IE 531 Linear Programming Spring 2019 Sungsoo Park

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IE 531 Linear Programming Spring 2019 Sungsoo Park 1

IE 531 Linear Programming Spring 2019 Sungsoo Park 1

q Instructor Ø Sungsoo Park (room 4112, sspark@kaist. ac. kr, tel: 3121) Ø Office

q Instructor Ø Sungsoo Park (room 4112, sspark@kaist. ac. kr, tel: 3121) Ø Office hour: Mon, Tue, Wed 13: 00 – 14: 30 or by appointment q Classroom: E 2 -2 room 1120 q Class hour: Tu, Thr 14: 30 – 16: 00 q Homepage: http: //solab. kaist. ac. kr q TA: Ø Junghwan Kwak (junghoan@kaist. ac. kr ), Jaehee Jeong (jh 5290@kaist. ac. kr ) Room: 4113, Tel: 3161 Ø Office hour: Mon, Wed 14: 30 – 16: 30 or by appointment q Grading: Midterm 30 -40%, Final 40 -60%, (closed book/notes) HW 10 -20% (including Software CPLEX/Xpress-MP) Linear Programming 2019 2

q Text: "Introduction to Linear Optimization" by D. Bertsimas and J. Tsitsiklis, 1997, Athena

q Text: "Introduction to Linear Optimization" by D. Bertsimas and J. Tsitsiklis, 1997, Athena Scientific (not in bookstore, reserved in library) and class Handouts (Chapter 1 on homepage) 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 2019 3

Course Objectives q Why need to study LP? Ø Important tool by itself Ø

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 2019 4

q Topics Ø Introduction and modeling (1 week) Ø System of linear inequalities, polyhedral

q Topics Ø Introduction and modeling (1 week) Ø System of linear inequalities, polyhedral theory (4 weeks) Ø Geometry of LP (1 week) Ø Simplex method, implementation (2 weeks) Ø Midterm exam (1 week) Ø Duality theory (2 weeks) Ø Sensitivity analysis (1 week) Ø Delayed column generation, Dantzig-Wolfe decomposition, Benders decomposition (2 weeks) Ø Core concepts of interior point methods (1 week) Ø Final exam (1 week) Linear Programming 2019 5

Brief History of LP (or Optimization) q Gauss: Gaussian elimination to solve systems of

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 2019 6

1980 s : personal computer, easy access to data, willingness to use models Karmarkar

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), Roth, Shapley (2012) : 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 2019 7

Application Areas of Optimization q Operations Managements Production Planning Scheduling (production, personnel, . .

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 https: //www. informs. org/About-INFORMS/History-and-Traditions/ORApplication-Areas … Linear Programming 2019 8

Resources q Societies: Ø INFORMS (the Institute for Operations Research and Management Sciences) :

Resources q Societies: Ø INFORMS (the Institute for Operations Research and Management Sciences) : https: //www. informs. org Ø EURO : https: //www. euro-online. org/web/pages/1/home Ø MOS (Mathematical Optimization Society) : http: //www. mathopt. org/ Ø Korean Institute of Industrial Engineers : http: //kiie. org Ø Korean Operations Research/Management Science 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, IIE Transactions, Interfaces, … Linear Programming 2019 9

Notation q Linear Programming 2019 10

Notation q Linear Programming 2019 10

q Linear Programming 2019 11

q Linear Programming 2019 11

q Linear Programming 2019 12

q Linear Programming 2019 12