A financing perspective on DEA-based resource allocation and the aggregate profit inefficiency decomposition

Identifying the sources of profit inefficiency is of great importance to practitioners and academics. In this paper, we tend to uncover profit drivers from the perspective of resource allocation. Specifically, we focus particularly on the DEA-based resource allocation approach with a possible financing strategy, which is significantly different from prior studies in the sense that it not only offers a flexible way to tackle the infeasibility problem associated with the potential conflicting constraints, but also provides a relatively more profitable allocation plan by taking a possible debt into account. First, we consider the situation in which each of DMUs allocates their resources independently, and develop a corresponding decentralised resource allocation DEA model concerning a possible financing strategy. In particular, a novel concept of profit to financing is defined to establish the linkage between potential profit gain and possible financing strategy. Second, we propose a centralised resource allocation DEA model to solve the problem in which all DMUs are controlled by a central authority, and provide a novel aggregate profit inefficiency decomposition method to uncover sources of the aggregate (or industry) profit inefficiency. Finally, an example of 20 fast-food restaurants is applied to illustrate the effectiveness of our proposed method.