Stochastic inventory control in dynamic environments

This dissertation studies some issues in stochastic inventory control.; The first focus of the dissertation is on stochastic continuous-time inventory control problems for a single item in dynamic environments. The demand process is modeled as a semi-Markov chain modulated Poisson process. It is shown that a myopic policy is optimal if the products can be purchased or bought-back at a single price. Conditions on the semi-Markov chain under which products will never be returned is derived. An algorithm to dynamically compute the optimal policy for a special case of the model is also provided. This demand model is next extended to a semi-Markov modulated renewal process, and several results are generalized to this more realistic model.; The next focus of the dissertation is a class of Markov modulated Poisson demand processes in which the transitions between the different states of the world is unobservable. A basic model with two demand states is first studied, and the optimal inventory policy is derived. An algorithm to compute this policy is also provided. Next the basic model is extended to multiple states, and a recursive formula is given which can be used to compute the optimal policy.; The inventory models with simultaneous ordering and pricing decisions are studied next. The demand process is dependent on the price. The joint pricing and inventory model under a price-sensitive Poisson demand environment is studied, and an algorithm to compute the optimal solution is given. Next the study is extended to the semi-Markov modulated Poisson demand environment, and it is shown that with certain approximation, the model can be solved in the similar way as in a Poisson demand environment.; The other focus of the dissertation is on stochastic inventory models for multiple items with both equal and unequal replenishment intervals under limited warehouse capacity. The optimality condition for equal replenishment intervals case is given, three heuristics are implemented, and it is proved that these heuristics provide the optimal solutions in the case of equal replenishment intervals. Extensive numerical tests are conducted, and the heuristics yield high quality solutions in very limited time.