# Accession Number:

## AD0773610

# Title:

## Integer and Mixed-Integer Programming Models: General Properties.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1973-12-01

# Pagination or Media Count:

## 26.0

# Abstract:

OGRAMMING, Nonlinear programming, Linear programming, Optimization, TheoremsInteger programming, Mixed integer programmingIt is well-known that mixed-integer formulations can be used to model important classes of non-convex functions such as fixed-charge functions and linear economy-of-scale cost functions. The purpose of the paper is to formulate a rigorous definition of a mixed-integer model of a given function, and to study the properties of the functions that can be so modelled. An interesting by-product of this approach is the identification of a simple class of functions that cannot be modelled by computer-representable mixed-integer formulations, even though mixed-integer models based on the use of a single arbitrary irrational constant are available for this class. Author

# Descriptors:

# Subject Categories:

- Operations Research