Transportation Problems

Transportation problems in linear programming are widely used in real-world scenarios. They are used to optimize the transportation of goods and services from production to consumption, minimizing costs and maximizing efficiency. Examples include supply chain management, distribution planning, and logistics optimization. 

The objective of transportation problems in linear programming is to minimize the cost of shipping goods from a set of sources to a set of destinations while satisfying certain constraints, such as supply and demand. The goal is to find the optimal shipping plan that minimizes the total transportation cost. Of course, who wouldn’t want to save? Even the biggest firms want to minimize their shipping costs. 

The steps for solving a transportation problem are as follows:

1. Formulate the problem as a linear programming model

2. Find an initial feasible solution using any method (e.g. North-West Corner Rule, Least Cost Method, Vogel's Approximation Method)

3. Improve the solution using any method (e.g. Stepping Stone Method, MODI Method)

4. Check the optimality of the solution using the optimality conditions (e.g. no negative cell in the solution matrix)

5. If the solution is optimal, stop. Otherwise, go back to step 3 until an optimal solution is found.

These steps will be expounded in the video lecture above :)