2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University
2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University
2008-2009 Bulletin â 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>