Browsing by Subject "Location problems (Programming)"

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Open Access
Exact solution methodologies for the p-center problem under single and multiple allocation strategies
(2013) Çalık, Hatice
The p-center problem is a relatively well known facility location problem that involves locating p identical facilities on a network to minimize the maximum distance between demand nodes and their closest facilities. The focus of the problem is on the minimization of the worst case service time. This sort of objective is more meaningful than total cost objectives for problems with a time sensitive service structure. A majority of applications arises in emergency service locations such as determining optimal locations of ambulances, fire stations and police stations where the human life is at stake. There is also an increased interest in p-center location and related location covering problems in the contexts of terror fighting, natural disasters and human-caused disasters. The p-center problem is NP-hard even if the network is planar with unit vertex weights, unit edge lengths and with the maximum vertex degree of 3. If the locations of the facilities are restricted to the vertices of the network, the problem is called the vertex restricted p-center problem; if the facilities can be placed anywhere on the network, it is called the absolute p-center problem. The p-center problem with capacity restrictions on the facilities is referred to as the capacitated p-center problem and in this problem, the demand nodes can be assigned to facilities with single or multiple allocation strategies. In this thesis, the capacitated p-center problem under the multiple allocation strategy is studied for the first time in the literature. The main focus of this thesis is a modelling and algorithmic perspective in the exact solution of absolute, vertex restricted and capacitated p-center problems. The existing literature is enhanced by the development of mathematical formulations that can solve typical dimensions through the use of off the-shelf commercial solvers. By using the structural properties of the proposed formulations, exact algorithms are developed. In order to increase the efficiency of the proposed formulations and algorithms in solving higher dimensional problems, new lower and upper bounds are provided and these bounds are utilized during the experimental studies. The dimensions of problems solved in this thesis are the highest reported in the literature.
Open Access
Fiber optical network design problems : case for Turkey
(2013) Yazar, Başak
The problems within scope of this thesis are based on an application arising from one of the largest Internet service providers operating in Turkey. There are mainly two different problems: the green field design and copper field re-design. In the green field design problem, the aim is to design a least cost fiber optical network from scratch that will provide high bandwidth Internet access from a given central station to a set of aggregated demand nodes. Such an access can be provided either directly by installing fibers or indirectly by utilizing passive splitters. Insertion loss, bandwidth level and distance limitations should simultaneously be considered in order to provide a least cost design to enable the required service level. On the other hand, in the re-design of the copper field application, the aim is to improve the current service level by augmenting the network through fiber optical wires. Copper rings in the existing infrastructure are augmented with cabinets and direct fiber links from cabinets to demand nodes provide the required coverage to distant nodes. Mathematical models are constructed for both problem specifications. Extensive computational results based on real data from Kartal (45 points) and Bakırköy (74 points) districts in Istanbul show that the proposed models are viable exact solution methodologies for moderate dimensions.
Open Access
Hub & regenerator location and survivable network design
(2010) Özkök, Onur
With the vast development of the Internet, telecommunication networks are employed in numerous different outlets. In addition to voice transmission, which is a traditional utilization, telecommunication networks are now used for transmission of different types of data. As the amount of data transmitted through the network increases, issues such as the survivability and the capacity of the network become more imperative. In this dissertation, we deal with both design and routing problems in telecommunications networks. Our first problem is a two level survivable network design problem. The topmost layer of this network consists of a backbone component where the access equipments that enable the communication of the local access networks are interconnected. The second layer connects the users on the local access network to the access equipments, and consequently to the backbone network. To achieve a survivable network, one that stays operational even under minor breakdowns, the backbone network is assumed to be 2-edge connected while local access networks are to have the star connectivity. Within the literature, such a network is referred to as a 2-edge connected/star network. Since the survivability requirements of networks may change based on the purposes they are utilized for, a variation of this problem in which local access networks are also required to be survivable is also analyzed. The survivability of the local access networks is ensured by providing two connections for every component of the local access networks to the backbone network. This architecture is known as dual homing in the literature. In this dissertation, the polyhedral analysis of the two versions of the two level survivable network design problem is presented; separation problems are analyzed; and branch-and-cut algorithms are developed to find exact solutions. The increased traffic on the telecommunications networks requires the use of high capacity components. Optical networks, composed of fiber optical cables, offer solutions with their higher bandwidths and higher transmission speeds. This makes the optical networks a good alternative to handle the rapid increase in the data traffic. However, due to signal degradation which makes signal regeneration necessary introduces the regenerator placement problem as signal regeneration is a costly process in optical networks. In the regenerator placement problem, we study a location and routing problem together on the backbone component of a given telecommunications network. Survivability is also considered in this problem simultaneously. Exact solution methodologies are developed for this problem: mathematical models and some valid inequalities are proposed; separation problems for the valid inequalities are analyzed and a branch-and-cut algorithm is devised.
Open Access
The hub covering problem over incomplete hub networks
(2006) Kalaycılar, Murat
The rising trend in the transportation and telecommunication systems increases the importance of hub location studies in recent years. Hubs are special types of facilities in many-to-many distribution systems where flows are consolidated and disseminated. Analogous to location models, p-hub median, p-hub center and hub covering problems have been studied in the literature. In this thesis, we focus on a special type of hub covering problem which we call as “Hub Covering Problem over Incomplete Hub Networks”. Most of the studies in the hub location literature assume that the hub nodes are fully interconnected. We observe that, especially in cargo delivery systems, hub network is not complete. Thus, in this study we relax this fundamental assumption and propose integer programming models for single and multi allocation cases of the hub covering problem. We also propose three heuristics for both single and multi allocation cases of the problem. During the computational performance of proposed models and heuristics, CAB data was used. Results and comparisons of these heuristics will also be discussed.
Open Access
Hub location and Hub network design
(2009) Alumur, Sibel Alev
he hub location problem deals with finding the location of hub facilities and allocating the demand nodes to these hub facilities so as to effectively route the demand between origin–destination pairs. Hub location problems arise in various application settings in telecommunication and transportation. In the extensive literature on the hub location problem, it has widely been assumed that the subgraph induced by the hub nodes is complete. Throughout this thesis we relax the complete hub network assumption in hub location problems and focus on designing hub networks that are not necessarily complete. We approach to hub location problems from a network design perspective. In addition to the location and allocation decisions, we also study the decision on how the hub network must be designed. We focus on the single allocation version of the problems where each demand center is allocated to a single hub node. We start with introducing the 3-stop hub covering network design problem. In this problem, we aim to design hub networks so that all origin– destination pairs receive service by visiting at most three hubs on a route. Then, we include hub network design decisions in the classical hub location problems introduced in the literature. We introduce the single allocation incomplete p-hub median, hub location with fixed costs, hub covering, and p-hub center network design problems to the literature. Lastly, we introduce the multimodal hub location and hub network design problem. We include the possibility of using different hub links, and allow for different transportation modes between hubs, and for different types of service time promises between origin–destination pairs, while designing the hub network in the multimodal problem. In this problem, we jointly consider transportation costs and travel times, which are studied separately in hub location problems presented in the literature. Computational analyses with all of the proposed models are presented on the various instances of the CAB data set and on the Turkish network.
Open Access
Hub location under competition
(2013) Mahmutoğulları, Ali İrfan
Hubs are consolidation and dissemination points in many-to-many flow networks. The hub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this thesis, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide the locations of their hubs and then customers choose the firm according to provided service levels. Each decision-maker aims to maximize his/her market share. Having investigated the existing studies in the field of economy, retail location and operation research, we propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r|Xp) hub-medianoid and (r|p) hub-centroid problems. After defining them as combinatorial optimization problems, the problems are proved to be NP-hard. Linear programming models are presented for these problems as well as exact solution algorithms for the (r|p) hub-centroid problem that outperform the linear model in terms of memory requirement and CPU time. The performance of models and algorithms are tested by the computational analysis conducted on two well-known data sets from the hub location literature.
Open Access
Modeling and heuristic approaches for the Hub covering problem over incomplete Hub networks
(2009) Çalık, Hatice
Hubs are the accumulation points within the transportation and the telecommunication networks that collect and distribute the flow or data, which is originated from a starting point and needs to be transferred to a destination point. The main application areas of the hub location problem are airline systems, telecommunication network design and cargo delivery systems. In the literature, a common treatment of hub location problems is under the classification dating back to the location literature. In this classification, four different types are identified. Namely, the p-hub median problem, the hub location problem with fixed costs, the p-hub center problem, and the hub covering problem in the literature. In most of the hub location studies, the hub networks are assumed to be complete; however, the observations on the real life cases showed that this may not be the case. Therefore, in this thesis, we relax this assumption and focus on the single allocation version of the hub covering problem over incomplete hub networks. We propose two new mathematical formulations and a tabu search based heuristic algorithm for this problem. We perform several computational experiments on the formulations with the CAB data set from the literature and a larger scale network corresponding to the cities in Turkey. The results we obtained from our experimentations reveals that designing incomplete hub networks to provide service within a given service time bound is cost effective in accordance with designing complete hub networks.
Open Access
Outer approximation algorithms for the congested p-median problem
(2011) Şelfun, Selva
In this thesis, we study a generalization of the p-median problem, which is a well-known facility location problem. Given a set of clients, a set of potential facilities, and a positive integer p, the p-median problem is concerned with choosing p facilities and assigning each client to an open facility in such a way that the sum of the travel times between each client and the facility that serves that client is as small as possible. The classical p-median problem takes into account only the travel times between clients and facilities. However, in many applications, the disutility of a client is also closely related to the waiting time at a facility, which is typically an increasing function of the demand allocated to that facility. In an attempt to address this issue, for a given potential facility, we define the disutility of a client as a function of the travel time and the total demand served by that facility. The latter part reflects the level of unwillingness of a client to be served by a facility as a function of the level of utilization of that facility. By modeling this relation using an increasing convex function, we develop convex mixed integer nonlinear programming models. By exploiting the fact that nonlinearity only appears in the objective function, we propose different variants of the well-known outer approximation algorithm. Our extensive computational results reveal that our algorithms are competitive in comparison with the off-the-shelf solvers.
Open Access
P-hub maximal covering problem and extensions for gradual decay functions
(2013) Peker, Meltem
Hubs are special facilities that serve as switching, transshipment and sorting nodes in many to many distribution systems. The hub location problem deals with the selection of the locations of hub facilities and finding assignments of demand nodes to hubs simultaneously. The p-hub maximal covering problem, that is one of the variations of the hub location problems, aims to find locations of hubs so as to maximize the covered demand that are within the coverage distance with a predetermined number of hubs. In the literature of hub location, p-hub maximal covering problem is conducted in the framework of only binary coverage; origin-destination pairs are covered if the total path length is less than coverage distance and not covered at all if the path length exceeds the coverage distance. Throughout this thesis, we extend the definition of coverage and introduce “partial coverage” that changes with the distance, to the hub location literature. In this thesis, we study the p-hub maximal covering problem for single and multiple allocations and provide new formulations that are also valid for partial coverage. The problems are proved to be NP-Hard. We even show that assignment problem with a given set of hubs for the single allocation version of the problem is also NP-Hard. Computational results for all the proposed formulations with different data sets are presented and discussed.
Open Access
Routing and scheduling decisions in the hierarchical hub location problem
(2013) Dükkancı, Okan
Hubs are facilities that consolidate and disseminate flow in many-to-many distribution systems. The hub location problem considers decisions including the locations of hubs on a network and also the allocations of the demand (non-hub) nodes to these hubs. In this study, a hierarchical multimodal hub network is proposed. Based on this network, a hub covering problem with a service time bound is defined. The hierarchical network consists of three layers. In this study, two different structures, which are ring(s)-star-star (R-S-S) and ring(s)-ring(s)-star (R-R-S), are considered. The multimodal network has three different types of vehicles at each layer, which are airplanes, big trucks and pickup trucks. For the proposed problems (R-S-S and R-R-S), two mathematical models are presented and strengthened with some valid inequalities. The computational analysis is conducted over Turkish and CAB data sets. Finally, we propose a heuristic algorithm in order to solve large-sized problems and also test the performance of this heuristic approach on Turkish network data set.