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The Transportation Problem is a fundamental concept in operations research and mathematical optimization. It deals with the efficient allocation of goods from multiple suppliers to multiple consumers while minimizing transportation costs. In the course of solving transportation problems using techniques like the North-West Corner Rule or the Modified Distribution Method, you might encounter a phenomenon known as degeneracy. Degeneracy can complicate the solution process and impact the optimal solution. In this blog, we will explore what degeneracy is, its causes, and its significance in transportation problems.

**Contents**

## What Is Degeneracy In Transportation Problem?

Degeneracy in the context of transportation problems refers to a situation where the number of allocations or assignments made in the initial basic feasible solution (i.e., the initial distribution of goods) is fewer than the total number of sources (suppliers) and destinations (consumers). In simpler terms, it means that you have more suppliers or consumers than you have allocations. This situation can make solving the transportation problem more challenging.

## Causes Of Degeneracy

Degeneracy can occur due to several reasons:

- Excess Supply or Demand: When the total supply of goods exceeds the total demand, or vice versa, degeneracy can arise. In such cases, there may not be enough allocations to utilize all the available supply or satisfy all the demand.
- Blocked Cells: Blocked cells are a crucial concept in transportation problems. A blocked cell occurs when the allocation in a cell becomes zero. These blocked cells can restrict the transportation problem from achieving an optimal solution.
- Choosing the Wrong Starting Corner: The selection of the initial cell in the North-West Corner Rule or any other initial method can sometimes result in a degenerate solution. Choosing the wrong starting point may lead to fewer allocations and more blocked cells.

## Significance Of Degeneracy

Degeneracy can have several implications in solving transportation problems:

- Complexity: Degeneracy can complicate the solution process. Solvers need to take extra steps to address the blocked cells and ensure a feasible and optimal solution.
- Increased Iterations: Degenerate transportation problems often require more iterations to reach an optimal solution, which can be time-consuming and resource-intensive.
- Non-Optimal Solutions: Ignoring or mishandling degeneracy may lead to non-optimal solutions, which defeats the purpose of solving transportation problems.

## Managing Degeneracy

To manage degeneracy in transportation problems, you can employ a few strategies:

- Balancing Supply and Demand: Carefully assess the supply and demand constraints. If there is a significant imbalance, consider adjusting the problem parameters to ensure balance.
- Cycle Breaking: When faced with blocked cells, you can use cycle-breaking techniques, such as the stepping-stone method or the Russell’s approximation method, to resolve degeneracy and arrive at an optimal solution.
- Proper Initialization: Selecting the right initial cell can minimize the chances of degeneracy. Consider alternative starting points or use more advanced methods to find a suitable starting basic feasible solution.

## Conclusion

Degeneracy in transportation problems can be a challenging hurdle, but with the right approach and techniques, it can be effectively managed. Understanding its causes and implications is crucial for optimizing the transportation process and achieving cost savings in supply chain management and logistics. While degeneracy may complicate the solution process, addressing it systematically will help you reach an efficient and optimal solution to your transportation problem.

## FAQ

### What Is Degeneracy And Non Degeneracy In Transportation Problem?

Degeneracy: If a basic feasible solution to a transportation problem contains less than m+n-1 allocations, it is called a degenerate basic feasible solution and it cannot be tested for optimality. Here m is the number of rows and n is the number of columns in a transportation problem.

### How Can We Solve The Degeneracy In Transportation Problem?

Steps to convert unallocated cells into allocated cells:

- Start from the least value of the unallocated cell.
- Check the loop formation one by one.
- There should be no closed-loop formation.
- Select that loop as a new allocated cell and assign a value ‘e’.

### What Is The Concept Of Degeneracy?

A term referring to the fact that two or more stationary states of the same quantum-mechanical system may have the same energy even though their measurable wave functions are not the same. The common energy level of the stationary states is said to be degenerate.

### What Is Degeneracy Also Known As?

degradation, deterioration; decline, descent; deviance; state of having low moral values. Degeneracy may refer to: Science. Biology and medicine. * Codon Degeneracy.

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