ExampleModeling.jl
Documentation for ExampleModeling.jl
Formulation
We formulate the canonical mixed-integer linear program as follows:
\[\begin{aligned} \text{maximize }& ๐๐ฑ + ๐๐ฒ \\ \text{subject to } & ๐ ๐ฑ + ๐ ๐ฒ โค ๐ \\ & ๐ฑ,๐ฒ โฅ 0 \\ & ๐ฒ โ โค. \end{aligned}\]
We refer to the formulation as model. The model takes as inputs the indices and parameters.
Indices:
- $m,n,kโโค$
Parameters:
- $๐โโ^{n}$
- $๐โโ^{k}$
- $๐โโ^{m}$
- $๐โโ^{mรn}$
- $๐โโ^{mรk}$
The model outputs the variables and objectives.
Variables:
- $๐ฑโโ^{n}$
- $๐ฒโโค^{k}$
Objectives:
- $f(๐ฑ,๐ฒ)= ๐๐ฑ + ๐๐ฒ$
You can read more about the theory of integer programming from [1].
References
- 1Wolsey, L. A. (1998). Integer programming. Wiley.