Merging of units based on inverse data envelopment analysis

Inverse data envelopment analysis (InvDEA) is a remarkable and popular management tool. This paper deals with one application of this tool. In fact, the problem of the combination of the units is investigated in the presence of negative data. The problem of combining units refers to the fact that a set of units create a new unit based on synergy to improve their performance. We use multiple objective programming for this purpose and suggest new models based on predetermined conditions for the new unit. The proposed models estimate inputs and outputs simultaneously. Importance advantages of the proposed models are i) We can follow multiple goals in the problem of combining units because multiple objective programming is applied. ii) Models can simultaneously estimate the inputs and outputs of the combined unit. iii) Unlike the existing methods in the InvDEA-based merging literature, the negative data do not need to be transferred to positive data. Finally, a numerical example is used to explain and validate the model proposed in this paper.