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In solution of transportation model of dimension m x n, degeneracy occurs when it has:-
- a)more than (m+n -1) allocations
- b)fewer than (m+n-1) allocations
- c)exactly (m+n-1) allocations
- d)(m x n) allocations
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In solution of transportation modelof dimension m x n, degeneracyoccur...
If basic feasible solution has less
than (m + n - 1) allocations, it leads
to degeneracy.
than (m + n - 1) allocations, it leads
to degeneracy.
Most Upvoted Answer
In solution of transportation modelof dimension m x n, degeneracyoccur...
Explanation:
Degeneracy in the transportation model occurs when there are fewer than (m x n - 1) allocations.
Transportation Model:
The transportation model is a linear programming model used to solve transportation problems. It is used to determine the optimal transportation plan for goods from a set of sources to a set of destinations.
Degeneracy:
Degeneracy occurs in the transportation model when the number of allocations is fewer than (m x n - 1), where m represents the number of sources and n represents the number of destinations.
Explanation:
To understand why degeneracy occurs when there are fewer than (m x n - 1) allocations, we need to understand the concept of degeneracy in linear programming.
In linear programming, degeneracy refers to a situation where the basic feasible solution (BFS) of a linear programming problem has one or more zero-valued variables. These zero-valued variables create degeneracy in the problem, making it more difficult to find the optimal solution.
In the transportation model, each allocation represents the amount of goods transported from a source to a destination. The total number of allocations is given by m x n, where m is the number of sources and n is the number of destinations. The total number of variables in the transportation model is also given by m x n.
When there are fewer than (m x n - 1) allocations, it means that there are fewer variables than the total number of allocations. This creates a situation where there are not enough variables to fully determine the optimal solution. As a result, one or more variables will have a value of zero, leading to degeneracy in the problem.
Therefore, the correct answer is option 'B' - degeneracy occurs when there are fewer than (m x n - 1) allocations in the transportation model.
Degeneracy in the transportation model occurs when there are fewer than (m x n - 1) allocations.
Transportation Model:
The transportation model is a linear programming model used to solve transportation problems. It is used to determine the optimal transportation plan for goods from a set of sources to a set of destinations.
Degeneracy:
Degeneracy occurs in the transportation model when the number of allocations is fewer than (m x n - 1), where m represents the number of sources and n represents the number of destinations.
Explanation:
To understand why degeneracy occurs when there are fewer than (m x n - 1) allocations, we need to understand the concept of degeneracy in linear programming.
In linear programming, degeneracy refers to a situation where the basic feasible solution (BFS) of a linear programming problem has one or more zero-valued variables. These zero-valued variables create degeneracy in the problem, making it more difficult to find the optimal solution.
In the transportation model, each allocation represents the amount of goods transported from a source to a destination. The total number of allocations is given by m x n, where m is the number of sources and n is the number of destinations. The total number of variables in the transportation model is also given by m x n.
When there are fewer than (m x n - 1) allocations, it means that there are fewer variables than the total number of allocations. This creates a situation where there are not enough variables to fully determine the optimal solution. As a result, one or more variables will have a value of zero, leading to degeneracy in the problem.
Therefore, the correct answer is option 'B' - degeneracy occurs when there are fewer than (m x n - 1) allocations in the transportation model.
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Community Answer
In solution of transportation modelof dimension m x n, degeneracyoccur...
If allocation is less than m+n-1 then solution will become denegerate.
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In solution of transportation modelof dimension m x n, degeneracyoccurs when it has:-a)more than (m+n -1) allocationsb)fewer than (m+n-1) allocationsc)exactly (m+n-1) allocationsd)(m x n) allocationsCorrect answer is option 'B'. Can you explain this answer?
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