Transportation Problem Solver

This project provides a set of Python functions and methods to solve the Transportation Problem using various allocation methods. It includes functions to print the transportation problem in a tabular format and solutions for the problem using the Northwest Corner Method, Vogel’s Approximation Method (VAM), and Russell’s Approximation Method. Additionally, it calculates the total transportation cost based on the solution.

Features

• Transportation Table Printing: Formats and displays the transportation costs, supply, and demand in a readable table.
• Balance Checker: Ensures that the total supply equals total demand, required for feasible solutions.
• Allocation Methods:
  • Northwest Corner Method: A basic method to allocate supply and demand in a top-left to bottom-right approach.
  • Vogel's Approximation Method (VAM): A heuristic method that aims to minimize cost by reducing the penalty in allocation.
  • Russell's Approximation Method: Another heuristic method that uses row and column maxima to allocate supplies and demands.
• Total Cost Calculation: Computes the total cost of transportation based on the final allocation.

Example Input

Enter coefficients of supply in one line separated by spaces:
75 125 100

Enter costs for each source separated by spaces:
464 513 654 867
352 416 690 791
995 682 388 685

Enter coefficients of demand in one line separated by spaces:
80 65 70 85

Example Output

The program will display:

1. The transportation problem table, showing supply, demand, and costs.
2. A balance check message indicating whether the problem is balanced.
3. Solutions using Northwest Corner, Vogel’s Approximation, and Russell’s Approximation methods.
4. The total cost for each method's solution.

Functions

• print_transportation_table(costs, supply, demand): Prints a formatted table displaying the transportation problem.
• is_balanced(supply, demand): Checks if total supply equals total demand.
• northwest_corner(supply, demand): Solves the problem using the Northwest Corner Method.
• vogel_approximation(costs, supply, demand): Solves the problem using Vogel's Approximation Method.
• russell_approximation(costs, supply, demand): Solves the problem using Russell’s Approximation Method.
• calculate_total_cost(solution, costs): Calculates the total cost of transportation for a given solution.