop-Constrained Minimum Spanning Tree Problem (HMSTP) is a NP-hard problem arising in the design of centralized telecommunication networks with quality of service constraints. We show that the HMSTP is equivalent to a Steiner Tree Problem (STP) in an adequate layered graph. We prove that the directed cut formulation for the STP defined in the … Read more
This paper deals with the ring star problem that consists in designing a ring that pass through a central depot, and then assigning each non visited customer to a node of the ring. The objective is to minimize the total routing and assignment costs. A new chain based formulation is proposed. Valid inequalities are proposed … Read more
This report combines the contributions to INOC 2005 (Wessälly et al., 2005) and DRCN 2005 (Gruber et al., 2005). A new integer linear programming model for the end-to-end survivability concept deman d-wise shared protection (DSP) is presented. DSP is based on the idea that backup capacity is dedicated to a particular demand, but shared within … Read more
We investigate a network design problem under traffic uncertainty which arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network so as to support all … Read more
A traffic matrix $D^1$ dominates a traffic matrix $D^2$ if $D^2$ can be routed on every (capacitated) network where $D^1$ can be routed. We prove that $D^1$ dominates $D^2$ if and only if $D^1$, considered as a capacity vector, supports $D^2$. We show several generalizations of this result. Citation Centro Vito Volterra, Universita’ di Roma … Read more
In this study, a lifting procedure is applied to some existing formulations of the Diameter Constrained Minimum Spanning Tree Problem. This problem typically models network design applications where all vertices must communicate with each other at minimum cost, while meeting or surpassing a given quality requirement. An alternative formulation is also proposed for instances of … Read more
The Facility Location Model with Risk Pooling (LMRP) extends the uncapacitated fixed charge model to incorporate inventory decisions at the distribution centers (DCs). In this paper, we introduce a capacitated version of the LMRP that handles inventory management at the DCs such that the capacity limitations at the DCs are not exceeded. We consider a … Read more
Given an undirected graph G with nonnegative edges costs and nonnegative vertex penalties, the prize collecting Steiner problem in graphs (PCSPG) seeks a tree of G with minimum weight. The weight of a tree is the sum of its edge costs plus the sum of the penalties of those vertices not spanned by the tree. … Read more