Ph.D. in Industrial Engineering & Operations 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
 Depending on their background, students might be asked to take
the required courses of the "M.S. in Industrial Engineering"
program:
 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 566 Scheduling
 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
 INDR 531 Real Analysis I **
 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 531 Introduction to Computational Science
 ECOE 556 Algorithms and Computational Complexity
 * These courses are 1.5 credits.
 ** These courses are 4 credits.
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.
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 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 tradeoffs among these components using mathematical models and quantitative techniques.
 Prerequisite: INDR 501 or consent of the instructor.
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 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.
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 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 insite sensing and on and offline control will be studied with examples.
 Prerequisite: INDR 505 or consent of the instructor.
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 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, justintime, flexible manufacturing systems.
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 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.
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 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 wellknown analysis methods and variance reduction techniques. Recent developments in the area will also be discussed.
 Prerequisite: INDR 503 or consent of the instructor.
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 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 cuttrees. The minimum cost network flow problem. Matching problems. Generalized flows. Multicommodity flows and solution by Lagrangean relaxation, column generation and DantzigWolfe decomposition. Network design problems including the Steiner tree problem and the multicommodity capacitated network design problem; formulations, branchandcut approaches and approximation algorithms.
 Prerequisite: INDR 262 or consent of the instructor.
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 INDR 530 Decision Analysis (3 Credits)
 Tools, techniques, and skills needed to analyze decisionmaking problems characterized by uncertainty, risk, and conflicting objectives. Methods for structuring and modeling decision problems and applications to problems in a variety of managerial decisionmaking 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 multiattribute utility theory, and risk management. Decision making with multiple objectives.
 Prerequisite: ENG 200 or consent of instructor.
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 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; flowshop models; flexible flowshop models; jobshop models; shifting bottleneck heuristic; openshop models; models in computer systems; survey of other scheduling problems; advanced concepts.
 Prerequisite: Consent of instructor.
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 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, Newtontype, and conjugate gradient methods for unconstrained optimization, KarushKuhnTucker conditions for optimality, algorithms for constrained nonlinear programming problems, applications in combinatorial and nonlinear optimization.
 Prerequisite: INDR 501 or consent of the instructor.
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 INDR 552 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.
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 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 semiregenerative 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.
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 INDR 560 Large Scale Optimization (3 Credits)
 Methods for the solution of complex real world problems modeled as largescale linear, nonlinear and stochastic programming, network optimization and discrete optimization problems. Solution methods include Decomposition Methods: Benders's, DantzigWolfe, Lagrangian Methods; Metaheuristics: 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, supplychain management, financial engineering, and telecommunications systems planning.
 Prerequisite: INDR 501 or consent of the instructor.
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 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.
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 INDR 570 Queueing Theory (3 Credits)
 Markovian queues: M/M/1, M/M/C, M/M/C/K systems and applications. Phasetype distributions and matrixgeometric methods: PH/PH/1 systems. Queueing networks: reversibility and productform 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 or consent of the instructor.
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 INDR 572 Reliability Theory (3 Credits)
 Basic concepts and definitions of system reliability. Series, parallel, koutof n systems. Structure functions, coherent systems, minpath and mincut 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.
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 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; BlackScholes model; foreign exchange, bond and interest rate markets.
 Prerequisite: INDR 503 or consent of the instructor.
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 INDR 576 Inventory Control Theory (3 Credits)
 Development and application of mathematical models for inventory management. Basic economicorderquantity with extensions; timevarying 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 timevarying, stochastic demand.
 Prerequisite: INDR 503 or consent of the instructor.
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 INDR 578 Advanced Models in Supply Chain Management (3 Credits)
 Dynamic inventory policies for singlestage inventory systems: concepts of optimality and optimal policies. MultiEchelon 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.
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 INDR/OPSM 590 Seminar (3 Credits)
 A series of lectures given by faculty or outside speakers. Participating students must also make presentations during the semester.
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 INDR 591 Project (3 Credits)
 Independent research towards M.S. degree without thesis option.
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 INDR 595 M.S. Thesis (3 Credits)
 Independent research towards M.S. degree with thesis option.
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 INDR 596 Ph.D. Thesis (3 Credits)
 Independent research towards Ph.D. degree.
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 MATH 503 Applied Mathematics (3 Credits)
 Linear algebra: generalized vector space, eigenvalue problem, diagonalization, quadratic forms. Field theory: divergence theorem, Stokes' theorem, irrotational fields. SturmLiouville theory, Bessel functions, Legendre polynomials. Partial differential equations: diffusion and Laplace equations by separation of variables and SturmLiouville 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.
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 MATH 504 Numerical Methods I (3 Credits)
 A graduate level introduction to matrixbased 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.
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 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.
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 MATH 531 Real Analysis I (4 Credits)
 Lebesgue measure and Lebesgue integration on Rn, general measure and integration, decomposition of measures, RadonNikodym theorem, extension of measures, Fubini's theorem.
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 MATH 532 Real Analysis II (4 Credits)
 Normed and Banach spaces, Lpspaces and duals, HahnBanach 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.
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 MATH 544 Stochastic Processes and Martingales (4 Credits)
 Stochastic processes, stopping times, DoobMeyer decomposition, Doob's martingale convergence theorem, characterization of square integrable martingales, RadonNikodym theorem, Brownian motion, reflection principle, law of iterated logarithms.
 Prerequisite: MATH 541
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 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 BlackScholes equation, stochastic differentialequations, FeynmanKac theorem, CoxIngersollRoss and Vasicek term structure models, Girsanov's theorem and risk neutral measures, HeathJarrowMorton term structure model, exchangerate instruments.
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 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.
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 MECH 534 Computer Based Simulation and Modeling (3 Credits)
 The course will explore geometric, physicsbased, and probabilistic modeling methodology and associated computational methods for tackling theoretical and practical problems in engineering and science.
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 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.
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 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.
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 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; 3D Vision: projection geometry, camera calibration, shape from stereo/silhouette/shading, modelbased 3D object recognition; color texture, radiometry and BDRF; motion analysis.
 Prerequisite: Consent of the instructor.
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 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.
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 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 realtime systems.
 Prerequisite: Consent of the instructor.
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 ECOE 519 Introduction to Artificial Intelligence (3 Credits)
 A graduatelevel 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.
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 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.
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 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. Handson 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.
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 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.
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 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. Unionfind data structure. Heaps. Hashing. Amortized complexity analysis. Randomized algorithms. Introduction to NPcompleteness and approximation algorithms. The shortest path methods. Network flow problems.
 Prerequisite: COMP 202 or consent of instructor.
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