Browsing by Subject "Polyhedral analysis"

Now showing 1 - 6 of 6

Open Access
A branch and cut algorithm for hub location problems with single assignment
(Springer, 2005) Labbé, M.; Yaman, H.; Gourdin, E.
The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results.
Open Access
Polyhedral analysis for concentrator location problems
(Springer, 2006) Labbé, M.; Yaman, H.
The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We develop a branch and cut algorithm and present computational results.
Open Access
Polyhedral analysis for the uncapacitated hub location problem with modular arc capacities
(Society for Industrial and Applied Mathematics, 2005) Yaman, H.
We consider the problem of installing a two-level telecommunication network. Terminal nodes communicate with each other through hubs. Hubs can be installed on terminal nodes and they are interconnected by a complete network. Each terminal is connected directly to a hub node. Integer amounts of capacity units are installed on the arcs between hub pairs and terminals and their hubs. The aim is to minimize the cost of installing hubs and capacity units on arcs. We present valid and facet defining inequalities for the polyhedron associated with this problem.
Open Access
Projecting the flow variables for hub location problems
(John Wiley & Sons, 2004) Labbé, M.; Yaman, H.
We consider two formulations for the uncapacitated hub location problem with single assignment (UHL), which use multicommodity flow variables. We project out the flow variables and determine some extreme rays of the projection cones. Then we investigate whether the corresponding inequalities define facets of the UHL polyhedron. We also present two families of facet defining inequalities that dominate some projection inequalities. Finally, we derive a family of valid inequalities that generalizes the facet defining inequalities and that can be separated in polynomial time.
Open Access
The robust network loading problem under hose demand uncertainty: formulation, polyhedral analysis, and computations
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Altın, A.; Yaman, H.; Pınar, M. Ç.
We consider the network loading problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity flow formulation of the problem, we state a decomposition property obtained from projecting out the flow variables. This property considerably simplifies the resulting polyhedral analysis and computations by doing away with metric inequalities. Then we focus on a specific choice of the uncertainty description, called the "hose model," which specifies aggregate traffic upper bounds for selected endpoints of the network. We study the polyhedral aspects of the NLP under hose demand uncertainty and use the results as the basis of an efficient branch-and-cut algorithm. The results of extensive computational experiments on well-known network design instances are reported.
Open Access
Solving the hub location problem in a star-star network
(John Wiley & Sons, 2008) Labbé, M.; Yaman, H.
We consider the problem of locating hubs and assigning terminals to hubs for a telecommunication network. The hubs are directly connected to a central node and each terminal node is directly connected to a hub node. The aim is to minimize the cost of locating hubs, assigning terminals and routing the traffic between hubs and the central node. We present two formulations and show that the constraints are facet-defining inequalities in both cases. We test the formulations on a set of instances. Finally, we present a heuristic based on Lagrangian relaxation.