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

Tang Fung Chu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 79-81). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- The Multivariate Model and Bayesian Analysis of Stochastic Prior Information --- p.4 / Chapter 2.1 --- The Model --- p.4 / Chapter 2.2 --- Identification of the Model --- p.5 / Chapter 2.3 --- Bayesian Analysis of Stochastic Prior Information --- p.8 / Chapter 2.4 --- Computational Procedure --- p.10 / Chapter 2.4.1 --- Optimization Procedures --- p.11 / Chapter 2.4.2 --- Analytical Expressions --- p.12 / Chapter Chapter 3. --- Example and Simulation Study --- p.18 / Chapter 3.1 --- Example --- p.18 / Chapter 3.2 --- Simulation Study --- p.19 / Chapter 3.2.1 --- Designs --- p.20 / Chapter 3.2.2 --- Results --- p.23 / Chapter Chapter 4. --- Conclusion --- p.26 / Tables --- p.29 / References --- p.79

Wong Yuen Kwan Virginia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Deletion and Distance Measure --- p.6 / Chapter 2.1 --- Mahalanobis and Cook's Distances --- p.6 / Chapter 2.2 --- Defining New Measure Di --- p.8 / Chapter 2.3 --- Derivation of cov(s(i) ´ؤ s) --- p.10 / Chapter 3 --- Procedures for Detecting Influential Observations --- p.18 / Chapter 3.1 --- The One-Step Method --- p.18 / Chapter 3.1.1 --- The Method --- p.18 / Chapter 3.1.2 --- Design of Simulation Studies --- p.19 / Chapter 3.1.3 --- Results of Simulation Studies --- p.21 / Chapter 3.1.4 --- Higher Dimensional Cases --- p.24 / Chapter 3.2 --- The Forward Search Procedure --- p.24 / Chapter 3.2.1 --- Idea of the Forward Search Procedure --- p.25 / Chapter 3.2.2 --- The Algorithm --- p.26 / Chapter 4 --- Examples and Observations --- p.29 / Chapter 4.1 --- Example 1: Brain and Body Weight Data --- p.29 / Chapter 4.2 --- Example 2: Stack Loss Data --- p.34 / Chapter 4.3 --- Example 3: Percentage of Cloud Cover --- p.40 / Chapter 4.4 --- Example 4: Synthetic data of Hawkins et al.(1984) . --- p.46 / Chapter 4.5 --- Observations and Comparison --- p.52 / Chapter 5 --- Discussion and Conclusion --- p.54 / Tables --- p.56 / Figures --- p.77 / Bibliography --- p.85

by Lai-seung Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 58-59). / Abstract also in Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- The Bivariate Model and Maximum Likelihood Estimation --- p.5 / Chapter 2.1 --- The Model --- p.5 / Chapter 2.2 --- Likelihood function of the model --- p.7 / Chapter 2.3 --- Derivatives of likelihood equations --- p.8 / Chapter 2.4 --- Asymptotic properties --- p.11 / Chapter 2.5 --- Optimization procedures --- p.12 / Chapter Chapter 3. --- Generalization to Multivariate Model --- p.14 / Chapter 3.1 --- The Model --- p.14 / Chapter 3.2 --- The Partition Maximum Likelihood (PML) Estimation --- p.15 / Chapter 3.3 --- Asymptotic properties of the PML estimates --- p.19 / Chapter 3.4 --- Optimization procedures --- p.21 / Chapter Chapter 4. --- Simulation Study --- p.22 / Chapter 4.1 --- Designs --- p.22 / Chapter 4.2 --- Results --- p.26 / Chapter Chapter 5. --- Conclusion --- p.30 / Tables --- p.32 / References --- p.58

Lam, Hiu Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 58-60). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.