A combinatorial data envelopment analysis with uncertain interval data with application to ICT evaluation

Information and Communication Technologies (ICTs) have been extensively adopted by firms worldwide due to the significant positive effect on their performance. This fact contrasts with the uncertainty faced by decision makers when entering a country and selecting local firms with which to interact. Consider selecting Decision Making Units (DMUs) according to their relative efficiency, this efficiency being determined via Data Envelopment Analysis (DEA) based on the potential inputs consumed and outputs produced. The values of these variables are uncertain and defined through interval evaluations. Assume now that the interactions may be interrupted several times and new DMUs selected in place of previous ones. The new DMUs may require higher or lower amounts of inputs to produce variable amounts of outputs. The consequences derived from the potential realizations resolving the uncertainty should be incorporated into the DEA problem when deciding which DMUs to interact with and in which order. We study the combinatorial decision framework arising from the potential interactions with new DMUs. A numerical example is provided to complement the problem statement and outline the drawbacks of the existing approaches. It is shown that the selected DMUs and their order may differ substantially when accounting for the complementarities existing among all the DMUs. Moreover, the selection process and any subsequent decision vary with the number of modifications considered relative to the DMU initially selected. A case study analyzing the productive and environmental efficiency of a group of European countries displaying uncertain interval levels of ICT development is presented.