ExampleModeling.jl

Documentation for ExampleModeling.jl

Formulation

We formulate the canonical mixed-integer linear program as follows:

\[\begin{aligned} \text{maximize }& 𝐚𝐱 + 𝐛𝐲 \\ \text{subject to } & 𝐀 𝐱 + 𝐁 𝐲 ≤ 𝐜 \\ & 𝐱,𝐲 ≥ 0 \\ & 𝐲 ∈ ℤ. \end{aligned}\]

We refer to the formulation as model. The model takes as inputs the indices and parameters.

Indices:

• $m,n,k∈ℤ$

Parameters:

• $𝐚∈ℝ^{n}$
• $𝐛∈ℝ^{k}$
• $𝐜∈ℝ^{m}$
• $𝐀∈ℝ^{m×n}$
• $𝐁∈ℝ^{m×k}$

The model outputs the variables and objectives.

Variables:

• $𝐱∈ℝ^{n}$
• $𝐲∈ℤ^{k}$

Objectives:

• $f(𝐱,𝐲)= 𝐚𝐱 + 𝐛𝐲$

You can read more about the theory of integer programming from ^[1].

References