How to solve the transportation problem in networks?

To solve the transportation problem in networks, we can use the transportation algorithm.

The transportation problem is a linear programming problem that involves finding the optimal way to transport goods from sources to destinations while minimizing the cost. The transportation algorithm is a method used to solve this problem.

The first step in the transportation algorithm is to set up the transportation matrix, which shows the supply and demand for each source and destination. The supply represents the amount of goods available at each source, while the demand represents the amount of goods required at each destination.

Next, we need to find an initial feasible solution using the northwest corner method, the least cost method, or the Vogel's approximation method. This involves allocating the available supply to the destinations in a way that satisfies the demand and minimizes the cost.

Once we have an initial feasible solution, we can improve it using the stepping stone method or the modified distribution method. These methods involve finding the optimal way to move goods from one cell to another while maintaining the balance of supply and demand.

Finally, we need to check the optimality of the solution using the optimality test. If the solution is not optimal, we need to repeat the process of finding an initial feasible solution and improving it until we reach an optimal solution.

In summary, the transportation algorithm is a useful method for solving the transportation problem in networks. It involves setting up the transportation matrix, finding an initial feasible solution, improving it, and checking its optimality.