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Consider the following statements:
The assignment problem is seen to be the special case of the transportation problem in which 1. m = n
2. All ai = 1
3. xij = 1
(The symbols have usual meaning)
2. All ai = 1
3. xij = 1
(The symbols have usual meaning)
Which of the statements given above are correct?
- a)1, 2 and 3
- b)1 and 2 only
- c)2 and 3 only
- d)1 and 3 only
Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements:The assignment problem is seen to be...
3 - is wrong 
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Consider the following statements:The assignment problem is seen to be...
Statement Analysis:
The given statements are as follows:
1. The assignment problem is seen to be the special case of the transportation problem in which m = n.
2. All ai = 1.
3. xij = 1.
Explanation:
- The assignment problem is a special case of the transportation problem where the number of sources (m) is equal to the number of destinations (n). In the assignment problem, we are trying to find the optimal assignment of n jobs to n workers with minimum cost or maximum profit.
- The transportation problem, on the other hand, involves finding the optimal transportation of goods from m sources to n destinations with minimum cost or maximum profit.
- Since the assignment problem is a special case of the transportation problem, statement 1 is correct.
- In the assignment problem, each job can be assigned to only one worker, and each worker can only perform one job. This implies that the supply and demand for each source and destination are equal to 1. Therefore, statement 2 is correct.
- The variable xij represents the assignment of job i to worker j. In the assignment problem, xij can only take the value of 0 or 1, indicating whether job i is assigned to worker j or not. Therefore, statement 3 is correct.
Conclusion:
From the above analysis, we can conclude that statements 1 and 2 are correct. Therefore, the correct answer is option 'B' - 1 and 2 only.
The given statements are as follows:
1. The assignment problem is seen to be the special case of the transportation problem in which m = n.
2. All ai = 1.
3. xij = 1.
Explanation:
- The assignment problem is a special case of the transportation problem where the number of sources (m) is equal to the number of destinations (n). In the assignment problem, we are trying to find the optimal assignment of n jobs to n workers with minimum cost or maximum profit.
- The transportation problem, on the other hand, involves finding the optimal transportation of goods from m sources to n destinations with minimum cost or maximum profit.
- Since the assignment problem is a special case of the transportation problem, statement 1 is correct.
- In the assignment problem, each job can be assigned to only one worker, and each worker can only perform one job. This implies that the supply and demand for each source and destination are equal to 1. Therefore, statement 2 is correct.
- The variable xij represents the assignment of job i to worker j. In the assignment problem, xij can only take the value of 0 or 1, indicating whether job i is assigned to worker j or not. Therefore, statement 3 is correct.
Conclusion:
From the above analysis, we can conclude that statements 1 and 2 are correct. Therefore, the correct answer is option 'B' - 1 and 2 only.
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