Browsing by Subject "Branch and cut"

Now showing 1 - 12 of 12

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
A branch and cut algorithm for the inventory routing problem
(2019-07) Mahmutoğulları, Özlem
The inventory routing problem arises in vendor managed systems where products are distributed from a supplier to a set of retailers by a homogeneous eet of capacitated vehicles. The routes of the vehicles and the quantities of products sent to each retailer in each time period are determined in such a way that no stockouts occur and total costs arising from inventory holding and transportation are minimized. Different inventory replenishment policies can be used while managing the inventories at retailers. We consider the problem with the maximum level inventory replenishment policy. We present a mixed integer linear programming model and derive valid inequalities using several structured relaxations. We relate our valid inequalities to those in the previous studies. We also propose new valid inequalities, implement a branch and cut algorithm and present computational results on benchmark instances from the literature as well as new randomly generated instances.
Open Access
Concentrator location in telecommunications
(Springer, 2004) Yaman, H.
We survey the main results in the author's PhD Thesis presented in December 2002 at the Université Libre de Bruxelles and supervised by Prof. Martine Labbé. The dissertation is written in English and is available at smg.ulb.ac.be. Several versions of concentrator location problems in telecommunication networks are studied. The thesis presents a list of polyhedral results for these problems and a branch and cut algorithm for the most general problem introduced.
Open Access
Hub location, routing, and route dimensioning: strategic and tactical intermodal transportation hub network design
(Institute for Operations Research and the Management Sciences (INFORMS), 2021-10) Yıldız, Barış; Yaman, Hande; Karaşan, Oya Ekin
We propose a novel hub location model that jointly eliminates some of the traditional assumptions on the structure of the network and on the discount as a result of economies of scale in an effort to better reflect real-world logistics and transportation systems. Our model extends the hub literature in various facets: instead of connecting nonhub nodes directly to hub nodes, we consider routes with stopovers; instead of connecting pairs of hubs directly, we design routes that can visit several hub nodes; rather than dimensioning pairwise connections, we dimension routes of vehicles; and rather than working with a homogeneous fleet, we use intermodal transportation. Decisions pertinent to strategic and tactical hub location and transportation network design are concurrently made through the proposed optimization scheme. An effective branch-and-cut algorithm is developed to solve realistically sized problem instances and to provide managerial insights.
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
Regenerator location problem and survivable extensions: a hub covering location perspective
(Elsevier, 2015) Yıldız, B.; Karaşan, O. E.
In a telecommunications network the reach of an optical signal is the maximum distance it can traverse before its quality degrades. Regenerators are devices to extend the optical reach. The regenerator placement problem seeks to place the minimum number of regenerators in an optical network so as to facilitate the communication of a signal between any node pair. In this study, the Regenerator Location Problem is revisited from the hub location perspective directing our focus to applications arising in transportation settings. Two new dimensions involving the challenges of survivability are introduced to the problem. Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment. All three variations of the problem are studied in a unifying framework involving the introduction of individual flow-based compact formulations as well as cut formulations and the implementation of branch and cut algorithms based on the cut formulations. Extensive computational experiments are conducted in order to evaluate the performance of the proposed solution methodologies and to gain insights from realistic instances.
Open Access
The ring/κ-rings network design problem: model and branch-and-cut algorithm
(John Wiley & Sons, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
This article considers the problem of designing a two-level network where the upper level consists of a backbone ring network connecting the so-called hub nodes, and the lower level is formed by access ring networks that connect the non-hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to κ, thus resulting in a ring/κ-rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch-and-cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable 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.
Open Access
Solving the hub location problem with modular link capacities
(Elsevier, 2005) Yaman, H.; Carello, G.
This paper deals with a capacitated hub location problem arising in the design of telecommunications networks. The problem is different from the classical hub location problem in two ways: the cost of using an edge is not linear but stepwise and the capacity of a hub restricts the amount of traffic transiting through the hub rather than the incoming traffic. In this paper both an exact and a heuristic method are presented. They are compared and combined in a heuristic concentration approach to investigate whether it is possible to improve the results within limited computational times.
Open Access
Survivability in hierarchical telecommunications networks under dual homing
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Karaşan, O. E.; Mahjoub, A. R.; Özkök, O.; Yaman, H.
The motivation behind this study is the essential need for survivability in the telecommunications networks. An optical signal should find its destination even if the network experiences an occasional fiber cut. We consider the design of a two-level survivable telecommunications network. Terminals compiling the access layer communicate through hubs forming the backbone layer. To hedge against single link failures in the network, we require the backbone subgraph to be two-edge connected and the terminal nodes to connect to the backbone layer in a dual-homed fashion, i.e., at two distinct hubs. The underlying design problem partitions a given set of nodes into hubs and terminals, chooses a set of connections between the hubs such that the resulting backbone network is two-edge connected, and for each terminal chooses two hubs to provide the dual-homing backbone access. All of these decisions are jointly made based on some cost considerations. We give alternative formulations using cut inequalities, compare these formulations, provide a polyhedral analysis of the smallsized formulation, describe valid inequalities, study the associated separation problems, and design variable fixing rules. All of these findings are then utilized in devising an efficient branch-and-cut algorithm to solve this network design problem.
Open Access
Time constrained maximal covering salesman problem with weighted demands and partial coverage
(Elsevier Ltd, 2016) Ozbaygin, G.; Yaman, H.; Karasan, O. E.
In a routing framework, it may not be viable to visit every single customer separately due to resource limitations or efficiency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in which the aim is to find a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide flow and cut formulations and derive valid inequalities. Since the connectivity constraints and the proposed valid inequalities are exponential in the size of the problem, we devise different branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the effectiveness of the proposed valid inequalities in terms of strengthening the linear relaxation bounds as well as speeding up the solution procedure. Moreover, the results indicate the superiority of using a branch-and-cut methodology over a flow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments. © 2016 Elsevier Ltd