MSPresentation_Spring2011
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Shaun Douglas Smith's graduate studies focused on operations research, industrial engineering, statistics, and quality engineering. His coursework covered topics like optimization theory, simulation, stochastic processes, experiment design, statistical modeling, production and inventory control, and quality engineering. His final project applied an algorithm to solve a bin packing problem. Overall, his program equipped him with technical and analytical skills for improving production systems and decision-making.
MSPresentation_Spring2011
- 1. Review of Graduate Studies and Learning Outcomes Shaun Douglas Smith Candidate, MS Industrial Engineering April 14, 2011, 3:00 PM 2036 Durland Hall
- 2. Educational and Occupational Goals • Improve the production and research of goods and services by bringing complex situations down to an understandable level and find forward, lean-thinking solutions to reduce costs, contribute to Six-Sigma and value-added management projects and teams with expertise and dedication to continuous professional development through scientific inquiry. • Exercise sound leadership and management principles by making ethical decisions is any environment.
- 3. Approved Program of Study
- 4. IMSE 780: Method of Operations Research • Classical Optimization Theory – Using Hessian Matrix of f(x1, x2, x3....xn), where represents the elements of H. – Dichotomous, Fibonacci, Steepest Ascent, and Conjugate gradient search techniques. xx ji 2 The Principal: An overview in several topics of Operations Research including modern developments and applied problem-solving methodology. Emphasis on optimization theory and practical applications. • Constrained Optimization Theory – Karush-Kuhn-Tucker Equations ~ S(xi, λi) – Quadratic Programming, Wolfe’s Algorithm for linear programming solution to linear KKT equations with necessary conditions – DeNovo Programming (decision tree form of LP)
- 5. IMSE 780: Method of Operations Research • Dynamic Programming – Recursive optimization (iterations based on ‘best’ assignment of remaining resources) • Introduction to Stochastic Modeling – Markov Decision Process: “Taxicab” modeling with not only probability transition matrix, but expected return. Emphasis on ‘Best Policy” decision. • Stochastic Processes – Transition versus steady state behavior (Chapman-Kolomogorov) – Behavior of Markovian chains • Final Research Project – Sleator (1979) algorithm for ‘worst case’ solution to 2D Bin Packing Problem
- 6. IMSE 643: Industrial Simulation • Basic Modeling Techniques – Assessing distributional fits based on time between events and goodness of fit tests – Modeling transportation, process interruptions, occupying a resource, palletizing, et cetera The Principal: Theoretical introduction and applied use of simulation software for building models of real-world production systems for analysis. Statistical sensitivity analysis is used in order to improve existing systems based on resource constraints. • Analyzing ‘What if’ Scenarios – Dry Cleaner Final Project
- 7. IMSE 643: Industrial Simulation • Theoretical Aspect of Computer Simulation – Using random numbers to generate inter-arrival times – Linear Congruential Method for generating random numbers X1=(a*x0 + c) mod (m) such that m>0, a<m, c<m, x0<m • Variance Reduction – Antithetic Pairing
- 8. Stat 730: Multivariate Analysis • Mathematical structure of datasets in matrix form – Statistical manipulation through matrix algebra – Eigenvectors The Principal: Develop methods key in analyzing data structures common in all branches of science. Raw data takes the form of many variables measured on a large number of experimental units. Most methods focus on simplification and relationships among variables. • Graphically representing complex multivariate data • Almost All methods have canonical forms ~ Benefits?
- 9. Stat 730: Multivariate Analysis
- 10. Stat 730: Multivariate Analysis • Principal Component Analysis – Reduce a dataset into new, uncorrelated underlying variables – Based on Component Loading Vectors (Eigenvectors) • Factor Analysis – Additional Distributional Assumption (versus PCA) – Subjectivity and possibility for bias solutions • Discriminant Analysis – Multivariate method to predict class membership (Turkey Data) • Cluster Analysis – Cubic Cluster Criterion • MANOVA
- 11. Stat 722: Experiment Design for Product and Process Development • Mathematical structure of basic 2n Experiments – Why ANOVA may not be appropriate – Yate’s Method – Tests for significant effects The Principal: Extract reasonable estimated of factor effects using available degrees of freedom. Designs are often constrained by the number of experimental runs. Design experiments appropriate for data structures. • Extension to 3n Experiments – Adjusted Yate’s – Yate’s Method • Principal of Blocking – Confounding higher-order interactions & Alias Structures – Resolution of Designs
- 12. Stat 722: Experiment Design for Product and Process Development • Response Surface Modeling Methods – Optimizing a particular outcome(s) – Designing an experiment (assignment of Degrees of Freedom) – Analyzing the results
- 13. IMSE 802: Stochastic Processes and Theoretical Simulation • Random variable contained in a particular state space – Interested in understanding behavior as variable changes – Only previous state matters The Principal: Mathematically model stochastic processes (DTMC and CTMC) in order to understand and plan for the behavior of system. Develop principles key to simulating real-world scenarios. • Discrete Time Markov Chains (Event driven) – Time Homogeneous – One-step transition probability matrix – Chapman-Kolmogorov Equations (as opposed to IMSE 780) – First passage time, steady-state solution, expected variance….
- 14. IMSE 802: Stochastic Processes and Theoretical Simulation • Continuous Time Markov Chains – Pure birth versus pure death processes – Pure Birth Versus Pure Death Processes – Extension to theoretical simulation • Projects – Build a mathematical model for the game of CRAPS and find optimal strategy – Build a matrix-based simulation for a basic queuing system and find required number of servers
- 15. IMSE 802: Stochastic Processes and Theoretical Simulation
- 16. Stat 713: Applied Statistical Linear Models • Matrix-based regression – b=(X`X)-1X`Y, e=(I-X)(X`X)-1X`)Y, σ2=Y`*Y-b`X`Y/(n-2) – Detailed model building criteria – Assumptions, confidence intervals, prediction intervals – Decision-based approaches to consulting problems The Principal: Develop analytical skills by understanding mathematical and matrix-based regression and ANOVA models with extensions to higher-order problem solving techniques such as advanced model building and diagnostics, transformations, multifactor studies, ANVOCA, and experiment design.
- 17. Stat 713: Applied Statistical Linear Models
- 18. Stat 713: Applied Statistical Linear Models • Extension to ANOVA – Comparison of Assumptions – Various parameterizations – Multiple comparisons • ANCOVA • Mathematical forms of Experiment Design common in consulting – Blocking – Split-plot designs – Mixed effects – Balanced incomplete block designs – Nested designs
- 19. Stat 716: Nonparametric Statistics • Ranks and the Binomial Distribution The Principal: Expand our toolbox of statistical tests to better handle real- world type data by using more robust methods of testing when normal assumptions may not be met. • Common Nonparametric Methods – Correlation: Pearson → Spearman – T-test → Mann-Whitney – 1 way ANOVA → Kruskal-Wallis test – Matched pairs T-test → Wilcoxon test – Repeated Measured ANOVA → Friedman’s test – Measurement of “Agreement” →Kendall’s Coefficient of Concordance
- 20. IMSE 641: Quality Engineering The Principal: Design and application of statistical and non-statistical methods to improve and control a production system from implementation to constant monitoring. Develop the technical knowledge to continually learn and keep quality engineering knowledge ‘up to date.’ • Overview of Quality Systems – Quality Control ~ 3 Levels • Basic SQC Charting Schemes (Phase-I) – and R: ARL, ATSX • Extensions to Phase-II type Charting – Detecting small shifts in both mean and variance – Interested in Long term behavior of a system
- 21. IMSE 641: Quality Engineering 464136312621161161 70 60 50 40 30 20 10 Observation IndividualValue _ X=50 UCL=69.00 LCL=31.00 1 1 1 1 1 1 1 1 1 1 1 1 X-bar Chart for T=50 Shaun D Smith Imse 641 ~ Spring 2011 70605040302010 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 Process Data Density 58.71 6.051 21 34.03 10.00 29 Mean StDev N 1 2 Distribuiton Histogram of Process Data Normal 464136312621161161 100 0 -100 -200 -300 -400 Sample CumulativeSum 0 UCL=25.3 LCL=-25.3 CUMSUM Shaun D Smith IMSE 641 ~ Spring 2011 464136312621161161 60 50 40 30 20 Sample EWMA __ X=50 UCL=56.33 LCL=43.67 EWMA Chart Shaun D Smith Imse 641 ~ Spring 2011
- 22. IMSE 641: Quality Engineering • Design of Phase-II Controllers – CumSum & EWMA – Fast initial response, Moving Centerline – Optimal parameters based on ML estimates • SPC with Autocorrelated Data – Various filtering techniques 18161412108642 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag Autocorrelation Sample Autocorrelation for Molecular Weight Data
- 23. IMSE 641: Quality Engineering • Extensions to Multivariate Control – Often based on canonical variables – Principal Components or Factor Analysis • Short Production Runs – DNOM – Evans and Hubele ~ Multiple comparisons • Applications to the ‘Big Picture” • Database and Mining – For collection of historical data
- 24. IMSE 811: Advanced Production / Inventory Control The Principal: Learn advanced techniques for inventory control, operations management, logistics, and production control as best understood with scientific management. With this, we mathematically understand the principles of modern techniques such as MRP, JIT, Lean, et cetera. • Basic EOQ Model – EOQ vs POQ – Balances Holding Cost, setup cost, production cost, and demand • Extensions of EOQ
- 25. IMSE 811: Advanced Production / Inventory Control • Dynamic Lot Sizing – Part –period balancing – Wagner-Whittin (Dynamic Programming) • Introduction to Statistical Inventory Models – Newsvendor – Base stock model – (Q,r) model – Service Levels
- 26. IMSE 811: Advanced Production / Inventory Control • Understanding and Reducing Variance in Production – Tortoise and the Hare – Combining Little’s Laws to develop simple WIP/Queuing models
- 27. IMSE 811: Advanced Production / Inventory ControlMEASURE: STATION: 1 2 3 4 5 Arrival Rate (parts/hr) ra 10.000 9.800 9.310 8.845 7.960 Arrival CV ca 2 1.000 0.181 0.031 0.061 0.035 Natural Process Time (hr) t0 0.090 0.090 0.095 0.090 0.090 Natural Process SCV c0 2 0.500 0.500 0.500 0.500 0.500 Number of Machines m 1 1 1 1 1 MTTF (hr) mf 200 200 200 200 200 MTTR (hr) mr 2 2 8 4 4 Availability A 0.990 0.990 0.962 0.980 0.980 Effective Process Time (failures only) te' 0.091 0.091 0.099 0.092 0.092 Eff Process SCV (failures only) ce 2 ' 0.936 0.936 6.729 2.209 2.209 Batch Size k 100 100 100 100 100 Setup Time (hr) ts 0.000 0.500 0.500 0.000 0.000 Setup Time SCV cs 2 1.000 1.000 1.000 1.000 1.000 Arrival Rate of Batches ra/k 0.100 0.098 0.093 0.088 0.080 Eff Batch Process Time (failures+setups) te = kt0/A+ts 9.090 9.590 10.380 9.180 9.180 Eff Batch Process Time Var (failures+setups) k*0 2 /A 2 + 2mr(1-A)kt0/A+s 2 0.773 1.023 6.818 1.861 1.861 Eff Process SCV (failures+setups) ce 2 0.009 0.011 0.063 0.022 0.022 Utilization u 0.909 0.940 0.966 0.812 0.731 Departure SCV cd 2 0.181 0.031 0.061 0.035 0.028 Yield y 0.980 0.950 0.950 0.900 0.950 Final Departure Rate ra*y 9.800 9.310 8.845 7.960 7.562 Final Departure SCV ycd 2 +(1-y) 0.198 0.079 0.108 0.132 0.077 Utilization u 0.909 0.940 0.966 0.812 0.731 Throughput TH 9.800 9.310 8.845 7.960 7.562 Queue Time (hr) CTq 45.825 14.421 14.065 1.649 0.716 Cycle Time (hr) CTq+te 54.915 24.011 24.445 10.829 9.896 Cumulative Cycle Time (hr) i(CTq(i)+te(i)) 54.915 78.925 103.371 114.200 124.096 WIP in Queue (jobs) raCTq 458.249 141.321 130.948 14.587 5.700 WIP (jobs) raCT 549.149 235.303 227.586 95.780 78.773 Cumulative WIP (jobs) i(ra(i)CT(i)) 549.149 784.452 1012.038 1107.818 1186.591
- 28. IMSE 811: Advanced Production / Inventory Control • The Challenges of a Modern Factory – Push versus Pull Systems – Understanding variability as it applies to JIT/Lean – Extensions to industry supply-chain management
- 29. IMSE 888: Research Methods in Industrial Engineering The Principal: Design a proper experimental research method as it applies to our discipline. By choosing an area of interest, emphasis is placed on developing a useful idea, evaluating it’s demand, and how to fit our research into current developments. • Developing a Proper Research Method – Identifying an area – Performing a literature review with quantitative analysis – Using literature maps – Developing a problem description – Constructing a proposal
- 30. Master of Science: Industrial Engineering The Principal: Applying the scientific method to design and improve the production of goods and services through identifying problems, analyzing solutions, and implementing efficient and effective production process controls. • How do I benefit from an MS of Industrial Engineering?
- 31. If I could….. • More Operations Research – Graph theory – Logistics Engineering – Integer Programming (?) • Thesis – Nonparametric Control Charting