Linear Programming and Extensions (IE 501)

2021 Fall
Faculty of Engineering and Natural Sciences
Industrial Engineering(IE)
3
10.00
Ezgi Karabulut T├╝rkseven ezgi.turkseven@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture,Interactive lecture
Interactive,Discussion based learning,Project based learning
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CONTENT

Theory of linear programming; convexity; simplex and algorithmic aspects; duality and sensitivity; computational issues; decomposition and column generation; introduction to integer and nonlinear programming.

OBJECTIVE

This course focuses on the theory of linear programming (LP) although we will discuss some practical implementation issues as well. In the first part of the course, we will review LP modeling, convexity, some essential linear algebra, certain aspects of polyhedral theory, and then present the foundations of linear programming. In the second part of the course, we will discuss the simplex method for solving linear programs and its algorithmic aspects, some related computational issues, duality and sensitivity. Finally, we will cover Dantzig-Wolfe decomposition and column generation for solving large-scale linear programs. If time permits at the end of the semester, we will briefly introduce further decomposition methods that rely on linear programming and interior point algorithms for solving linear programs. Issues related to computer implementations of linear programming algorithms will generally not be discussed in class, but you will be exposed to the computational aspects of linear programming during assignments.

LEARNING OUTCOME

to identify, model, and solve linear programming problems
to describe the connection of the structure of linear programming problems to linear algebra and polyhedral theory
to leverage on LO-2 in order to design and implement an efficient solution method for linear programming
to describe the relationship between primal and dual linear programming problems and exploit it in sensitivity analysis
to describe the main difficulties associated with solving large-scale linear programming problems and overcome them by employing decomposition methods

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 35
Midterm 30
Participation 5
Homework 30

RECOMENDED or REQUIRED READINGS

Textbook

Linear Programming and Network Flows, Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali. John Wiley, 2010. Fourth edition.

Readings

Linear programming and network flows. Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali. John Wiley, 2009. 4th ed.

Introduction to Linear Optimization. Dimitris Bertsimas, John N. Tsitsiklis. Athena Scientific, 1997.

Linear programming : foundations and extensions. Robert J. Vanderbei. Kluwer Academic Publishers, 1997.

Linear algebra and its applications. Gilbert Strang. Harcourt, Brace, Jovanovich, Publishers, 1988.