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Since Briec developed a family of the least distance based inefficiency measures satisfying weak monotonicity over weakly efficient frontier, the existence of a least distance based efficiency measure sat- isfying strong monotonicity on the strongly efficient frontier is still an open problem. This paper gives a negative answer to the open problem and its relaxed open problem. Modifying Briec's inefficiency measures gives an alternative solution to the relaxed open problem, that can be used for theoretical and practical applications.

LEAST DISTANCE BASED INEFFICIENCY MEASURES ON THE PARETO-EFFICIENT FRONTIER IN DEA