This thesis introduces the successive lumping procedure (SLP) to compute the steady state probabilities for a class of Markov Chains with large state spaces. In this procedure we introduce one or...Show moreThis thesis introduces the successive lumping procedure (SLP) to compute the steady state probabilities for a class of Markov Chains with large state spaces. In this procedure we introduce one or multiple successive lumping states processes. Also, this thesis studies the classical reorder quantity, order point (Q, r) continuous review stochastic inventory model. This model has been extensively studied in the literature and its use in practice is widespread. Using the SLP efficient calculations can be done for this model when there are Bernoulli arrivals, a mixture of backorders, lost sales and a random lead time. In addition, this work extends previous research in this area by providing efficient algorithms for the computation of the optimal (Q∗ , r∗ ) values when there are Poisson arrivals, a multi-breakpoint discount pricing structure and a fixed lead time.Show less
