In a transportation problem, degeneracy occurs when
A)the number of used (or full)cells equals the number of rows plus columns minus one.
B)in an initial solution, both a row total and a column total are satisfied simultaneously.
C)during an improvement, two positive cells contain the same smallest amount.
D)the number of rows exceeds the number of columns.

Question

Quizplus · Accepted Answer

Degeneracy occurs in a transportation problem when the number of used (or full) cells equals the number of rows plus columns minus one. However, the occurrence of degeneracy does not cause a problem in the solution process. The real problem arises when the degeneracy causes the transportation problem to have more than one initial basic feasible solution. This makes it difficult to choose the best starting point for the optimization process. In such cases, the selection of an arbitrary basic feasible solution may cause the optimization process to converge to a suboptimal solution, and additional efforts may be required to identify the optimal solution. In contrast, when both a row total and a column total are satisfied simultaneously in an initial solution, it means that there are fewer basic variables than the total number of rows and columns. This results in degeneracy, which affects the efficiency and accuracy of the optimization process. Thus, option B is the correct choice.

In a Transportation Problem, Degeneracy Occurs When