3. What is degeneracy? How does the problem of degeneracy arise in a transportation problem? How can we deal with this problem?
difficulty that sometimes occurs in transportation problems is degeneracy. For any non-degenerate solution, the number of used squares must be equal to the number of rim requirements minus 1. [ Alternatively, the number of rows plus the number of columns minus 1. Where this rule is not met the solution is Degenerate. Failure to meet the test for degeneracy in the transportation problem is indicated in two ways: There may be an excessive number of stone squares in a solution; the number of stone squares is greater than the number of rim requirements minus 1. This type of degeneracy arises
only in developing the initial solution and is caused by an improper assignment or an error in formulating the problem. In such cases, one must modify the initial solution to get a solution that satisfies the rule of rim requirement minus 1. There may be an insufficient number of stone squares in a solution. Degeneracy of this type may occur either in the initial or subsequent solutions. This type of degeneracy requires special procedures to resolve. With an insufficient number of stone squares in a solution, it would be impossible to trace a closed path for each unused square, and with the MODI method it would be impossible to compute the row and column values. source: ]
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