https://github.com/pooya-mohammadi/linear-programming
Linear Programming and Mixed-Integer Linear Programming with Python
https://github.com/pooya-mohammadi/linear-programming
linear-programing linear-programming lp mixed-integer-linear-programming python
Last synced: 2 months ago
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Linear Programming and Mixed-Integer Linear Programming with Python
- Host: GitHub
- URL: https://github.com/pooya-mohammadi/linear-programming
- Owner: pooya-mohammadi
- Created: 2022-12-19T17:25:56.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2022-12-19T17:29:16.000Z (over 2 years ago)
- Last Synced: 2023-03-05T06:39:47.058Z (over 2 years ago)
- Topics: linear-programing, linear-programming, lp, mixed-integer-linear-programming, python
- Language: Python
- Homepage:
- Size: 1000 Bytes
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: Readme.md
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README
# Linear Programing
## LP Explanation
Linear Programing is used to extract the minimum or maximum of **linear equations**.
The cool part about linear programing is that it can handle constraints over the input arguments.
## Mixed-integer LP:
An extension of LP. In these problems, at least one variable takes a discrete integer value rather than continuous.
The number of items like vehicles in an optimization problem can be represented with Mixed-integer LP.
## LP with Python:
1) Almost all the LP libraries are written in C, Fortran, or C++ because it's computationally intensive.
## Small LP problem
1) maximize: `z = 3x + 2y`
2) subject to:
1) `2x + 2y < 10`
2) `x > 0`
3) Mixed-Integer: by imposing the idea that x should be discrete or integer, the LP becomes Mixed-Integer LP.
### Notations:
1) independent variables or decision variables: x, y
2) objective function, the cost function, or just the goal: z
3) inequality constraints: 1, 2
4) Infeasible Linear Programming problem: if no solution satisfies all the constraints.
5) Unbounded LP problem: If the number of solutions is not finite.
## Python packages:
1) scipy
2) PuLP
## Installation:
https://realpython.com/linear-programming-python/#installing-scipy-and-pulp
```commandline
pip install -r requirements.txt
```
or
```commandline
python -m pip install -U git+https://github.com/coin-or/pulp
```
## References:
1) https://realpython.com/linear-programming-python/