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
This thesis describes the research done at the BC Cancer Agency in Vancouver, Canada, as part of a CIHR-team, using operations research to solve health care problems. Appointment booking data is...Show moreThis thesis describes the research done at the BC Cancer Agency in Vancouver, Canada, as part of a CIHR-team, using operations research to solve health care problems. Appointment booking data is used to determine where problems occur in the Chemo unit. One of these problems is the mismatch of capacity and demand. Some days there is slack capacity and other days appointments need to be rescheduled due to lack of capacity. A Markov Decision Process of the process is introduced and via Markov Chain theory a simulation model is introduced. New booking methods and ways to add capacity are tested using this simulation model. We conclude that using a booking method that is a bit more advanced and uses the booking tolerance earlier in the process gives the best results, and is significantly better than adding extra capacity.Show less
Robustness is the ability of a network to continue performing well when it is subject to failures or attacks. In this thesis we survey robustness measures on simple, undirected and unweighted...Show moreRobustness is the ability of a network to continue performing well when it is subject to failures or attacks. In this thesis we survey robustness measures on simple, undirected and unweighted graphs, network failures being interpreted as vertex or edge deletions. We study graph measures based on connectivity, distance, betweenness and clustering. Besides these, reliability polynomials and measures based on the Laplacian eigenvalues are considered. In addition to surveying existing measures, we propose a new robustness measure, the normalized effective resistance, which is derived from the total effective resistance. Total effective resistance is — within the field of electric circuit analysis — defined as the sum of the pairwise effective resistances over all pairs of vertices. The strength of this measure lies in the fact that all (not necessarily disjoint) paths are considered, in other words, the more backup possibilities, the larger the normalized effective resistance and the larger the robustness. A chapter is dedicated to optimizing the normalized effective resistance, first for graphs with a fixed number of vertices and diameter, and second for the addition of an edge to a given graph. For all of the measures described above we evaluate the effectiveness as a measure of network robustness. The discussion and comparison of robustness measures is illustrated by a number of examples. Where possible we make extensions to weighted graphs and for all statements we provide either an elaboration of the original proof, or — when a rigorous proof is not available — we provide one ourselves.Show less
