Optimization Theory and Applications

TIM 206 (30155)  Introduction to Optimization Theory and Applications



Dr James G. Shanahan

Location Campus (JB 156); SVC (Room 303)

6:00PM-9:30PM Thursdays

From January 10, 2013 to March 13, 2013

with a final exam during week 11 of the quarter (Week of March 18, 2013)

Recorded Lectures

Click here 

Instructor Office Hours:

By Appointment only

James.Shanahan_AT_ gmail.com and Shanahan_AT_soe.ucsc.edu

In your emails please use the following subject line format otherwise responses might be late or overlooked

"TIM 206 Winter 2013: topic of email" E.g., "TIM 206 Winter 2013: location of final exam"


Course Description:

Essentially, every problem in business, computer science and engineering can be formulated as the optimization of some function under some set of constraints. This universal reduction automatically suggests that such optimization tasks are intractable. Fortunately, most real world problems have special structure, such as convexity, locality, decomposability or submodularity. These properties allow us to formulate optimization problems that can often be solved efficiently. As such operations research is a quantitative discipline that deals with the application of advanced analytical methods to help make better decisions. The terms management science and decision science are sometimes used as more modern-sounding synonyms. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. 

Techniques from operations research are leveraged within many industries, in both online and offline modes, and are responsible for both batch and real-time decision-making involving trillions of dollars ($10^12) annually worldwide. For example:

  • Finance: How Wall Street manages stock portfolios?
  • Digital Advertising: How publishers optimize advertiser revenue online?
  • Logistics: How Fedex ships billions of packages annually across 220 countries?
  • Social networks: How to suggest people you may know?
  • Web search: How to rank web pages with out queries?
  • Healthcare: How do hospitals run? From organ allocation to schedule generation?

These application fields serve a backdrop to this survey class on optimization and will be routinely infused into lectures as motivational and pedagogical examples. More concretely, this class serves as a first graduate course in optimization with an emphasis on theory, intuition, and problem solving in management and engineering.  This class will focus on problem formulation, software technologies and analytical methods for optimization serving as an introduction to a wide variety of optimization problems and techniques including linear and nonlinear programming, dynamic programming, network flows, integer programming, heuristic approaches, Markov chains, game theory, and decision analysis.

Approved elective in most SOE majors, and a requirement for TIM.  Excellent tools for engineers, economists, mathematicians, computer scientists.

Skills Needed:

Students should have some background in probability, statistics, calculus, and linear algebra, though most of the concepts from these areas, which are core to optimization, will be reviewed for completeness during the course.


Course Objectives:

At the conclusion of the course, participants should be able to:                        

  • Describe core optimization techniques, e.g., linear programming, nonlinear programming, convex optimization, dynamic programming, genetic algorithms, Markov processes and more
  • Discuss the pros and cons of these approaches
  • Explain how to use these approaches and solve problems in the fields of digital advertising and marketing, healthcare, logistics and planning, airline industry, ecommerce
  • Identify real-world problems that could be solved using optimization techniques
  • Solve real-world optimization problems in the above fields using solvers, and other optimization software (and possibly implement a couple of the above algorithms from scratch; this is not a requirement though)
  • Optional: gain a proficiency in optimization problem solving in Excel and in R (R is optional but a great skill to develop!).


Performance Evaluation:

Homework                   30%

Midterm                      20% (Week 6 of the Quarter)

Class participation         20%

Final Exam                  30%  (Week 11 of the Quarter)



Required Texts:

(HL) Hillier and Lieberman: Introduction to Operations Research, McGraw-Hill, 9th Edition.  This book is available for purchase from the UCSC bookstore (in eBook form at a negotiated reduced price of ~$80 compared with the print version prices of $250; please use ISBN 9781121774254 for purchasing) and comes with very useful software. There should be copies available in the Library also.


Other Suggested Reading: To be added as needed

Instructors and Assistants