Separating the effect of undesirable outputs generation from the inefficiency of desirable outputs production in efficiency measurement

Undesirable outputs are by-products of producing desirable outputs which can be reduced only in proportion with the reduction of desirable outputs as asserted in weak disposability. This paper proposes a model to determine the minimum level of the undesirable outputs that cannot be avoided in producing the desirable outputs of a production unit under weak disposability. The difference between the efficiencies of the production unit and the corresponding hypothetical unit that generates the minimum level of the undesirable outputs is a measure of the effect of generating excessive amount of the undesirable outputs on efficiency. The proposed model is able to separate the effect of generating the undesirable outputs from the inefficiency of producing the desirable outputs in measuring the efficiency of a production unit. There are two forms of weak disposability, one requires all production units to have the same proportion and another allows each production unit to have its own proportion in reducing the desirable and undesirable outputs. It is shown that the individual-proportion model is able to find lower levels of the undesirable outputs that are allowed to be generated in the production process which provides more stringent standards to better protect the environment.