Scania CV AB is a world leading provider of sustainable transport solutions. This includes trucks and buses, as well as an extensive offering of product-related services. This project takes place at the Södertälje plant and is carried out under the Transmissions Manufacturing department, with the output shaft line as the main focus. Due to a higher scale of product demand, the department aims to extend the line's production capacity to include both additional components and a higher production volume. The line under investigation consists of eleven serial processes. The project sets out to investigate the line's dynamic, find a theoretical maximum capacity for different product types and derive a reasonable OPE goal. Moreover, the project's final objective refers to how un-utilized capacity can be revealed. The project's results are delivered in three distinct parts. Firstly, a complex and thorough simulation model is delivered to the department alongside usage instructions. The model in its entirety is found in appendix A3. It is crucial to ensure that the model describes the real system. Therefore, the second result is an extensive model verification and validation. Lastly, results to where un-utilized capacity can be found is presented. General findings are that, reducing the cycle times to the times stated in the buy-in contract alongside with reducing the length (but not frequency) of shutdowns gives a considerable capacity enhancement. All further optimization endeavours assumes that the line's cycle times have already been reduced to the purchased times. Moreover, it is possible to increase product type one's manufacturing capacity by 11,4%, product type two's capacity by 13,1% and product types three and four's capacity with 7,2%. The capacity enhancements depends on several parameters for the different product types. / Scania CV AB är världsledande leverantörer av hållbara transportlösningar. Dessa involverar lastbilar och bussar, tillsammans med ett stort utbud av produktrelaterade tjänster. Detta projekt har genomförts på Scanias produktionsenhet i Södertälje, närmare bestämt på Transmissionsbearbetningen, med fokus på bearbetningslinan för utgående axel. På grund av högre produktefterfrågan önskar avdelningen att utöka linans kapacitet genom att tillverka fler produktertyper samt öka produktionsvolymen. Bearbetningslinan som undersöks består av elva stycken seriella processer. Projektet önskar att undersöka linans dynamik, hitta ett teoretiskt maximum för de olika produkttyperna samt presentera ett rimligt OPE mål för dessa. Slutligen önskar projektet att undersöka hur outnyttjad kapacitet kan återfinnas. Projektets resultat presenteras i tre olika delar. Först överlämnas simuleringsmodellen till avdelningen tillsammans med en grundlig genomgång av uppbyggnad och funktion. Modellen i dess helhet återfinns i appendix A3. Det är avgörande att säkerställa modellen beskriver det verkliga systemet. Därför innehåller den andra delen av resultatet en omfattande verifiering och validering. Slutligen presenteras resultat rörande var outnyttjad kapacitet kan återfinnas. Projektets övergripande fynd är att en reducering av cykeltiderna till maskinernas inköpta cykeltider tillsammans med en reducering i maskinstoppens längd (inte frekvens) skulle öka linans kapacitet avsevärt. Alla vidare beskrivna optimeringsförsök förutsätter att linans cykeltider redan reducerats till de inköpta tiderna. I och med detta kan kapaciteten för produkttyp ett ökas med totalt 11,4%, produkttyp två med 13,1% och produkttyperna tre och fyra med 7,9%. kapacitetsökningarna beror på flertalet skilda parametrar för de olika produkttyperna.

In this project, we implement portfolio theory to construct our portfolio, applying the theory to real practice. There are 3 parts in this project, including portfolio optimization, Capital Asset Pricing Model (CAPM) analysis and Factor Model analysis. We implement portfolio theory in the portfolio optimization part. In the second part, we use the CAPM to analyze and improve our portfolio. In the third part we extend our CAPM to factor models to get a deeper analysis of our portfolio.

Li, Zhening. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 138-146). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Tang Shu Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 75-76). / Introduction --- p.1 / Chapter 1 --- Efficient point and proper efficient point --- p.3 / Chapter 1.1 --- Introduction --- p.3 / Chapter 1.2 --- Definition and properties --- p.4 / Chapter 1.3 --- Existence of bases and proper efficient points --- p.14 / Chapter 2 --- Density theorem for positive proper efficient point in normed space --- p.18 / Chapter 2.1 --- "Theorem of Arrrow, Barankin and Blackwell" --- p.18 / Chapter 2.2 --- Cone with strictly positive linear functionals --- p.20 / Chapter 2.3 --- Cone with closed bounded base --- p.25 / Chapter 2.4 --- Density theorem for other proper efficiency --- p.34 / Chapter 3 --- Density theorem in Topological Vector Space --- p.43 / Chapter 3.1 --- D-cone --- p.43 / Chapter 3.2 --- Space ordered by a D-cone --- p.47 / Chapter 3.3 --- Space ordered by a cone with closed bounded base --- p.49 / Chapter 4 --- Some results on multifunction --- p.52 / Chapter 4.1 --- Open mapping theorem --- p.53 / Chapter 4.2 --- Inverse function theorem --- p.63 / Chapter 4.3 --- Subtraction theorem --- p.66 / Bibliography

by Chow Wai Chuen. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 66-67.

by Ng Sze-Kui. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 42.

by Peter Au. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 87-88). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminaries --- p.7 / Chapter 2.1 --- Recession and Conjugate Functions --- p.7 / Chapter 2.2 --- Directional derivative and Subgradient --- p.10 / Chapter 2.3 --- Well-Posedness and E-subgradient --- p.15 / Chapter 2.4 --- Exact Penalization --- p.17 / Chapter 3 --- Some Recent Results on Error Bounds --- p.20 / Chapter 3.1 --- Hoffman's Error Bound --- p.20 / Chapter 3.2 --- Extension of Hoffman's Error Bound to Polynomial Systems --- p.26 / Chapter 3.2.1 --- An Error Bound to Polynomial Systems --- p.28 / Chapter 3.2.2 --- Error Bound for Convex Quadratic Inequali- ties Systems --- p.30 / Chapter 3.3 --- Error Bounds for a Convex Inequality --- p.41 / Chapter 3.3.1 --- Unconstrained Case --- p.42 / Chapter 3.3.2 --- Constrained Case --- p.47 / Chapter 3.4 --- Error Bounds for System of Convex Inequalities --- p.55 / Chapter 3.4.1 --- Unconstrained Case --- p.56 / Chapter 3.4.2 --- Constrained Case --- p.60 / Chapter 4 --- Some Recent Results on Certain Proper Efficient Points --- p.63 / Chapter 4.1 --- Scalarization of Henig Proper Efficient Points --- p.63 / Chapter 4.1.1 --- Preliminaries --- p.64 / Chapter 4.1.2 --- Scalarization by Monotone Minkowski Func- tionals --- p.68 / Chapter 4.1.3 --- Scalarization by Continuous Norms --- p.73 / Chapter 4.2 --- Pareto Optimizing and Scalarly Stationary Sequence --- p.75 / Bibliography

Yu Xiaohui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 98-115). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Related Work --- p.6 / Chapter 2.1 --- Query Optimization --- p.6 / Chapter 2.2 --- Query Rewriting --- p.8 / Chapter 2.2.1 --- Optimizing Multi-Block Queries --- p.8 / Chapter 2.2.2 --- Semantic Query Optimization --- p.13 / Chapter 2.2.3 --- Query Rewriting in Starburst --- p.15 / Chapter 2.3 --- Plan Generation --- p.16 / Chapter 2.3.1 --- Dynamic Programming Approach --- p.16 / Chapter 2.3.2 --- Join Query Processing --- p.17 / Chapter 2.3.3 --- Queries with Aggregates --- p.23 / Chapter 2.4 --- Statistics and Cost Estimation --- p.24 / Chapter 2.5 --- Histogram Techniques --- p.27 / Chapter 2.5.1 --- Definitions --- p.28 / Chapter 2.5.2 --- Trivial Histograms --- p.29 / Chapter 2.5.3 --- Heuristic-based Histograms --- p.29 / Chapter 2.5.4 --- V-Optimal Histograms --- p.32 / Chapter 2.5.5 --- Wavelet-based Histograms --- p.35 / Chapter 2.5.6 --- Multidimensional Histograms --- p.35 / Chapter 2.5.7 --- Global Histograms --- p.37 / Chapter 3 --- New Histogram Techniques --- p.39 / Chapter 3.1 --- Piecewise Linear Histograms --- p.39 / Chapter 3.1.1 --- Construction --- p.41 / Chapter 3.1.2 --- Usage --- p.43 / Chapter 3.1.3 --- Error Measures --- p.43 / Chapter 3.1.4 --- Experiments --- p.45 / Chapter 3.1.5 --- Conclusion --- p.51 / Chapter 3.2 --- A-Optimal Histograms --- p.54 / Chapter 3.2.1 --- A-Optimal(mean) Histograms --- p.56 / Chapter 3.2.2 --- A-Optimal(median) Histograms --- p.58 / Chapter 3.2.3 --- A-Optimal(median-cf) Histograms --- p.59 / Chapter 3.2.4 --- Experiments --- p.60 / Chapter 4 --- Global Histograms --- p.64 / Chapter 4.1 --- Wavelet-based Global Histograms --- p.65 / Chapter 4.1.1 --- Wavelet-based Global Histograms I --- p.66 / Chapter 4.1.2 --- Wavelet-based Global Histograms II --- p.68 / Chapter 4.2 --- Piecewise Linear Global Histograms --- p.70 / Chapter 4.3 --- A-Optimal Global Histograms --- p.72 / Chapter 4.3.1 --- Experiments --- p.74 / Chapter 5 --- Dynamic Maintenance --- p.81 / Chapter 5.1 --- Problem Definition --- p.83 / Chapter 5.2 --- Refining Bucket Coefficients --- p.84 / Chapter 5.3 --- Restructuring --- p.86 / Chapter 5.4 --- Experiments --- p.91 / Chapter 6 --- Conclusions --- p.95 / Bibliography --- p.98

by Chung Shun Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 158-170). / Abstracts in English and Chinese. / List of Figures --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background and Historical Development --- p.1 / Chapter 1.2 --- Practical Problems --- p.3 / Chapter 1.2.1 --- Statistics --- p.3 / Chapter 1.2.2 --- Aerodynamics --- p.4 / Chapter 1.2.3 --- Factory Allocation Problem --- p.5 / Chapter 1.2.4 --- Parameter Problem --- p.5 / Chapter 1.2.5 --- Chemical Engineering --- p.5 / Chapter 1.2.6 --- Operational Research --- p.6 / Chapter 1.2.7 --- Economics --- p.6 / Chapter 1.3 --- Mathematical Models for Optimization Problems --- p.6 / Chapter 1.4 --- Unconstrained Optimization Techniques --- p.8 / Chapter 1.4.1 --- Direct Method - Differential Calculus --- p.8 / Chapter 1.4.2 --- Iterative Methods --- p.10 / Chapter 1.5 --- Main Objectives of the Thesis --- p.11 / Chapter 2 --- Basic Concepts in Optimizations of Smooth Func- tions --- p.14 / Chapter 2.1 --- Notation --- p.14 / Chapter 2.2 --- Different Types of Minimizer --- p.16 / Chapter 2.3 --- Necessary and Sufficient Conditions for Optimality --- p.18 / Chapter 2.4 --- Quadratic Functions --- p.22 / Chapter 2.5 --- Convex Functions --- p.24 / Chapter 2.6 --- "Existence, Uniqueness and Stability of a Minimum" --- p.29 / Chapter 2.6.1 --- Existence of a Minimum --- p.29 / Chapter 2.6.2 --- Uniqueness of a Minimum --- p.30 / Chapter 2.6.3 --- Stability of a Minimum --- p.31 / Chapter 2.7 --- Types of Convergence --- p.34 / Chapter 2.8 --- Minimization of Functionals --- p.35 / Chapter 3 --- Steepest Descent Method --- p.37 / Chapter 3.1 --- Background --- p.37 / Chapter 3.2 --- Line Search Method and the Armijo Rule --- p.39 / Chapter 3.3 --- Steplength Control with Polynomial Models --- p.43 / Chapter 3.3.1 --- Quadratic Polynomial Model --- p.43 / Chapter 3.3.2 --- Safeguarding --- p.45 / Chapter 3.3.3 --- Cubic Polynomial Model --- p.46 / Chapter 3.3.4 --- General Line Search Strategy --- p.49 / Chapter 3.3.5 --- Algorithm of Steepest Descent Method --- p.51 / Chapter 3.4 --- Advantages of the Armijo Rule --- p.54 / Chapter 3.5 --- Convergence Analysis --- p.56 / Chapter 4 --- Iterative Methods Using Second Derivatives --- p.63 / Chapter 4.1 --- Background --- p.63 / Chapter 4.2 --- Newton's Method --- p.64 / Chapter 4.2.1 --- Basic Concepts --- p.64 / Chapter 4.2.2 --- Convergence Analysis of Newton's Method --- p.65 / Chapter 4.2.3 --- Newton's Method with Steplength --- p.69 / Chapter 4.2.4 --- Convergence Analysis of Newton's Method with Step-length --- p.70 / Chapter 4.3 --- Greenstadt's Method --- p.72 / Chapter 4.4 --- Marquardt-Levenberg Method --- p.74 / Chapter 4.5 --- Fiacco and McComick Method --- p.76 / Chapter 4.6 --- Matthews and Davies Method --- p.79 / Chapter 4.7 --- Numerically Stable Modified Newton's Method --- p.80 / Chapter 4.8 --- The Role of the Second Derivative Methods --- p.89 / Chapter 5 --- Multi-step Methods --- p.92 / Chapter 5.1 --- Background --- p.93 / Chapter 5.2 --- Heavy Ball Method --- p.94 / Chapter 5.3 --- Conjugate Gradient Method --- p.99 / Chapter 5.3.1 --- Some Types of Conjugate Gradient Method --- p.99 / Chapter 5.3.2 --- Convergence Analysis of Conjugate Gradient Method --- p.108 / Chapter 5.4 --- Methods of Variable Metric and Methods of Conju- gate Directions --- p.111 / Chapter 5.5 --- Other Approaches for Constructing the First-order Methods --- p.116 / Chapter 6 --- Quasi-Newton Methods --- p.121 / Chapter 6.1 --- Disadvantages of Newton's Method --- p.122 / Chapter 6.2 --- General Idea of Quasi-Newton Method --- p.124 / Chapter 6.2.1 --- Quasi-Newton Methods --- p.124 / Chapter 6.2.2 --- Convergence of Quasi-Newton Methods --- p.129 / Chapter 6.3 --- Properties of Quasi-Newton Methods --- p.131 / Chapter 6.4 --- Some Particular Algorithms for Quasi-Newton Methods --- p.137 / Chapter 6.4.1 --- Single-Rank Algorithms --- p.137 / Chapter 6.4.2 --- Double-Rank Algorithms --- p.144 / Chapter 6.4.3 --- Other Applications --- p.149 / Chapter 6.5 --- Conclusion --- p.152 / Chapter 7 --- Choice of Methods in Optimization Problems --- p.154 / Chapter 7.1 --- Choice of Methods --- p.154 / Chapter 7.2 --- Conclusion --- p.157 / Bibliography --- p.158

Pong Ting Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 79-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Notations --- p.7 / Chapter 2.3 --- On properties of Normal Cones --- p.9 / Chapter 2.4 --- Polar Calculus --- p.13 / Chapter 2.5 --- Notions of Relative Interior --- p.17 / Chapter 2.6 --- Properties of Minkowski functional --- p.18 / Chapter 2.7 --- Properties of Epigraphs --- p.19 / Chapter 3 --- The Strong Conical Hull Intersection Property (Strong CHIP): Definition and Some Properties --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Definition of the strong CHIP --- p.24 / Chapter 3.3 --- Relationship between the strong CHIP and projections onto sets --- p.26 / Chapter 3.4 --- Relationship between the strong CHIP and the Basic Constraint Qualifications (BCQ) --- p.35 / Chapter 3.5 --- The strong CHIP of extremal subsets --- p.42 / Chapter 4 --- Sufficient Conditions for the Strong CHIP --- p.46 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- ̐ưجI̐ưجis finite --- p.47 / Chapter 4.2.1 --- Interior point conditions --- p.47 / Chapter 4.2.2 --- Boundedly linear regularity --- p.52 / Chapter 4.2.3 --- Epi-sum --- p.54 / Chapter 4.3 --- ̐ưجI̐ưجis infinite --- p.56 / Chapter 4.3.1 --- A Sum Rule --- p.57 / Chapter 4.3.2 --- The C-Extended Minkowski Functional --- p.58 / Chapter 4.3.3 --- Relative Interior Point Conditions --- p.62 / Chapter 4.3.4 --- Bounded Linear Regularity --- p.68 / Chapter 5 --- "The SECQ, Linear Regularity and the Strong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces" --- p.69 / Chapter 5.1 --- Introduction --- p.69 / Chapter 5.2 --- The strong CHIP and the SECQ --- p.71 / Chapter 5.3 --- Linear regularity and the SECQ --- p.73 / Chapter 5.4 --- Interior-point conditions and the SECQ --- p.76 / Bibliography --- p.79