| The dissertation presents research in two areas. First, we try to establish a general production and inventory problem, characterize its optimal policies, and find strong planning and forecast horizons which make the whole problem decomposible into a set of smaller problems each of which can be solved separately. A forward branch and bound algorithm is developed to determine such horizons and solve the whole problem. We then try to open up the way to studying oligopoly theory with a small number of participants and under widely varying conditions. We consider both monopoly and oligopoly pricing and advertising models for a new product during its introductory period when production learning curve phenomenon is most pronounced. The monopoly model is solved by an application of Green's theorem. The oligopoly model is studied by using the theory of differential games. We also characterize its policies, and discuss three different pricing rules: the optimal variable pricing, the instantaneous marginal pricing, and the optimal constant pricing rules. |
