Which technique is commonly used to solve unbalanced transportation problems?

Solving Unbalanced Transportation Problems with Dummy Destinations

In transportation problems, a situation may arise where the total supply exceeds the total demand or vice versa, leading to an unbalanced problem. To resolve this, a common technique is to introduce a dummy destination.

A dummy destination is a fictitious location that is added to the transportation network to absorb the excess supply or demand. This destination does not represent an actual destination for the goods or services being transported but serves as a mathematical construct to balance the problem.

Balancing the Problem

The introduction of a dummy destination allows the problem to be balanced by creating a new demand equal to the excess supply. The dummy destination is assigned a zero demand for all supply points and a demand equal to the excess supply for the dummy demand point.

Cost Considerations

Assigning a zero demand to the dummy destination for all supply points means that no goods or services are actually transported to the dummy destination. Therefore, no transportation costs are incurred for the dummy shipments.

Optimal Solution

The optimal solution to the unbalanced transportation problem is found by solving the modified problem with the dummy destination using a standard transportation algorithm. The solution will provide the optimal transportation plan that minimizes the total transportation costs, considering the dummy shipments.

Advantages of Using Dummy Destinations

• Ensures Balance: Dummy destinations guarantee that supply equals demand, making the problem solvable.
• Simplifies Calculation: Introducing a dummy destination reduces the complexity of the problem by converting it into a balanced problem.
• Maintains Cost Optimality: The dummy shipments do not incur any actual transportation costs, preserving the optimality of the solution.

Conclusion

Unbalanced transportation problems can be effectively solved using dummy destinations. This technique ensures that the problem is balanced, simplifies calculations, and maintains the optimality of the solution. By absorbing excess supply or demand, dummy destinations enable the problem to be solved efficiently and provide an optimal transportation plan that minimizes transportation costs.