A data envelopment analysis approach for resource allocation and reallocation in a noncooperative decision-making environment

The efficient allocation of resources among sub-units constitutes a classic challenge in operations research and management science. In contexts characterised by incomplete market information, data envelopment analysis (DEA) has been successfully employed to address such allocation problems. Prevailing models typically assume a centralised decision-making environment with a central decision maker (CDM) overseeing all sub-units. In practice, however, decentralised environments without a powerful CDM are common, in which sub-units must compete for resources. To address this gap, this paper develops a DEA-based resource allocation model tailored for non-cooperative settings. An iterative solution algorithm is designed to derive a stable average game allocation scheme. Furthermore, the proposed model is extended to a reallocation scenario, in which original variable resources can be reallocated. Lastly, we use a numerical example to illustrate the proposed models and then apply our approach to address an additional capital allocation across universities in the Spanish public university system. The results demonstrate that the reallocation model yields higher total outputs than the allocation model when the reallocation of original resources is permissible.