Degeneracy occurs during the Simplex method when there is a tie in the minimum ratio test, which is used to select the leaving variable.

When two or more constraints yield the exact same minimum positive ratio, it indicates that multiple constraint boundaries intersect at that single corner point (vertex). Consequently, one or more basic variables equal zero at the current solution. When the solver pivots to the next iteration, the objective value remains unchanged, which can cause the algorithm to stall—or, in rare un-cycled cases, loop endlessly through identical non-improving bases.

Degeneracy occurs during the Simplex method when the minimum ratio test results in a tie, causing a basic variable to become zero in the next tableau. In other words, the solution is still feasible, but one or more basic variables have a value of zero. Degeneracy does not necessarily mean there is an error; however, it can cause the Simplex method to make an iteration without improving the objective value and, in rare cases, lead to cycling.