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2008-2009 Bulletin – PDF - SEAS Bulletin - Columbia University

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164<br />

Lect: 2. 3 pts. Professor Iyengar.<br />

Prerequisites: Linear algebra (APMA E3101 or<br />

the equivalent) and optimization (IEOR E6613 or<br />

the equivalent). Robust convex optimization problems,<br />

reformulating robust problems as nominal<br />

problems, computational techniques. Adjustably<br />

robust optimization. Chance constrained problems<br />

and robust chance constrained problems.<br />

Applications from portfolio optimization, truss<br />

design, inventory theory, revenue management,<br />

dynamic programming, etc.<br />

IEOR E6613x Optimization, I<br />

Lect: 3. 4.5 pts. Professor Goldfarb.<br />

Prerequisite: linear algebra. Theory and geometry<br />

of linear programming. The simplex method.<br />

Duality theory, sensitivity analysis, column generation<br />

and decomposition. Interior point methods.<br />

Introduction to nonlinear optimization: convexity,<br />

optimality conditions, steepest descent and<br />

Newton's method, active set and barrier methods.<br />

IEOR E6614y Optimization, II<br />

Lect: 3. 4.5 pts. Professor Stein.<br />

Prerequisite: linear algebra. An introduction to<br />

combinatorial optimization, network flows and<br />

discrete algorithms. Shortest path problems, maximum<br />

flow problems. Matching problems, bipartite<br />

and cardinality nonbipartite. Introduction to<br />

discrete algorithms and complexity theory:<br />

NP-completeness and approximation algorithms.<br />

IEOR E6702x Reliability theory<br />

Lect: 2. 3 pts. Not given in <strong>2008</strong>–<strong>2009</strong>.<br />

Prerequisites: IEOR E4701 or E4106, and SIEO<br />

W4150. An overview of the techniques available<br />

to formulate the reliability structure of a problem,<br />

to model the various element probabilities, to estimate<br />

parameters of element probability distributions<br />

based on data, and to unite these steps to<br />

obtain the reliability function of a system.<br />

IEOR E6703x Advanced financial engineering<br />

Lect: 2. 3 pts. Professor Kou.<br />

Prerequisites: IEOR E4106 or E4701, and SIEO<br />

W4150. Review of basic mathematics, including<br />

renewal theory and stochastic calculus.<br />

Martingale approach to Black-Scholes formula.<br />

Optimal stopping and American options. Pricing<br />

of continuous and discerete exotic options. Term<br />

structure models and pricing of bond options.<br />

Jump diffusion models. Applications, including<br />

pricing of real and electricity options and hedging<br />

of real options.<br />

IEOR E6704y Queueing theory and applications<br />

Lect: 2. 3 pts. Professor Sigman.<br />

Prerequisite: IEOR E4106 or E4701. Introduction<br />

to congestion and related stochastic models.<br />

Topics include birth and death models, measures<br />

of performance, Little’s Law, conservation law,<br />

PASTA, work in system, service disciplines and<br />

priorities, regenerative processes, stability and<br />

stationary distributions, approximations and<br />

bounds. Examples from telecommunications,<br />

production, inventory, and computer science.<br />

IEOR E6706y Queueing networks<br />

Lect: 2. 3 pts. Professor Yao.<br />

Prerequisite: IEOR E4106 or E4701. An<br />

introduction to the analysis of queuing networks.<br />

Applications to computer and communication systems.<br />

The course covers reversibility, local balance,<br />

open and closed network models, computational<br />

procedures, and other related topics.<br />

IEOR E6707y Advanced topics in queueing<br />

theory<br />

Lect: 2. 3 pts. Professor Whitt.<br />

Prerequisite: IEOR E6704 or the instructor’s permission.<br />

Queueing models with general arrival<br />

and service processes, Loyne’s construction,<br />

Harris recurrence, coupling, stability, steady-state<br />

moments and tail asymptotics, heavy-traffic and<br />

light-traffic approximations. Recent literature and<br />

open problems are discussed.<br />

IEOR E6708x Discrete event stochastic systems<br />

Lect: 2. 3 pts. Not given in <strong>2008</strong>–<strong>2009</strong>.<br />

Prerequisites: IEOR E4004, E4404, and E4106.<br />

Modeling, analysis, control, and optimization of<br />

discrete event stochastic systems. Generalized<br />

semi-Markov process models; sample path analysis;<br />

stochastic optimization optimal control.<br />

Applications to manufacturing and communication<br />

problems.<br />

IEOR E6710y Markovian decision processes<br />

Lect: 2. 3 pts. Instructor to be announced.<br />

Prerequisite: IEOR E4106 or E4701. Dynamic<br />

systems observed periodically and partially controlled<br />

by decisions made at each time of observation.<br />

Methods of determining optimal decision<br />

policies. Applications to inventory, inspection,<br />

maintenance, and replacement theories.<br />

IEOR E6711x Stochastic models, I<br />

Lect: 3. 4.5 pts. Professor Whitt.<br />

Prerequisite: SIEO W4105 or the equivalent.<br />

Advanced treatment of stochastic modeling in the<br />

context of queueing, reliability, manufacturing,<br />

insurance risk, financial engineering and other<br />

engineering applications. Review of elements of<br />

probability theory; exponential distribution; renewal<br />

theory; Wald’s equation; Poisson processes.<br />

Introduction to both discrete and continuous-time<br />

Markov chains; introduction to Brownian motion.<br />

IEOR E6712y Stochastic models, II<br />

Lect: 3. 4.5 pts. Professor Yao.<br />

Prerequisite: IEOR E6711 or the equivalent.<br />

Continuation of IEOR E6711, covering further<br />

topics in stochastic modeling in the context of<br />

queueing, reliability, manufacturing, insurance<br />

risk, financial engineering, and other engineering<br />

applications. Topics from among generalized<br />

semi-Markov processes; processes with a<br />

nondiscrete state space; point processes;<br />

stochastic comparisons; martingales; introduction<br />

to stochastic calculus.<br />

IEOR E6801x Monte Carlo methods<br />

Lect: 2. 3 pts. Professor Blanchet.<br />

Prerequisites: IEOR E4106 or E4701, and SIEO<br />

4150, plus a working knowledge of programming.<br />

No prior knowledge of simulation is required.<br />

Random variate generation, discrete event simulation,<br />

Monte Carlo simulation, simulation output<br />

analysis, variance reduction, improving simulation<br />

efficiency, simulation-based derivative-estimation/<br />

sensitivity-analysis, and quasi–Monte Carlo techniques.<br />

Application of these techniques to financial<br />

engineering and performance analysis/ optimization<br />

of computer networking, telecommunications,<br />

and production systems.<br />

IEOR E8100 Advanced topics in IEOR<br />

Lect: 1–3. 1 to 3 pts. Instructor to be announced.<br />

Prerequisite: faculty adviser’s permission.<br />

Selected topics of current research interest.<br />

May be taken more than once for credit.<br />

IEOR E9101x and y, and s Research<br />

1 to 6 pts. The faculty.<br />

Before registering, the student must submit an<br />

outline of the proposed work for approval by the<br />

supervisor and the chair of the Department.<br />

Advanced study in a specialized field under the<br />

supervision of a member of the department staff.<br />

This course may be repeated for credit.<br />

IEOR E9800x and y, and s Doctoral research<br />

instruction<br />

3, 6, 9, or 12 pts. The faculty.<br />

A candidate for the Eng.Sc.D. degree in industrial<br />

engineering or operations research must register<br />

for 12 points of doctoral research instruction.<br />

Registration in IEOR E9800 may not be used to<br />

satisfy the minimum residence requirement for<br />

the Ph.D. degree.<br />

IEOR E9901x and y Operations research<br />

seminar<br />

Sem: 2. 1 to 3 pts. The faculty.<br />

Open to doctoral candidates, and qualified M.S.<br />

candidates with the instructor’s permission. This<br />

course may be repeated for credit. Selected topics<br />

of interest. Topics may vary from year to year.<br />

IEOR E9940x or y Industrial engineering<br />

seminar<br />

Sem: 2. 1 to 3 pts. The faculty.<br />

Open to doctoral candidates and qualified M.S.<br />

candidates with the instructor’s permission. The<br />

course may be repeated for credit. Selected topics<br />

of interest. Topics may vary from year to year.<br />

<strong>SEAS</strong> <strong>2008</strong>–<strong>2009</strong>

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