**IE 500 Mathematics of Operations Research **

Introduction to methods of proof, sets and functions, metric spaces, functions on metric spaces, differential and integral equations, fundamentals of linear algebra. *Credit units: 3.*

**IE 505 Mathemaical Programming**

The course aims to give a comprehensive introduction to mathematical programming techniques for graduate students who are expected to become intelligent users of modern optimization tools and software. Subjects covered include linear and network programming, convexity, Karush-Kuhn-Tucker conditions in nonlinear programming and quadratic programming. The emphasis is on modeling and solution of problems of relevance to engineers rather than on theory. The course involves programming exercises using high level modeling languages GAMS and/or AMPL. *Credit units: 3.*

**IE 507 Discrete Mathematical Models **

This course is designed to illustrate both the applications of discrete mathematics to a broad range of topics in the social, biological and environmental sciences, and the influence of those applications on the development of mathematics. The use of mathematical modelling will be emphasized by encompassing tools such as graphs, weighted digraphs; Markov chains and n-person games. *Credit units: 3.*

**IE 512 Graph Theory**

Undirected and directed graphs and their subgraphs. Traversal of graphs. Trees. Connectivity. Shortest paths. Optimal spanning trees. Eulor tours. Hamilton cycles. Matchings. Independent sets and cliques. Vertex and edge colorings. Planar graphs. Maximum flow and its applications to structure of graphs. Cycle and co-cycle spaces. Data structures for representation of graphs and trees. Perfect graphs. *Credit units: 3.*

**IE 513 Linear Programming**

Theory, algorithms, and computational aspects of linear programming. Formulation of problems as linear programs. Development of simplex algorithm, geometry of simplex method, duality theory, and economic interpretations. Sensitivity analysis. Variants of simplex method. *Credit units: 3.*

**IE 514 Network Flows **

Flow problems on networks. Transportation and assignment problems, special purpose algorithms and advanced computational techniques. Maximum flow problem, theory, algorithms, and applications. Shortest paths. Minimum cost flows. Network simplex method. Multicommodity flow problems. Generalized networks. *Credit units: 3.*

**IE 515 Convex Analysis **

Convex sets in IR and their basic properties, separation of convex sets, properties of convex polyhedra (and polytones). Convex functions continuity and differentiability properties, subdifferentiability, duality of convex sets, Fenchel dual of a convex function, bipolar theorem. Convex programming, dual convex programs, perturbation and lagrangian approaches to duality, the connection between the two approaches, saddle point theorems. Applications of convex analysis: inequalities, interior-point methods, approximation, merit functions. *Credit units: 3.*

**IE 518 Discrete Optimization **

The models and methods of integer programming. Structure of integer programs, pure integer and mixed integer programming problems. Zero-one programming, branch and bound methods. Cutting plane and polyhedral approach. Lagrangean relaxation. Applications to combinatorial optimization, heuristic methods and dynamic programming. Applications in resource allocation, facility location, scheduling, capital budgeting. Computer implementation. *Credit units: 3.*

**IE 519 Approximation Algorithms **

The course covers combinatorial and mathematical programming techniques to derive approximation algorithms for np-hard optimization problems. Possible topics include greedy algorithms for vertex/set cover, approximation schemes via dynamic programming, rounding LP relaxations of integer programs, and semi definite relaxations. The course is complemented by the implementation of selected algorithms using a high-level language such as matlab.*Credit units: 3*

**IE 520 Stochastic Calculus **

Multivariate normal random variables and accompanying linear algebra. The central limit theorem for iid random variables. Brownian motion. Conditional expectations and conditional probabilities. The relationship between Brownian motion and partial differential equations. Hittings probabilities and the reflection principle. Sets of paths, partial information, and conditional expectation as projections. martingales and the martingale property of conditional expectations. Progressively measurable functions. The Ito integral with respect to Brownian motion. Ito’s lemma and Dynkin’s theorem as tools for solving Ito differantial equations and Ito integrals. Partial differential equations for transition probabilities and conditional expectations for general Ito differential equations. Change of measure Feynman Kac, and Girsanov’s theorem. Convergence of random walks and tree models to Ito processes. Applications in finance. Black-Scholes model. *Credit units: 3*

**IE 521 Stochastic Processes
**Stochastic processes with independent increments, Wiener process and Poisson process. Non-homogeneous and compound Poisson processes. Discrete time Markov chains (classification of states, ergodic properties), random walks, branching processes. Continuous-time Markov processes, Kolmogorov’s differential equations. Birth and death processes, applications to Markov queueing models. Non-Markov processes, renewal process, renewal reward process, alternating and regenerative processes, ergodic theorems. Semi-Markov processes. Applications in reliability and inventory models. Selected topics from stationary processes and time-series.

*Credit units: 3.*

**IE 522 Queueing Systems **

Classification of queueing systems. Markov processes in discrete and continuous time. Birth and death processes. Markov queueing systems M/M/k/m. Little’s formula. Bulk arrival and service systems. Non-Markov queueing systems. Semi-Markov processes. System M/G/1/ *oo *(stationary regime, Pollaczek-Kninchin formula, waiting time and busy period). Systems G/M/1/ *oo *and G/G/1/ *oo . *Jackson’s type queueing networks, balance equations, stationary distribution. Approximate methods in queueing models. Application in manufacturing, computer networks, information systems and simulation. *Credit units:3.*

**IE 523 Probabilistic Analysis **

Axiomatic construction of probability theory, properties of probability, conditional probability, independence. Discrete and continuous random variables and vectors (distribution function, expectation, variance, moments). Chebyshev inequality and law of large numbers. Conditional expectation. Transformations of random variables. Generating and characteristics functions. Asymptotic methods in probability theory, types of convergence of random variables. Sums of independence random variables, central limit theorem, Poisson theorem. Selected topics. *Credit units: 3.*

**IE 524 Simulation **

The design and analysis of simulations. The use of simulation for estimation, comparison of policies, and optimization. Variance estimation techniques including the regenerative methods, time series methods, and batch means. Variance reduction. Statistical analysis of output of simulations, applications to modeling stochastic systems in computer science, engineering and operations research. *Credit units: 3.*

**IE 525 Advanced Statistics **

Basic statistical definitions. Notion of statistical estimator, unbiased, consistent, asymptotically normal estimators. Emprical distribution function. Efficient estimators, Cramer-Rao inequality. Sufficient statistics. Confidence intervals. Moment and maximum likelihood methods. Method of least squares. Regression, linear and multiple regression. Testing hypotheses. Goodness of fit tests. Chi-square test, hypothesis of independence. Neyman-Pearson theorem. Selected topics from factor analysis, classification theory and cluster analysis. Elemens of time series analysis and design of experiments. *Credit units: 3.*

**IE 528 Dynamic Programming **

Deterministic and discrete-time stochastic dynamic programming. Markov Decision Process under discounted and average payoff criteria, Adaptive Control Processes, bandit problems, stochastic games, and applications. *Credit units: 3.*

**IE 530 Logistics Modeling and Optimization **

Logistics involve making goods and services available at the right points, at the right times and in the right quantities. It is a wide rangeing human activity that gives rise to a host problems including distrubition, location, transportation, scheduling and routeing. The course gives various mathematical techniques to model and optimize logistical systems. *Credit units: 3*

**IE 534 Stochastic Models in Operations Research **

Review of conditional probability; Markov chains, example models, Markov Chains with rewards; Markov decision processes, solution algorithms; an introduction to renewal theory and applications; queueing models, example applications in service systems; reliability models; other topics. *Credit units: 3*

**IE 535 Stochastic and Risk-Sensitive Optimization **

Models, solution methods, and theory for optimization problems under uncertainty and risk. Introduction to stochastic programming, optimization problems with probabilistic constraints, two-stage and multi-stage stochastic programming problems, Markov decision processes, utility functions, mean-risk optimization models, coherent measures of risk, and concept of stochastic dominance. *Credit units: 3*

**IE 540 Inroduction to Financial Engineering **

Financial markets (bonds, stocks, futures, forwards, options, interest rates and their term structures), models of security prices (Brownian motion, geometric Brownian motions, Ornstein-Uhlenbeck processes, Cox-Ross-Rubinstein binomial model, Merton-Black-Scholes model), pricing and hedging financial derivatives (Ito’s rule, stochastic integration, diffusion processes, probabilistic solutions of PDEs, no-arbitrage pricing in a complete market of futures, forwards, European and American type options, pricing in incomplete markets), Hedging with futures and options, bond hedging, numerical methods (pricing using trees, Monte-Carlo simulations, finite-difference methods), mean-variance analysis of portfolios, value at risk, optimal consumption and portfolio strategies (formulations and solutions of appropriate dynamic programming models and Hamilton-Jacobi-Bellman equations). *Credit units: 3*

**IE 542 Investment Decision Modeling **

The meaning of investment process in general and for creating systems to produce products and services in particular. Classification of investment decision problems with respect to context and the precision of informational support, i.e., certainty, risk and uncertainty. A general mathematical structure for modeling for investment decisions. Deterministic, stochastic, combinatorial, sequential and dynamic investment decision models, and optimization techniques used for their solutions. A mathematical basis for deriving suitable value measures for evaluating investment alternatives and derivation of such measures. Types of risk taking as the fundamental dimension of a class of investment decision making situations. *Credit units: 3*

**IE 543 Multiple Criteria Decision Making **

Discrete and continuous multiple criteria problems. Solution methods for multiple criteria decision making problems. Methods of generating non-dominated solutions. Interactive approaches. Multiple criteria ranking and sorting techniques. Multiple criteria decision making applications. *Credit units: 3*

**IE 546 Introduction to Continuous time Finance **

Application of systems analysis and industrial engineering to the design, planning, and analysis of manufacturing systems. Characteristics of flexible manufacturing systems (FMS). Elements of systems and their interaction with each other. Consideration of technical and economic aspects of equipment and process design. Integration aspects of the elements of manufacturing systems. *Credit units: 3*

**IE 551 Applied Statistics **

Exploratory data analysis, kernel density estimation, multivariate regression, nonparametric and semiparametric regression, scatterplot smoothing, linear mixed models, logistic regression, recursive partitioning, anova, ancova, hidden Markov models, dynamic linear models, graphical models, principal component analysis. Applications on real datasets using statistical software. *Credit units: 3*

**IE 553 Applied Statistical Modeling and Data Analysis**

No catalog information. *Credit units: 3*

**IE 561 Manufacturing Systems **

Application of systems analysis and industrial engineering to the design, planning, and analysis of manufacturing systems. Characteristics of flexible manufacturing systems (FMS). Elements of systems and their interaction with each other. Consideration of technical and economic aspects of equipment and process design. Integration aspects of the elements of manufacturing systems. *Credit units: 3*

**IE 563 Game Theory With Applications in Operations Management **

Introduction to Game Theory: Pre-commitment, the normal form, the extensive form; static games with complete information: pure strategy nash equilibrum, mixed strategy nash equilibrum; dynamic games with complete information: sub-game perfect equilibrum; games with incomplete information: bayesian nash equilibrum, perfect bayesian nash equilibrum; applications: oligopoly, supply chain management, queuing, competitive location. *Credit units: 3*

**IE 564 Inventory Management **

This course focuses on various inventory control problems in service and manufacturing environments. First, deterministic models and their extensions are introduced. Single and multi item problems, quantity discount case, effect of inflation, classification of inventories are discussed. Second part of the course focuses on finite and infinite horizon problems with stochastic demand. Models for periodic and continuous review policies, coordinated replenishment problems, perishable items are examined. Finally, multi echelon inventory problems in supply chain context are introduced. *Credit units: 3*

**IE 566 Supply Chain Management **

Supply chain management deals with the management of materials, information and financial flows in a network logistics consisting of suppliers, manufacturers, distributors, and customers. the topics that are covered in this course include network configuration of the supply chain using contracts and other mechanisms, distribution strategies for the supply chain and product design for supply chain efficiency. *Credit units: 3*

**IE 568 Theory of Pricing and Revenue Management**

An introduction to pricing and revenue management and their applications. Single-resource capacity allocation. Network capacity control. Modeling customer-behavior and market response. Estimation and forecasting for pricing and revenue management. Dynamic pricing. Assortment optimization. *Credit Units: 3*

**IE 571 Analytical Models for Supply Chain**

Theoretical and practical issues in the design and management of the supply chain. Logistic network configuration, risk pooling and multi-echelon inventory systems, value of information and bullwhip effect in supply chains, coordination of the supply chain using contracts, distribution strategies and strategic alliances for the supply chain and product design for supply chain efficiency. *Credit units: 3.*

**IE 572 Production Planning Systems Design **

Theoretical and practical issues in the design of systems for planning and control of production activity. Critical examination of tools and techniques of industrial engineering and operations research applicable to integrated manufacturing management. *Credit units: 3*

**IE 573 Theory of Machine Scheduling **

An overview of of computational complexity, heuristic problem solving, and implicit enumeration. Deterministic machine scheduling problems: single stage, open shop, flow shop, and job shop problems with single and parallel machines. Dynamic scheduling problems and priority dispatching. A survey of other scheduling problems. Applications in manufacturing systems. *Credit units: 3*

**IE 574 Location and Layout Optimization **

Single or multiple facilities location in the plane with minimum or minimax criteria. Discrete or continuous layout optimization. Single facility network location. Applications in public service, production, distribution, warehousing, emergency service, flexible manufacturing. *Credit units: 3*

**IE 576 Network Design **

This course deals with network design problems arising in telecommunications, transportation and supply chains. It gives an overview of optimization models and solution techniques for basic problems. It covers multicommodity flows, common topologies like cliques, paths, trees and rings, fixed charge network design problems, capacity planning and quality issues.* Credit units: 3*

**IE 577 Facility Location on Networks **

Applications, modeling, theory and algorithms for optimal location of service facilities on distribution, transportation, communication networks. The course progresses from simple models to complex models. Well known median and center problems as well as other models will be covered. The course ends with a discussion of areas open to research. *Credit units: 3*

**IE 578 Location Models **

Tools for the analysis of location problems; linear programming and lagrangean relaxation. Elements of location models: facilities, space, distance, objectives, customers. Covering models: formulations, dominances, and solution methods. I-median and I-center problems in the plane and in networks. P-median and multi-weber problems. Other objectives: push, pull and balancing. Location of undesirable facilities. Other location problems: Fixed charge facility location problems, hierarchical location problems, hub location problems, location routing problems. Competitive location problems. The basic scenario, duopoly locations in some simple spaces. Von-stackelberg (leader follower) solutions. Layout problems. *Credit units: 3*

**IE 583 Advanced Operations Research Models in Health Care **

Operations research applications in health-care industry. Utilization of stochastic OR models, Markov decision processes in medical decision making; applications of operations research on health care operations management, clinical decision analysis, and health policy. Optimization applications in influenza vaccination, radiation therapy treatment planning, breast cancer screening, organ transplantation, infectious diseases; capacity planning and management in hospitals, ambulance service planning. *Credit units: 3*

**IE 585 Special Topics in Mathematical Programming **

This course is designed for advanced master’s students and PhD Students with a strong foundation in linear algebra and advanced calculus who wish to pursue research in mathematical programming. Varying topics in linear and nonlinear optimization, discrete optimization, and combinatorial optimization may be offered. *Credit units: 3*

**IE 586 Computational Optimization**

Strong models and valid inequalities. Extended formulations. Cutting plane and column generation algorithms. Decomposition approaches in deterministic and stochastic optimization. Applications in production planning, network design and logistics. *Credit Units: 3*

**IE 590 Research Topics in IE & OR **

The purpose of this series of seminars is to illustrate and discuss research interests of faculty members and research groups within the Department of Industrial Engineering. A faculty member, or guest will present his research interests and discuss the current status and future research areas in that field. *Credit units: None.*

**IE 599 Master’s Thesis **

*Credit units: None.*

**IE 613 Advanced Linear Programming**

Theory of simplex method. Duality. Polyhedral theory. Theorems of alternatives. Parametric analysis. Dantzig-Wolfe decomposition. Generalized and variable upper bounding. LU decomposition and stable implementation of simplex method. Non-simple approaches to LP, ellipsoidal and interior point algorithms. *Credit units: 3*

**IE 614 Nonlinear Programming **

Local and global optima. Newton-type, quasi-Newton, and conjugate gradient methods for unconstrained optimization. Kuhn-Tucker theory and Lagrangean duality. Algorithms for linearly constrained optimization, including steepest ascent and reduced gradient methods with applications to linear and quadratic programming. Non-linearly constrained optimization including penalty and barrier function methods, reduced and projected gradient methods, Lagrangean methods. Computer implementation. *Credit units: 3*

**IE 616 Combinatorial Optimization **

Emphasis will be on Polyhedral Combinatorics. Integral Polyhedra. Polarity, blocking and anti-blocking theory. Total Dual Integrity. Examples of Polyhedra: Matchings, matroid, TSP, Linear Ordering, Vehicle Routing. Polyhedral approach to NP-Hard problems. *Credit units: 3*

**IE 690 Advanced Research Topics in IE&OR **

The purpose of this series of seminars is to illustrate and discuss research intersets of faculty members and research groups within the Department of Industrial Engineering. A faculty member, or guest will present his/her research interests and discuss the current status and future research areas in that field. *Credit units: 3*

**IE 691 Research Practice **

Students starting to direct Ph.D. program are required to fulfill the summer research requirement in the first summer after enrollment. Students individually work on research topic under the supervision of a faculty member. the results of the study are to be compiled as a research report. the report is evulated on the basis of novelty and contribution by a committee of three members composed of the coordinator, the supervisor of the research and a third faculty determined by the coordinator. *Credit units: 3*

**IE 699 Ph.D. Dissertation **

*Credit units: None.*