Closest target on the frontier of the free disposal hull

Abstract

In data envelopment analysis (DEA) the production possibility set (PPS) constructed from the observed decision making units (DMUs) under only the free disposability postulate is referred to as the free disposal hull (FDH), based on which efficiencies are measured. The conventional non-radial DEA models that take both the inputs and outputs into consideration seek the target on the FDH frontier that is farthest to the DMU to be assessed to measure efficiency. A consequence is that greater effort is needed to make an inefficient DMU efficient. This paper proposes a method to find the target on the frontier that is closest to the assessed DMU. The target is found by examining only the orthogonal projection points of the assessed DMU on the frontier and the weakly efficient corner points of the PPS that dominate the assessed DMU. The effort needed to reach this point is the least. The case of twenty-four non-life insurance companies in Taiwan widely used in the literature is used in this paper for illustrative purposes. Surprisingly, the difference between the longest and shortest distances can be hundreds of times, which implies that the effort for an inefficient DMU to become efficient can be reduced to less than one-hundredth of what is usually needed. JEL Classification C61, C67