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published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

This dissertation focuses on three cases of the following two stage problem in the context of multi-product inventories of vertically differentiated products. In Stage 1 of the problem, the manager determines the optimal production quantities of different products when the demands are uncertain. In Stage 2 of the problem, the demands for different products are observed. Now, the manager meets the demand of each product using the inventory of the product or by carrying out a downward substitution from the inventories of higher performance products. The manager’s objective is to maximize the expected revenue from the decisions made at the two stages collectively. The first problem addressed in this dissertation focuses on the case when different products are produced simultaneously on the same set of machines due to random variations in the manufacturing process. These systems, referred to as co-production systems, are very common in the semi- conductor industry, the textile industry and the agriculture industry. For this problem, we provide an analytical solution to the two stage problem, and discuss managerial insights that are specific to co-production systems and are not extendible to multi-item inventories of products that can be ordered or manufactured independently. The second problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently, and no constraints to meet minimum fill rate requirements or to restrict the total inventory below a certain level are present. We present an analytical solution to this problem. The third problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently and fill rate constraints and total inventory constraints are present. When the demands are multivariate normal, we show that this two stage problem can be reduced to a non-linear program using some new results for the determination of partial expectations. We also extend these results to higher order moments of the multivariate distribution and discuss their applications in solving some common operations management problems. / text

by Chiu Yiu Ming. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 127-129.

by Linda Hoi-ying Yau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter Chapter 1 --- Preliminary / Chapter § 1.1 --- Introduction page --- p.1 / Chapter § 1.2 --- Notations page --- p.3 / Chapter Chapter 2 --- Multilevel Analysis of Structural Equation Models with Multivariate Normal Distribution / Chapter § 2.1 --- The Multilevel Structural Equation Model page --- p.4 / Chapter § 2.2 --- "First Stage Estimation of and Σkmkm-1---ki+1wo for i=1,...,m-1 page" --- p.5 / Chapter § 2:3 --- Second Stage Estimation of Structural Parameters page --- p.10 / Chapter Chapter 3 --- Generalization to Arbitrary and Elliptical Distributions / Chapter § 3.1 --- Asymptotically Distribution-Free Estimation page --- p.25 / Chapter § 3.2 --- Elliptical Distribution Estimation page --- p.30 / Chapter Chapter 4 --- Artificial Examples / Chapter § 4.1 --- Examples on Multivariate Normal Distribution Estimation Page --- p.34 / Chapter § 4.2 --- Examples on Elliptical Distribution Estimation page --- p.40 / Chapter §4.3 --- Findings and Summary Page --- p.42 / Chapter Chapter 5 --- Conclusion and Discussion page --- p.44 / References page --- p.47 / Figure 1 page --- p.49 / Appendices page --- p.50 / Tables Page --- p.59

by Man-lai Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter PART I ： --- ANALYSIS OF DATA WITH POLYTOMOUS VARIABLES --- p.1 / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Model with Incomplete Data --- p.5 / Chapter §2.1 --- The Model --- p.5 / Chapter §2.2 --- Two-stage Estimation Method --- p.7 / Chapter Chapter 3 --- Generalization to Several Populations --- p.16 / Chapter §3.1 --- The Model --- p.16 / Chapter §3.2 --- Two-stage Estimation Method --- p.18 / Chapter Chapter 4 --- Computation of the Estimates --- p.23 / Chapter §4.1 --- Maximum Likelihood Estimates in Stage I --- p.23 / Chapter §4.2 --- Generalized Least Squares Estimates in Stage II --- p.27 / Chapter §4.3 --- Approximation for the weight matrix W --- p.28 / Chapter Chapter 5 --- Some Illustrative Examples --- p.31 / Chapter §5.1 --- Single Population --- p.31 / Chapter §5.2 --- Multisample --- p.37 / Chapter PART II ： --- ANALYSIS OF CONTINUOUS AND POLYTOMOUS VARIABLES --- p.42 / Chapter Chapter 6 --- Introduction --- p.42 / Chapter Chapter 7 --- Several Populations Structural Equation Models with Continuous and Polytomous Variables --- p.44 / Chapter §7.1 --- The Model --- p.44 / Chapter §7.2 --- Analysis of the Model --- p.45 / Chapter Chapter 8 --- Analysis of Structural Equation Models of Polytomous and Continuous Variables with Incomplete Data by Multisample Technique --- p.54 / Chapter §8.1 --- Motivation --- p.54 / Chapter §8.2 --- The Model --- p.55 / Chapter §8.3 --- The Method --- p.56 / Chapter Chapter 9 --- Computation of the Estimates --- p.60 / Chapter §9.1 --- Optimization Procedure --- p.60 / Chapter §9.2 --- Derivatives --- p.61 / Chapter Chapter 10 --- Some Illustrative Examples --- p.65 / Chapter §10.1 --- Multisample Example --- p.65 / Chapter §10.2 --- Incomplete Data Example --- p.67 / Chapter §10.3 --- The LISREL Program --- p.69 / Chapter Chapter 11 --- Conclusion --- p.71 / Tables --- p.73 / Appendix --- p.85 / References --- p.89

by Kwan-Moon Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 77-79. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Model with Some Polytomous Entries Missed --- p.5 / Chapter §2.1 --- The Model --- p.5 / Chapter §2.2 --- Full Maximum Likelihood (FML) Estimation --- p.7 / Chapter Chapter 3 --- Estimation of the Model with Some Continuous and Polytomous Entries Missed --- p.13 / Chapter §3.1 --- The Model --- p.13 / Chapter §3.2 --- Pseudo Maximum Likelihood (PsML) Estimation --- p.15 / Chapter Chapter 4 --- Indirect Methods --- p.19 / Chapter §4.1 --- Listwise Deletion Method --- p.19 / Chapter §4.2 --- Mean Imputation Method --- p.19 / Chapter §4.3 --- Regression Imputation Method --- p.20 / Chapter Chapter 5 --- Computation of the Estimates --- p.23 / Chapter §5.1 --- Optimization Procedure --- p.23 / Chapter §5.2 --- Starting Value and Gradient Vector of the Model with Some Polytomous Entries Missed --- p.25 / Chapter §5.3 --- Starting Value and Gradient Vector of the Model with Some Continuous and Polytomous Entries Missed --- p.29 / Chapter Chapter 6 --- Partition Maximum Likelihood (PML) Estimation --- p.35 / Chapter §6.1 --- Motivation --- p.35 / Chapter §6.2 --- PML Procedure of the Model with Some Polytomous Entries Missed --- p.35 / Chapter §6.3 --- PML Procedure of the Model with Some Continuous and Polytomous Entries Missed --- p.37 / Chapter Chapter 7 --- Simulation Studies and Comparison --- p.39 / Chapter §7.1 --- Simulation Study I --- p.39 / Chapter §7.2 --- Simulation Study II --- p.44 / Chapter Chapter 8 --- Summary and Discussion --- p.43 / Tables / Appendix / References

Tactile sensation is a complex manifestation of mechanical stimuli applied to the skin. At the most fundamental level of the somatosensory system is the cutaneous mechanoreceptor, making it the logical starting point in the bottom-up approach to understanding the somatosensory system and sensation, in general. Unfortunately, a consensus has not been reached in terms of the afferent behavior of mechanoreceptors subjected to compressive stimulation. In this study, several afferent mechanoreceptors were isolated, mechanically stimulated with controlled compressive loads. Their responses were recorded and the sensitivities of the individual receptors to compressive stimulation were statistically evaluated by correlating the compressive state of the skin to the observed“all-or-nothing" responses. A host of linear techniques have been employed previously to describe this multiple-input, binary-output system; however, each of these techniques has associated shortcomings when employed in this context. In particular, two shortcomings are the assumption of linear system input-output and the inability of the model to assess individual input-output associations relative to concurrent input in a multivariate context with interacting input. Therefore, a non-linear regression technique called logistical regression was selected for characterizing the mechanoreceptor system. From this model, the relative contributions that each component of the stimulus has upon the neural response of the receptor can be quantitatively assessed and extrapolated to the greater population of cutaneous mechanoreceptors. Since this study represents a novel approach to receptor characterization, a framework for the application of logistical regression to the time-series representation of the multiple-input, binary-output mechanoreceptor system was established and validated. Subsequently, in-vitro experiments were performed in which the afferent behavior of tactile receptors in rat hairy skin were recorded and the relative association between a number of biologically meaningful stimulus metrics and the observed neural response was evaluated for each receptor. Through the application of logistical regression, it was determined that cutaneous mechanoreceptors are preferentially sensitive to the rate of change of compressive stress when force-control stimulated and both stress and its rate of change when position-control stimulated.