2
Basics
In this chapter we introduce some of the basic concepts that will be useful for the study of
integer programming problems.
2.1 Notation
Let A Rmn be a matrix with row index set M = cfw_1, . . ., m and column index set N =
cfw_1, . . ., n. We writ

1
Introduction
Linear Programs can be used to model a large number of problems arising in practice. A
standard form of a Linear Program is
(LP)
cT x
max
(1.1a)
(1.1b)
(1.1c)
Ax ! b
x " 0,
where c Rn , b Rm are given vectors and A Rmn is a matrix. The focu

College of Management, NCTU
Operation Research II
Spring, 2009
Chap11 Integer Programming
Sometimes, integer variables mean reality.
LP + All variables must be integers = IP (Integer Programming)
9 If integer variables are either 0 or 1 (binary variable

Chapter 6
Integer Programming
Integer programming (IP) deals with solving linear models in which some or all
the variables are restricted to be integer. There are algorithms especially designed
for IP problems which basically nd the optimal solution by so

INTEGER
PROGRAMMING
Theory and Practice
The Operations Research Series
Series Editor: A. Ravi Ravindran
Dept. of Industrial & Manufacturing Engineering
The Pennsylvania State University, USA
Operations Research: A Practical Approach
Michael W. Carter and