Program Description Profitable
design and operation of modern industrial systems requires integration
of human, material, equipment and financial resources. In recent years
this integration has become tighter due to the inclusion of information
technology, and resulted in more complex systems. Industrial
Engineering research focuses on quantitative analysis, synthesis and
management of such complex systems. The affiliated faculty members come
from the Industrial Engineering department of the College of
Engineering, the Operations and Information Systems group of the
College of Administrative Sciences and Economics, and other related
fields. Our research areas are diverse, including Logistics, Supply
Chain Management, Service Operations, Production Systems, Stochastic
Processes, Financial Engineering, Mathematical Programming, Data Mining
and Bioinformatics. The programs are built on the basic methodologies
of operations research and their applications in manufacturing,
distribution and service industries. Graduates of the M.Sc. program
have been placed in respectable Ph.D. programs in North America, Europe
and Turkey as well as various professional positions in industry. We
expect to have the first graduates of the Ph.D. program in 2008.
Research Areas - Bioinformatics
- Data Mining
- Financial Engineering Logistics
- Optimization Theory and Algorithms
- Production Systems and Scheduling
- Service Operations
- Supply Chain Management
Curriculum All
Ph.D. students have to take at least 7 courses out of the courses
listed below to complete at least 21 credits. The students who are
accepted only with a B.S. have to take at least 7 additional courses to
earn at least 21 additional credits. The curriculum of each student will be determined by his/her program advisor. All courses have 3 credits unless specified.
Students
with a B.S. or M.S. degree in Industial Engineering, Business
Administration, Economics and Mathematics or any related area can apply
to the Ph.D. program in IEOM.
The following courses are required for Ph.D. students:
- INDR 551 Advanced Optimization Methods
- INDR 553 Advanced Stochastic Methods
- MATH 531 Real Analysis I **
Depending
on their background, students might be asked to take the required
courses of the "M.S. in Industrial Engineering" program in addition to
the following courses:
- INDR 501 Optimization Models and Algorithms
- INDR 503 Stochastic Models and Their Applications
Moreover,
Ph.D. students can take any of the courses listed under the "M.S. in
Industrial Engineering" program in addition to the following courses:
- INDR 560 Large Scale Optimization
- INDR 564 Dynamic Programming
- INDR 570 Queueing Theory
- INDR 572 Reliability Theory
- INDR 574 Stochastic Models in Financial Engineering
- INDR 576 Inventory Control Theory
MATH 503 Applied Mathematics
- MATH 504 Numerical Methods I
- MATH 506 Numerical Methods II
- MATH 532 Real Analysis II **
- MATH 544 Stochastic Processes and Martingales **
- MATH 545 Mathematics of Finance **
MECH 531 Modern Control Systems
- MECH 534 Computer Based Simulation and Modeling
- MECH 543 Computer Integrated Manufacturing and Automation
ECOE 505 Linear Systems and Estimation Theory
- ECOE 508 Computer Vision and Pattern Recognition
- ECOE 510 Computer Graphics
- ECOE 515 Distributed Computing Systems
- ECOE 516 Computer Networks
- ECOE 519 Introduction to Artificial Intelligence
- ECOE 529 Parallel Computing
- CMSE 501 Introduction to Computational Science
- ECOE 556 Algorithms and Computational Complexity
** These courses are 4 credits.
Students
who have TA assignments must take TEAC 500: Teaching Experience during
the semesters of their assignments. Students must also take ENGL 500:
Graduate Writing course.
Course Descriptions INDR 501 Optimization Models and Algorithms (3 Credits)
Convex
analysis, optimality conditions, linear programming model formulation,
simplex method, duality, dual simplex method, sensitivity analysis;
assignment, transportation, and transshipment problems.
Prerequisite: An undergraduate level Operations Research course or consent of the instructor.
INDR 502 Logistics and Supply Chain Systems (3 Credits)
Introduction
to the concepts and terminology of logistics and supply chain
management. Examination of components of logistics and supply chain
systems such as purchasing, storage, production, inventory, and
transportation systems. Analysis of interactions and trade-offs among
these components using mathematical models and quantitative techniques.
Prerequisite: INDR 501 or consent of the instructor.
INDR 503 Stochastic Models and Their Applications (3 Credits)
The
basic theory of the Poisson process, renewal processes, Markov chains
in discrete and continuous time, as well as Brownian motion and random
walks are developed. Applications of these stochastic processes are
emphasized by examples, which are drawn from inventory and queueing
theory, reliability and replacement theory, finance, population
dynamics and other biological models.
Prerequisite: An undergraduate level statistics course or consent of the instructor.
INDR 504 Advanced Engineering Materials Manufacturing (3 Credits)
Advanced
Engineering Material Manufacturing Processes will be studied for (i)
metals and (ii) plastics and composites. Material removal, addition,
and change of form processes will be studied for metals. In the
plastics and composites part, similarities/differences,
advantages/disadvantages, and proper selection of manufacturing
processes such as Injection Molding, Compression Molding, Extrusion,
Sheet Forming, Tow Placement, Pultrusion, Liquid Molding, Filament
Winding, Pultrusion and Autoclave Processing will be illustrated with
applications from aerospace, automotive, biomedical, sporting goods and
civil infrastructure industries. Issues and their solutions with
in-site sensing and on- and off-line control will be studied with
examples.
Prerequisite: INDR 505 or consent of the instructor.
INDR 505 Manufacturing Systems (3 Credits)
This
course will cover the basic concepts and techniques in hierarchical
design, planning, and control of manufacturing systems. Topics include
flow line and assembly systems, group technology and cellular
manufacturing, just-in-time, flexible manufacturing systems.
INDR 506 Computer Integrated Manufacturing and Automation (3 Credits)
This
course introduces Computer Aided Design and Manufacturing (CAD/CAM)
Systems, Computer Numerical Control (CNC) Machine Tools, Modern Sensors
in Manufacturing, Machining Processes, Rapid Prototyping, and
Fundamentals of Industrial Robotics.
INDR 508 Discrete Event Simulation (3 Credits)
Topics
on distribution fitting and generating random numbers and random
variates will be covered as well as the statistical analysis of
simulation output including some well-known analysis methods and
variance reduction techniques. Recent developments in the area will
also be discussed.
Prerequisite: INDR 503 or consent of the instructor.
INDR 520 Network Models and Optimization (3 Credits)
Network
flow models and optimization problems. Algorithms and applications.
Minimum spanning tree problem. Shortest path problems. Maximum flow
problems, minimum cuts in undirected graphs and cut-trees. The minimum
cost network flow problem. Matching problems. Generalized flows.
Multicommodity flows and solution by Lagrangean relaxation, column
generation and Dantzig-Wolfe decomposition. Network design problems
including the Steiner tree problem and the multicommodity capacitated
network design problem; formulations, branch-and-cut approaches and
approximation algorithms.
Prerequisite: INDR 262 or consent of instructor.
INDR 530 Decision Analysis (3 Credits)
Tools,
techniques, and skills needed to analyze decision-making problems
characterized by uncertainty, risk, and conflicting objectives. Methods
for structuring and modeling decision problems and applications to
problems in a variety of managerial decision-making contexts.
Structuring decision problems: Decision trees, model building, solution
methods and sensitivity analysis; Bayes' rule, the value of information
and using decision analysis software. Uncertainty and its measurement:
Probability assessment. Utility Theory: Risk attitudes, single- and
multi-attribute utility theory, and risk management. Decision making
with multiple objectives.
Prerequisite: ENG 200 or consent of instructor.
INDR 551 Advanced Optimization Methods (3 Credits)
Combinatorial
optimization, structure of integer programs, pure integer and mixed
integer programming problems, branch and bound methods, cutting plane
and polyhedral approach, convexity, local and global optima,
Newton-type, and conjugate gradient methods for unconstrained
optimization, Karush-Kuhn-Tucker conditions for optimality, algorithms
for constrained nonlinear programming problems, applications in
combinatorial and nonlinear optimization.
Prerequisite: INDR 501 or consent of the instructor.
INDR 553 Advanced Stochastic Processes (3 Credits)
Brief
review of basic processes like Poisson, Markov and renewal processes;
Markov renewal processes and theory, regenerative and semi-regenerative
processes; random walk, Wiener process and Brownian motion;
martingales; stochastic differential equations and integrals;
applications in queueing, inventory, reliability and financial systems.
Prerequisite: INDR 503 or consent of the instructor.
INDR 560 Large Scale Optimization (3 Credits)
Methods
for the solution of complex real world problems modeled as large-scale
linear, nonlinear and stochastic programming, network optimization and
discrete optimization problems. Solution methods include Decomposition
Methods: Benders's, Dantzig-Wolfe, Lagrangian Methods; Meta-heuristics:
Local search, simulated annealing, tabu search, genetic algorithms;
Constraint Programming. Applications in transportation and logistics
planning, pattern classification and image processing, data mining,
design of structures, scheduling in large systems, supply-chain
management, financial engineering, and telecommunications systems
planning.
Prerequisite: INDR 501 or consent of the instructor.
INDR 564 Dynamic Programming (3 Credits)
Theory
and practice of dynamic programming, sequential decision making over
time; the optimal value function and Bellman's functional equation for
finite and infinite horizon problems; Introduction of solution
techniques: policy iteration, value iteration, and linear programming;
General stochastic formulations, Markov decision processes; application
of dynamic programming to network flow, resource allocation, inventory
control, equipment replacement, scheduling and queueing control.
Prerequisite: INDR 501, INDR 503 or consent of the instructor.
INDR 566 Scheduling (3 Credits)
Introduction
to scheduling: examples of scheduling problems, role of scheduling,
terminology, concepts, classifications; solution methods: enumerative
methods, heuristic and approximation algorithms; single machine
completion time, lateness and tardiness models; single machine sequence
dependent setup models; parallel machine models; flow-shop models;
flexible flow-shop models; job-shop models; shifting bottleneck
heuristic; open-shop models; models in computer systems; survey of
other scheduling problems; advanced concepts.
Prerequisite: Consent of the instructor.
INDR 568 Heuristic Methods (3 Credits)
Constructive
heuristics; improving heuristics; metaheuristics: simulated annealing,
genetic algorithms, tabu search, scatter search, path relinking, ant
colony optimization, variable neighborhood search, and their hybrids;
heuristic methods based on relaxation and decomposition; applications:
routing, scheduling, cutting and packing, inventory and production
management, location, assignment of resources, bioinformatics, and
telecommunications.
Prerequisite: INDR 501 or consent of the instructor.
INDR 570 Queueing Theory (3 Credits)
Markovian
queues: M/M/1, M/M/C, M/M/C/K systems and applications. Phase-type
distributions and matrix-geometric methods: PH/PH/1 systems. Queueing
networks: reversibility and product-form solutions. General arrival or
service time distributions: embedded Markov Chains, M/G/1 and G/M/c
queues, G/G/1 queues and the Lindley recursion, approximations.
Stochastic comparisons of queues: stochastic orders, sample path
properties.
Prerequisite: INDR 503 consent of the instructor.
INDR 572 Reliability Theory (3 Credits)
Basic
concepts and definitions of system reliability. Series, parallel,
k-out-of n systems. Structure functions, coherent systems, min-path and
min-cut representations. System reliability assessment and computing
reliability bounds. Parametric families of distributions, classes of
life distributions and their properties. Shock and wear models.
Maintenance, replacement and repair models. Current issues on
stochastic modelling of hardware and software reliability.
Prerequisite: INDR 503 or consent of the instructor.
INDR 574 Stochastic Models in Financial Engineering (3 Credits)
Review
of basic stochastic concepts; binomial market models and pricing of
derivative securities; Wiener process and Brownian motion; martingales;
stochastic integrals and differential equations; Itô's calculus;
pricing of derivative securities in continuous markets; Black-Scholes
model; foreign exchange, bond and interest rate markets.
Prerequisite: INDR 503 or equivalent; or consent of the instructor.
INDR 576 Inventory Control Theory (3 Credits)
Development
and application of mathematical models for inventory management. Basic
economic-order-quantity with extensions; time-varying demand and
purchase costs. Multiechelon inventory systems with multiple products
and/or multiple locations. Analysis of stochastic demand for single and
multiple products. Analysis of stochastic lead times. Policy
optimization under time-varying, stochastic demand.
Prerequisite: INDR 503 or consent of the instructor.
INDR 578 Advanced Models in Supply Chain Management (3 Credits)
Dynamic
inventory policies for single-stage inventory systems: concepts of
optimality and optimal policies. Multi-Echelon Systems: uncapacitated
models and optimal policies, capacitated models: different control
mechanisms. Multiple locations and multiple items: inventory and
capacity allocation. Decentralized control and the effects of
competition on the supply chain: coordination and contracting issues.
Prerequisite: INDR 503, INDR 505 or consent of the instructor.
MATH 503 Applied Mathematics (3 Credits)
Linear
algebra: generalized vector space, eigenvalue problem, diagonalization,
quadratic forms. Field theory: divergence theorem, Stokes' theorem,
irrotational fields. Sturm-Liouville theory, Bessel functions, Legendre
polynomials. Partial differential equations: diffusion and Laplace
equations by separation of variables and Sturm-Liouville theory, wave
equation. Weighted residuals method. Integral transform and Green's
function solution of partial differential equations, complex variables,
variational calculus and introduction to perturbation methods.
Engineering applications.
MATH 504 Numerical Methods I (3 Credits)
A
graduate level introduction to matrix-based computing. Stable and
efficient algorithms for linear equations, least squares and eigenvalue
problems. Both direct and iterative methods are considered and MATLAB
is used as a computing environment.
MATH 506 Numerical Methods II (3 Credits)
Development
and analysis of numerical methods for ODEs, an introduction to
numerical optimization methods, and an introduction to random numbers
and Monte Carlo simulations. The course starts with a short survey of
numerical methods for ODEs. The related topics include stability,
consistency, convergence and the issue of stiffness. Then it moves to
computational techniques for optimization problems arising in science
and engineering. Finally, it discusses random numbers and Monte Carlo
simulations. The course combines the theory and applications (such as
programming in MATLAB) with the emphasis on algorithms and their
mathematical analysis.
MATH 531 Real Analysis I (4 Credits)
Lebesgue
measure and Lebesgue integration on Rn, general measure and
integration, decomposition of measures, Radon-Nikodym theorem,
extension of measures, Fubini's theorem.
MATH 532 Real Analysis II (4 Credits)
Normed
and Banach spaces, Lp-spaces and duals, Hahn-Banach theorem, Baire
category and uniform boundedness theorems, strong, weak and
weak*-convergence, open mapping theorem, closed graph theorem.
Prerequisite: MATH 531 or consent of the instructor.
MATH 544 Stochastic Processes and Martingales (4 Credits)
Stochastic
processes, stopping times, Doob-Meyer decomposition, Doob's martingale
convergence theorem, characterization of square integrable martingales,
Radon-Nikodym theorem, Brownian motion, reflection principle, law of
iterated logarithms.
Prerequisite: MATH 541
MATH 545 Mathematics of Finance (4 Credits)
From
random walk to Brownian motion, quadratic variation and volatility,
stochastic integrals, martingale property, Ito formula, geometric
Brownian motion, solution of Black-Scholes equation, stochastic
differentialequations, Feynman-Kac theorem, Cox-Ingersoll-Ross and
Vasicek term structure models, Girsanov's theorem and risk neutral
measures, Heath-Jarrow-Morton term structure model, exchange-rate
instruments.
MECH 531 Modern Control Systems (3 Credits)
This
course is an introduction to modern control theory. The course will
cover mathematical modeling of engineering systems, feedback control,
stability and performance analysis, frequency and time response
methods. A software package, MATLAB, will be used for control system
analysis and design.
MECH 534 Computer Based Simulation and Modeling (3 Credits)
The
course will explore geometric, physics-based, and probabilistic
modeling methodology and associated computational methods for tackling
theoretical and practical problems in engineering and science.
MECH 543 Computer Integrated Manufacturing and Automation (3 Credits)
Product
realization systems from Computer Aided Design (CAD) to Computer Aided
Manufacturing (CAM). Manufacturing Automation. Modern sensors in
manufacturing. Computer control of manufacturing systems. Computer
Numerical Control (CNC) machine tools. Machining processes. Rapid
prototyping. Fundamentals of industrial robotics.
ECOE 505 Linear Systems and Estimation Theory (3 Credits)
Linear
functions and linear dynamical systems, Multiple Input Multiple Output
(MIMO) Systems, State Space Descriptions, Quadratic Forms, Maximum
Likelihood and Maximum Aposteriori Estimation, SVD and Its
Applications, Deterministic and Stochastic Least Squares, Wiener and
Kalman Filtering, Spectral Factorization.
Prerequisite: Linear Algebra, elementary course on signals and systems.
Corequisite: ECOE 501 or consent of the instructor.
ECOE 508 Computer Vision and Pattern Recognition (3 Credits)
Study
of computational models of visual perception and their implementation
in computer systems. Topics include: image formation; edge, corner and
boundary extraction, segmentation, matching, pattern recognition and
classification techniques; 3-D Vision: projection geometry, camera
calibration, shape from stereo/silhouette/shading, model-based 3D
object recognition; color texture, radiometry and BDRF; motion analysis.
Prerequisite: Consent of the instructor.
ECOE 510 Computer Graphics (3 Credits)
Theory
and practice of 3D computer graphics. Topics covered include 3D display
techniques, representations and transformations; illumination and color
models; 3D passive and active reconstruction techniques; animation and
rendering; scientific visualization; surface simplification;
multiresolution and progressive object modeling; mesh compression and
subdivision surfaces, Web3D/VRML.
Prerequisite: Consent of the instructor.
ECOE 515 Distributed Computing Systems (3 Credits)
Introduction
to distributed computing, overview of operating systems, process
synchronization and deadlocks, threads and thread synchronization,
communication protocols, synchronization in distributed systems,
management of time, causality, logical clocks, consistent global
states, distributed mutual exclusion, distributed deadlock detection,
election algorithms, agreement protocols, consensus, multicast
communication, distributed transactions, replication, shared memory
model, scheduling, distributed file systems, fault tolerance in
distributed systems, distributed real-time systems.
Prerequisite: Consent of the instructor.
ECOE 519 Introduction to Artificial Intelligence (3 Credits)A
graduate-level introduction to artificial intelligence with the goals
of understanding human intelligence from a computational point of view
and building applied systems that can reason, learn, and adapt. Review
of seminal work on language, vision, robotics, game playing with an
emphasis on machine learning techniques.
Prerequisite: Consent of the instructor.
ECOE 529 Parallel Computing (3 Credits)
Overview
of parallel architectures: interconnection networks, memory hierarchy.
Parallel programming models and languages: shared address space,
message passing, data driven, and data parallel models. Performance
modeling and scalability analysis,sources of parallel overhead. Design
of parallel algorithms and programs: partitioning, fundamental
communication operations, mapping, load balancing. Study of parallel
matrix, graph, and search algorithms.
Prerequisite: COMP 202 or consent of instructor.
CMSE 531 Introduction to Computational Science (3 Credits)
An
introduction to methods and software tools used in scientific
computing. Software development, data abstraction and the concept of
object oriented programming. Hands-on exploration of some of the
principal modern software tools of computational science including
computing environments, symbolic computing, numerical libraries and
software repositories. An introduction to high performance computing
and parallel programming.
ECOE 554 Machine Learning (3 Credits)
An
introduction to the fields of machine learning and data mining from a
statistical perspective. Machine learning is the study of computer
algorithms that improve automatically through experience. Vast amounts
of data generated in many fields from biology to finance to linguistics
make a good understanding of the tools and techniques of machine
learning indispensable. Topics covered include regression,
classification, kernel methods, model assessment and selection,
boosting, neural networks, support vector machines, nearest neighbors,
and supervised learning.
Prerequisite: Consent of instructor.
ECOE 556 Algorithms and Computational Complexity (3 Credits)
Advanced
topics in data structures, algorithms, and their computational
complexity. Asymptotic complexity measures. Graph representations,
topological order and algorithms. Forests and trees. Minimum spanning
trees. Bipartite matching. Union-find data structure. Heaps. Hashing.
Amortized complexity analysis. Randomized algorithms. Introduction to
NP-completeness and approximation algorithms. The shortest path
methods. Network flow problems.
Prerequisite: COMP 202 or consent of instructor.
INDR/ OPSM 590 Seminar
A
series of lectures given by faculty or outside speakers. Participating
students must also make presentations during the semester.
INDR 695 Ph.D. Thesis
Independent research towards Ph.D. degree.
TEAC 500 Teaching Experience
Provides
hands-on teaching experience to graduate students in undergraduate
courses. Reinforces students' understanding of basic concepts and
allows them to communicate and apply their knowledge of the subject
matter.
ENGL 500 Graduate Writing
This is a
writing course specifically designed to improve academic writing skills
as well as critical reading and thinking. The course objectives will be
met through extensive reading, writing and discussion both in and out
of class. Student performance will be assessed and graded by
Satisfactory/Unsatisfactory.