IE 531 Linear Programming Spring 2014 Sungsoo Park

IE 531 Linear Programming Spring 2014 Sungsoo Park 1

q Instructor Ø Sungsoo Park (room 4112, sspark@kaist. ac. kr, tel: 3121) Ø Office hour: Tue, Thr 14: 30 – 16: 00 or by appointment q Classroom: E 2 room 1120 q Class hour: Tue, Thr 16: 00 – 17: 30 q Homepage: http: //solab. kaist. ac. kr q TA: Ø Kiho Seo, Junghwan Kwak (room 4113, emffp 1410@kaist. ac. kr, junghoan@kaist. ac. kr, tel: 3161) Ø Office hour: Mon, Wed 14: 30 – 16: 00 or by appointment q Grading: Midterm 30 -40%, Final 40 -60%, HW 10 -20% (including Software CPLEX/Xpress-MP) Linear Programming 2014 2

q Text: "Introduction to Linear Optimization" by D. Bertsimas and J. Tsitsiklis, 1997, Athena Scientific (not in bookstore, reserved in library) and class Handouts q Prerequisite: basic linear algebra/calculus, earlier exposure to LP/OR helpful, mathematical maturity (reading proofs, logical thinking) q No copying of the homework. Be steady in studying. Linear Programming 2014 3

Course Objectives q Why need to study LP? Ø Important tool by itself Ø Theoretical basis for later developments (IP, Network, Graph, Nonlinear, scheduling, Sets, Coding, Game, … ) Ø Formulation + package is not enough for advanced applications and interpretation of results q Objectives of the class: Ø Understand theory of linear optimization Ø Preparation for more in-depth optimization theory Ø Modeling capabilities Ø Introduction to use of software (Xpress-MP and/or CPLEX) Linear Programming 2014 4

q Topics Ø Introduction and modeling Ø System of linear inequalities, polyhedral theory Ø Simplex method, implementation Ø Duality theory Ø Sensitivity analysis Ø Delayed column generation, Dantzig-Wolfe decomposition, Benders’ decomposition Ø Core concepts of interior point methods Linear Programming 2014 5

Brief History of LP (or Optimization) q Gauss: Gaussian elimination to solve systems of equations Fourier(early 19 C) and Motzkin(20 C) : solving systems of linear inequalities Farkas, Minkowski, Weyl, Caratheodory, … (19 -20 C): Mathematical structures related to LP (polyhedron, systems of alternatives, polarity) Kantorovich (1930 s) : efficient allocation of resources (Nobel prize in 1975 with Koopmans) Dantzig (1947) : Simplex method 1950 s : emergence of Network theory, Integer and combinatorial optimization, development of computer 1960 s : more developments 1970 s : disappointment, NP-completeness, more realistic expectations Khachian (1979) : ellipsoid method for LP Linear Programming 2014 6

1980 s : personal computer, easy access to data, willingness to use models Karmarkar (1984) : Interior point method 1990 s : 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 21 C (? ) : 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, . . . ) Linear Programming 2014 7

Application Areas of Optimization q 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 … Linear Programming 2014 8

Resources q Societies: Ø INFORMS (the Institute for Operations Research and Management Sciences) : http: //www. informs. org Ø MOS (Mathematical Optimization Society) : http: //www. mathopt. org/ Ø Korean Institute of Industrial Engineers : http: //kiie. org Ø Korean Operations Research Society : http: //www. korms. or. kr q Journals: Operations Research, Management Science, Mathematical Programming, Networks, European Journal of Operational Research, Naval Research Logistics, Journal of the Operational Research Society, Interfaces, … Linear Programming 2014 9

Notation q Linear Programming 2014 10

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q Linear Programming 2014 12