Transport Optimization Problem Solver

This project provides a Python implementation to solve the classical Transportation Problem, which aims to find the most cost-effective way to transport goods from multiple suppliers to multiple consumers, given supply capacities, demand requirements, and transportation costs.

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Overview

The transportation problem is a special type of linear programming problem that minimizes the total cost of distributing a product from several suppliers to several consumers while meeting supply and demand constraints.

This solver uses:

• Minimum Cost Method to generate an initial feasible basic solution.
• Potential Method (MODI Method) for iteratively improving the solution by adjusting allocations along cycles until optimality conditions are satisfied.

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Features

• Supports arbitrary numbers of suppliers and consumers.
• Calculates an initial feasible solution automatically.
• Iteratively optimizes the solution to reach minimum transportation cost.
• Handles degeneracy by adding artificial zero allocations if necessary.
• Displays intermediate iterations and the final total transportation cost.

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Structure

1. generator.py - containt a function that generates transport task input data example.
2. show.py - provide visualization during optimization process.
3. test.py- just a simple test case.
4. transport.py - contains code that solves Transport task.

Usage

Inputs

• suppliers: List of integers representing the supply available at each supplier.
• consumers: List of integers representing the demand required at each consumer.
• costs: 2D list (matrix) representing the transportation cost from each supplier to each consumer.

Example

Table(Matrix):

Suppliers \ Consumers	86	103	177	46	1	16	30	20
31	41	1	96	37	33	80	27	68
50	88	22	94	90	29	87	74	19
93	6	12	88	21	29	83	88	82
11	73	94	17	77	13	95	94	77
122	0	71	93	21	52	61	99	37
172	21	23	24	44	54	29	50	97

suppliers = [31, 50, 93, 11, 122, 172]
consumers = [86, 103, 177, 46, 1, 16, 30, 20]
costs = [
    [41, 1, 96, 37, 33, 80, 27, 68],
    [88, 22, 94, 90, 29, 87, 74, 19],
    [6, 12, 88, 21, 29, 83, 88, 82],
    [73, 94, 17, 77, 13, 95, 94, 77],
    [0, 71, 93, 21, 52, 61, 99, 37],
    [21, 23, 24, 44, 54, 29, 50, 97]
]
total_cost = optimize_transport(suppliers, consumers, costs)
print(f"Minimum total transportation cost: {total_cost}")