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The p-center problem is a relatively well known facility location problem thatinvolves locating p identical facilities on a network to minimize the maximumdistance between demand nodes and their closest facilities. The focus of theproblem is on the minimization of the worst case service time. This sort ofobjective is more meaningful than total cost objectives for problems with a timesensitive service structure. A majority of applications arises in emergency servicelocations such as determining optimal locations of ambulances, fire stations andpolice stations where the human life is at stake. There is also an increasedinterest in p-center location and related location covering problems in the contextsof terror fighting, natural disasters and human-caused disasters. The p-centerproblem is NP-hard even if the network is planar with unit vertex weights, unitedge lengths and with the maximum vertex degree of 3. If the locations of thefacilities are restricted to the vertices of the network, the problem is called thevertex restricted p-center problem; if the facilities can be placed anywhere on thenetwork, it is called the absolute p-center problem. The p-center problem withcapacity restrictions on the facilities is referred to as the capacitated p-centerproblem and in this problem, the demand nodes can be assigned to facilities withsingle or multiple allocation strategies. In this thesis, the capacitated p-centerproblem under the multiple allocation strategy is studied for the first time in theliterature.The main focus of this thesis is a modelling and algorithmic perspective inthe exact solution of absolute, vertex restricted and capacitated p-center problems.The existing literature is enhanced by the development of mathematicalformulations that can solve typical dimensions through the use of off the-shelfcommercial solvers. By using the structural properties of the proposed formulations,exact algorithms are developed. In order to increase the effciency of theproposed formulations and algorithms in solving higher dimensional problems,new lower and upper bounds are provided and these bounds are utilized duringthe experimental studies. The dimensions of problems solved in this thesis arethe highest reported in the literature.Not availabl