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

SIEO W4801x Introduction to property-liability
insurance models
Lect: 3. 3 pts. Not given in 2008–2009.
Prerequisites: IEOR E4007 and IEOR E4701,
or the instructor’s permission. Positive-valued
distributions used in property-liability insurance.
Empirical approximations. Estimation by moment
and percentile matching, minimum chi-square,
and maximum likelihood. Interval estimates of
parameters. Adjusting estimates for data restrictions.
Integer-valued distributions: building
families of and effects of parameters.
SIEO W4802y Introduction to life insurance
and aggregate loss models
Lect: 3. 3 pts. Not given in 2008–2009.
Prerequisites: IEOR E4007 and E4701, or E4106,
or the instructor’s permission. Introduction to actuarial
modeling and actuarial and statistical methods
useful in modeling life insurance risk and
aggregation of insurance risk to the portfolio level.
Survival models used in life insurance. Discrete
and continuous models. Life insurance and annuity
applications. Compound risk models, moments,
computation, and approximation. Continuous
processes of insurance events and probability
of eventual default.
IEOR E4900x, y, and s Master’s research or
project
1 to 3 pts. The faculty.
Prerequisite: approval by a faculty member who
agrees to supervise the work. Independent work
involving experiments, computer programming,
analytical investigation, or engineering design.
IEOR E4998x and y Managing technological
innovation and entrepreneurship
Lect: 3. 3 pts. Professor McGourty.
This course will focus on the management and
consequences of technology-based innovation.
The course explores how new industries are created,
how existing industries can be transformed
by new technologies, the linkages between technological
development and the creation of wealth
and the management challenges of pursuing
strategic innovation.
IEOR E4999x, y, and s Curricular practical
training
1 to 2 pts. Professor Derman.
Prerequisite: instructor’s written approval. Only for
IEOR graduate students who need relevant work
experience as part of their program of study. Final
reports required. This course may not be taken
for pass/fail credit or audited.
IEOR E6400y Scheduling: deterministic models
Lect: 2. 3 pts. Professor Stein.
Prerequisite: IEOR E4004. Classification of
deterministic scheduling models. Single machine,
parallel machines, flow shops, and job shops.
Makespan, flow time, sum of weighted tardinesses.
Applications of dynamic programming and
branch and bound.
IEOR E6403y Routing
Lect: 2. 2 or 3 pts. The faculty.
Prerequisite: IEOR E4004, SIEO W4150, or the
instructor’s permission. Vehicle routing in distribution
systems. Routing problems in VLSI. Effects
of randomness. Students registering for 3 points
are required to do a term project.
MSIE W6408y Inventory theory
Lect: 2. 3 pts. The faculty.
Prerequisite: SIEO W4150 and dynamic programming.
Construction and analysis of mathematical
models used in the design and analysis of inventory
systems. Deterministic and stochastic
demands and lead times. Optimality of (s, S)
policies. Multiproduct and multi-echelon systems.
Computational methods.
SIEO W6501x Stochastic processes and
applications, I
Lect: 2.5. 3 pts. The faculty.
Prerequisite: SIEO W4105 or the equivalent.
Advanced treatment of discrete and continuous-time
Markov chains; elements of renewal theory; martingales;
Brownian motion, stochastic integrals, Ito’s rule.
SIEO W6502y Stochastic processes and
applications, II
Lect: 2.5. 3 pts. Not given in 2007–2008.
Prerequisites: STAT G6104 and SIEO W6501.
Recommended corequisite: STAT G6105. With
the instructor’s permission, the second term may
be taken without the first. Introduction to martingales
in continuous time. Brownian motion:
construction, basic properties, sample paths.
Stochastic integration, Ito’s rule, applications.
Introduction to stochastic differential equations
and diffusion processes. Applications to financial
economics: option pricing, consumption/ investment
problems.
IEOR E6601y Advanced topics in linear
programming
Lect: 2. 3 pts. The faculty.
Prerequisite: IEOR E6613 or the equivalent.
Numerical linear algebra for simplex and interior
point methods: product-form LU, Cholesky and symmetric
indefinite factorizations, sparsity considerations.
Steepest-edge pivot rules, column generation,
and decomposition approaches. Analysis of interior
point methods including path-following, potential
reduction, and predictor- corrector methods.
IEOR E6602y Nonlinear programming
Lect: 2. 3 pts. Professor Goldfarb.
Prerequisite: IEOR E6613 or the equivalent.
Convex sets and functions, convex duality and
optimality conditions. Computational methods:
steepest descent, Newton and quasi-Newton
methods for unconstrained problems, active set,
penalty set, interior point, augmented Lagrangian
and sequential quadratic programming methods
for constrained problems. Introduction to nondifferentiable
optimization and bundle methods.
IEOR E6603x Combinatorial optimization
Lect: 2.5. 3 pts. Not given in 2007–2008.
Prerequisites: IEOR E6613 and E6614. Algorithms
for matching problems. Introduction to matroids;
polyhedral combinatorics. Complexity theory and NP
completeness. Perfect graphs and the ellipsoid method.
IEOR E6606y Advanced topics in network flows
Lect: 3. 3 pts. The faculty.
Prerequisite: Knowledge of elementary graph
algorithms and computational complexity, equivalent
to IEOR E6605, or COMS W4203 and W4231.
Analysis of algorithms and their complexity for a
variety of network routing problems. Topics: overall
minimum cuts, minimum cost network flows, flows
with losses and gains, parametric flows, dynamic
flows, multicommodity flows and applications.
IEOR E6608x Integer programming
Lect: 2. 3 pts. The faculty.
Prerequisite: IEOR E6613 or the equivalent.
Theoretical and algorithmical aspects of integer
programming (IP). Theoretical topics: structure
of the set of feasible solutions of an IP problem,
integral polyhedra, totally unimodular matrices,
totally dual integral systems, Lovasz’s lattice
reduction method, and Lenstra’s IP algorithm.
Algorithmical topics to center on branch and
bound algorithms and the ‘‘facet’’ approach to
cutting-plane algorithms.
IEOR E6609y Dynamic programming
Lect: 3. 3 pts. Instructor to be announced.
Prerequisite: IEOR E4701 or E4106 or the equivalent.
General discrete time deterministic, dynamic
programming, discrete time-parameter finite branching,
Markov decision chains, team decisions, certainty
equivalence, continuous time-parameter
Markov branching decision processes. Applications
include capital budgeting, portfolio selection, inventory
control, systems reliability, and maximization
of expected utility with constant risk posture.
IEOR E6610x Approximation algorithms
Lect: 2. 3 pts. Not given in 2007–2008.
Prerequisites: Basic knowledge of linear programming
and analysis of algorithms or combinatorial
optimization. The design and analysis of efficient
algorithms for providing near-optimal solutions to
NP-hard problems. Classic algorithms and recent
techniques for approximation algorithms.
IEOR E6611x Semidefinite and second-order
cone programming
Lect: 2. 3 pts. Professor Iyengar.
Duality theory for semidefinite programming
(SDP) and second-order cone programming
(SOCP). Jordan algebras and symmetrical cones.
Formulating engineering problems such as robust
linear programming, truss design, filter design,
and antenna design as SDPs and SOCPs. SDP
and SOCP approximations for combinatorial optimization
problems.
IEOR E6612 Robust optimization
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SEAS 2008–2009