1. 1 IE 531 Linear Programming Spring 2012 Sungsoo Park

2. Linear Programming 2012 2  Instructor  Sungsoo Park (room 4112, sspark@kaist.ac.kr, tel:3121)sspark@kaist.ac.krtel:3121  Office hour: Tu., Thr. 14:30 – 17:00 or by appointment  Classroom: E2 room 1120  Class hour: Tu., Thr. 13:00 – 14:30  Homepage: http://solab.kaist.ac.krhttp://solab.kaist.ac.kr  TA:  Kyoungmi Hwang (room 4113, emptycan82@hanmail.net, tel:3161)emptycan82@hanmail.nettel:3161  Office hour: Mon., Wed. 13:00 – 15:00  Grading: Midterm 30-40%, Final 40-60%, HW 10-20% (including Software CPLEX/Xpress-MP)

3.  Text: "Introduction to Linear Optimization" by D. Bertsimas and J. Tsitsiklis, 1997, Athena Scientific (not in bookstore, reserved in library) and class Handouts  Prerequisite: basic linear algebra/calculus, earlier exposure to LP/OR helpful, mathematical maturity (reading proofs, logical thinking)  Be steady in studying. Linear Programming 2012 3

4. 4 Course Objectives  Why need to study LP?  Important tool by itself  Theoretical basis for later developments (IP, Network, Graph, Nonlinear, scheduling, Sets, Coding, Game, … )  Formulation + package is not enough for advanced applications and interpretation of results  Objectives of the class:  Understand the theory of linear optimization  Preparation for more in-depth optimization theory  Modeling capabilities  Introduction to use of software (Xpress-MP and/or CPLEX)

5.  Topics  Introduction and modeling  System of linear inequalities, polyhedral theory  Simplex method, implementation  Duality theory  Sensitivity analysis  Delayed column generation, Dantzig-Wolfe decomposition  Core concepts of interior point methods Linear Programming 2012 5

6. 6 Brief History of LP (or Optimization)  Gauss: Gaussian elimination to solve systems of equations Fourier(early 19C) and Motzkin(20C) : solving systems of linear inequalities Farkas, Minkowski, Weyl, Caratheodory, … (19-20C): Mathematical structures related to LP (polyhedron, systems of alternatives, polarity) Kantorovich (1930s) : efficient allocation of resources (Nobel prize in 1975 with Koopmans) Dantzig (1947) : Simplex method 1950s : emergence of Network theory, Integer and combinatorial optimization, development of computer 1960s : more developments 1970s : disappointment, NP-completeness, more realistic expectations Khachian (1979) : ellipsoid method for LP

7. Linear Programming 2012 7 1980s : personal computer, easy access to data, willingness to use models Karmarkar (1984) : Interior point method 1990s : improved theory and software, powerful computers software add-ins to spreadsheets, modeling languages, large scale optimization, more intermixing of O.R. and A.I. Markowitz (1990) : Nobel prize for portfolio selection (quadratic programming) Nash (1994) : Nobel prize for game theory 21C (?) : Lots of opportunities more accurate and timely data available more theoretical developments better software and computer need for more automated decision making for complex systems need for coordination for efficient use of resources (e.g. supply chain management, APS, traditional engineering problems, bio, finance,...)

8. Linear Programming 2012 8 Application Areas of Optimization  Operations Managements Production Planning Scheduling (production, personnel,..) Transportation Planning, Logistics Energy Military Finance Marketing E-business Telecommunications Games Engineering Optimization (mechanical, electrical, bioinformatics,... ) System Design …

9. Linear Programming 2012 9 Resources  Societies:  INFORMS (the Institute for Operations Research and Management Sciences) : http://www.informs.org http://www.informs.org  MPS (The Mathematical Programming Society) : http://www.mathprog.orghttp://www.mathprog.org  Korean Institute of Industrial Engineers : http://kiie.orghttp://kiie.org  Korean Operations Research Society : http://www.korms.or.krhttp://www.korms.or.kr  Journals: Operations Research, Management Science, Mathematical Programming, Networks, European Journal of Operational Research, Naval Research Logistics, Journal of the Operational Research Society, Interfaces, …