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.
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?
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
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.
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
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60
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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
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0
-100
-200
-300
-400
Sample
CumulativeSum
0
UCL=25.3
LCL=-25.3
CUMSUM
Shaun D Smith
IMSE 641 ~ Spring 2011
464136312621161161
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40
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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
