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The degeneracy does not occur in transportation problem at which of the following stages?
(m and n represent number of sources and destinations, respectively)
(a) While the values of dual variables ui and vj cannot be computed
(b) While obtaining an initial solution, we may have less than m + n -1 allocations
(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously
(d) At a stage when the number of +ve allocation is exactly m + n - 1
(a) While the values of dual variables ui and vj cannot be computed
(b) While obtaining an initial solution, we may have less than m + n -1 allocations
(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously
(d) At a stage when the number of +ve allocation is exactly m + n - 1
- a)(a), (b) and (c)
- b)(a), (c) and (d)
- c)(a) and (d)
- d)(a), (b), (c) and (d)
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The degeneracy does not occur in transportation problem at which of th...
1. Degeneracy does not occur in transportation problem when the values of dual variables ui and vj cannot be computed.
2. Degeneracy does not occur in transportation problem when the number of positive allocation is exactly m + n - 1.
3. Degeneracy occurs when obtaining an initial solution, we may have less than m + n - 1 allocations.
4. At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously, then degeneracy will occur.
So, option (3) is correct.
2. Degeneracy does not occur in transportation problem when the number of positive allocation is exactly m + n - 1.
3. Degeneracy occurs when obtaining an initial solution, we may have less than m + n - 1 allocations.
4. At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously, then degeneracy will occur.
So, option (3) is correct.
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The degeneracy does not occur in transportation problem at which of th...
The degeneracy does not occur in transportation problem at which of the following stages?
The transportation problem is a mathematical model used to solve the problem of allocating a set of homogeneous goods from a set of sources to a set of destinations. It involves finding the minimum cost of shipping the goods while satisfying supply and demand constraints.
Degeneracy refers to a situation in the transportation problem where one or more allocations become unoccupied simultaneously, leading to difficulties in finding an optimal solution. Let's analyze each option to determine which stage degeneracy does not occur.
(a) While the values of dual variables ui and vj cannot be computed:
The dual variables ui and vj represent the shadow prices for the supply and demand constraints, respectively. These values are essential for determining the optimality of the solution. If the values of ui and vj cannot be computed, it indicates that the problem is not fully defined, and the degeneracy may occur. Therefore, option (a) is not the correct answer.
(b) While obtaining an initial solution, we may have less than m * n - 1 allocations:
In the transportation problem, the initial solution can be obtained using various methods such as the Northwest Corner Rule, Least Cost Method, or Vogel's Approximation Method. It is possible that the initial solution may have fewer than m * n - 1 allocations, where m and n represent the number of sources and destinations, respectively. This situation does not imply degeneracy but rather an underutilization of the available capacity. Therefore, option (b) is not the correct answer.
(c) At any stage while moving towards the optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously:
This option correctly identifies a stage where degeneracy may occur. During the iteration process of finding the optimal solution, it is possible that two or more occupied cells with the same minimum allocation become unoccupied simultaneously. This situation creates degeneracy and can make it challenging to find an optimal solution. Therefore, option (c) is the correct answer.
(d) At a stage when the number of zero allocations is exactly m * n - 1:
This option suggests that degeneracy occurs when the number of zero allocations is exactly m * n - 1. However, this is not necessarily true. The number of zero allocations alone does not determine degeneracy. Degeneracy occurs when specific conditions are met, as mentioned in option (c). Therefore, option (d) is not the correct answer.
Conclusion:
After analyzing each option, we can conclude that the degeneracy does not occur in the transportation problem at the stage mentioned in option (c): At any stage while moving towards the optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously.
The transportation problem is a mathematical model used to solve the problem of allocating a set of homogeneous goods from a set of sources to a set of destinations. It involves finding the minimum cost of shipping the goods while satisfying supply and demand constraints.
Degeneracy refers to a situation in the transportation problem where one or more allocations become unoccupied simultaneously, leading to difficulties in finding an optimal solution. Let's analyze each option to determine which stage degeneracy does not occur.
(a) While the values of dual variables ui and vj cannot be computed:
The dual variables ui and vj represent the shadow prices for the supply and demand constraints, respectively. These values are essential for determining the optimality of the solution. If the values of ui and vj cannot be computed, it indicates that the problem is not fully defined, and the degeneracy may occur. Therefore, option (a) is not the correct answer.
(b) While obtaining an initial solution, we may have less than m * n - 1 allocations:
In the transportation problem, the initial solution can be obtained using various methods such as the Northwest Corner Rule, Least Cost Method, or Vogel's Approximation Method. It is possible that the initial solution may have fewer than m * n - 1 allocations, where m and n represent the number of sources and destinations, respectively. This situation does not imply degeneracy but rather an underutilization of the available capacity. Therefore, option (b) is not the correct answer.
(c) At any stage while moving towards the optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously:
This option correctly identifies a stage where degeneracy may occur. During the iteration process of finding the optimal solution, it is possible that two or more occupied cells with the same minimum allocation become unoccupied simultaneously. This situation creates degeneracy and can make it challenging to find an optimal solution. Therefore, option (c) is the correct answer.
(d) At a stage when the number of zero allocations is exactly m * n - 1:
This option suggests that degeneracy occurs when the number of zero allocations is exactly m * n - 1. However, this is not necessarily true. The number of zero allocations alone does not determine degeneracy. Degeneracy occurs when specific conditions are met, as mentioned in option (c). Therefore, option (d) is not the correct answer.
Conclusion:
After analyzing each option, we can conclude that the degeneracy does not occur in the transportation problem at the stage mentioned in option (c): At any stage while moving towards the optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously.
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The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer?
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The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer?.
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The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The degeneracy does not occur in transportation problem at which of the following stages?(m and n represent number of sources and destinations, respectively)(a) While the values of dual variables ui and vj cannot be computed(b) While obtaining an initial solution, we may have less than m + n -1 allocations(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously(d) At a stage when the number of +ve allocation is exactly m + n - 1a)(a), (b) and (c)b)(a), (c) and (d)c)(a) and (d)d)(a), (b), (c) and (d)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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