README.md

Lippy - solving linear programming problems.

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Source Code: https://github.com/ispaneli/lippy

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Lippy is a module for solving linear programming problems on Python.

Provides:

1. Simplex method in primal linear programming
2. Simplex method in dual linear programming
3. Branch and bound in integer linear programming
4. Brute force method in integer linear programming
5. Cutting-plane method in integer linear programming
6. Zero-sum game in game theory using Simplex method

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Simplex method in primal linear programming

import lippy as lp


c_vec = [6, 6, 6]
a_matrix = [
    [4, 1, 1],
    [1, 2, 0],
    [0, 0.5, 4]
]
b_vec = [5, 3, 8]

simplex = lp.SimplexMethod(c_vec, a_matrix, b_vec)
solution, func_value = simplex.solve()

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Simplex method in dual linear programming

import lippy as lp


c_vec = [6, 6, 6]
a_matrix = [
    [4, 1, 1],
    [1, 2, 0],
    [0, 0.5, 4]
]
b_vec = [5, 3, 8]

c_vec, a_matrix, b_vec = lp.primal_to_dual_lp(c_vec, a_matrix, b_vec)
simplex = lp.SimplexMethod(c_vec, a_matrix, b_vec)
solution, func_value = simplex.solve()

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Branch and bound in integer linear programming

import lippy as lp


c_vec = [3, 3, 7]
a_matrix = [
    [1, 1, 1],
    [1, 4, 0],
    [0, 0.5, 3]
]
b_vec = [3, 5, 7]

bab = lp.BranchAndBound(c_vec, a_matrix, b_vec)
solution, func_value = bab.solve()

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Brute force method in integer linear programming

import lippy as lp


c_vec = [3, 3, 7]
a_matrix = [
    [1, 1, 1],
    [1, 4, 0],
    [0, 0.5, 3]
]
b_vec = [3, 5, 7]

force = lp.BruteForce(c_vec, a_matrix, b_vec)
solution, func_value = force.solve()

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Cutting-plane method in integer linear programming

import lippy as lp


c_vec = [3, 3, 7]
a_matrix = [
    [1, 1, 1],
    [1, 4, 0],
    [0, 0.5, 3]
]
b_vec = [3, 5, 7]

gomory = lp.CuttingPlaneMethod(c_vec, a_matrix, b_vec)
gomory.solve()

---

Zero-sum game in game theory using Simplex method

import lippy as lp


game_matrix = [
    [8, 1, 17, 8, 1],
    [12, 6, 11, 10, 16],
    [4, 19, 11, 15, 2],
    [17, 19, 6, 17, 16]
]

game = lp.ZeroSumGame(game_matrix)
strategies = game.solve()

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Logging

Existing logging modes:

1. FULL_LOG
2. MEDIUM_LOG
3. LOG_OFF (default)

Logging is set when initializing a class object.

For example:

simplex = lp.SimplexMethod(c_vec, a_matrix, b_vec, log_mode=lp.LogMode.FULL_LOG)

bab = lp.BranchAndBound(c_vec, a_matrix, b_vec, log_mode=lp.LogMode.MEDIUM_LOG)

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License

This project is licensed under the terms of the MIT license.