Browsing by Subject "network design"
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Item Open Access Exact solution methodologies for the p-center problem under single and multiple allocation strategies(Bilkent University, 2013) Çalık, HaticeThe 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.Item Open Access A mobile ammunition distribution system design on the battlefield(Bilkent University, 2010) Toyoğlu, HünkarAmmunition has been the most prominent factor in determining the outcome of combat. In this dissertation we study a military logistics problem in which ammunition requirements of the combat units, which are located on the battle- field, are to be satisfied in the right amount when and where they are needed. Our main objective is to provide a decision support tool that can help plan ammunition distribution on the battlefield. We demonstrate through an extensive literature review that the existing models are not capable of handling the specifics of our problem. Hence, we propose a mathematical programming model considering arc-based product-flow with O(n 4 ) decision variables and constraints. The model is a three-layer commodity-flow location routing formulation that distributes multiple products, respects hard time windows, allows demand points to be supplied by more than one vehicle or depot, and locates facilities at two different layers. We then develop a new mathematical programming model with only O(n 3 ) decision variables and constraints by considering node-based product-flow. We derive several valid inequalities to speed up the solution time of our models, illustrate the performance of the models in several realistically sized scenarios, and report encouraging results. Based on these mathematical models we propose two three-phase heuristic methods: a routing-first location-second and a location- first routing-second heuristic. The computational results show that complex real world problems can effectively be solved in reasonable times with the proposed heuristics. Finally, we introduce a dynamic model that designs the distribution system in consecutive time periods for the entire combat duration, and show how the static model can be utilized in dynamic environments.Item Open Access Modeling and heuristic approaches for the Hub covering problem over incomplete Hub networks(Bilkent University, 2009) Çalık, HaticeHubs 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.