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The purpose of this paper is introducing an alternative model to measure the relative efficiency of observations with undesirable products. Describing the reference set and benchmarking.

In this paper, an alternative definition of weak disposability assumption is introduced to handle undesirable outputs. Actually, two types of undesirable outputs are addressed and a substitute definition of weak disposability is presented.

Using this assumption a linear production technology set along with a performance analysis model is constructed to assess the relative efficiency of the decision-making units. To illustrate the radial application of the proposed approach, a real case on transportation system of USA during 1992-2009 is given.

To date, data envelopment analysis studies have investigated undesirable outputs by the assumption of weak disposability, defined as the proportional contraction of good and bad products, which leads to the null-joint assumption between good and bad outputs. Therefore, the only way to produce no undesirable outputs is producing zero desirable outputs. So the production process should be stopped while it is not economically cost-effective. However, in some processes there are some undesirable outputs, which are decreased with non-same percentages. So these undesirable outputs can be stopped while the good outputs have a strictly positive value. In this situation, the good outputs are not null-joint with this type of bad outputs. In the current paper, a new definition of the weak disposability of outputs was represented while two groups of undesirable outputs were considered. Hence, desirable outputs and the first kind of undesirable outputs were decreased proportionally. However, the reduction value was different for the second kind of undesirable outputs. Hence, the null-joint assumption is removed from the production technology. Then, a new technology was proposed based on five postulates as inclusion of observations, free disposability of desirable outputs and inputs, new weak disposability, convexity and minimum extrapolation.