Using data envelopment analysis to solve unconstrained two-objective binary integer linear programming

A subset of projects, from a set of feasible projects, is treated as a portfolio. The problem of selecting and evaluating all possible collective projects is modeled as unconstrained binary integer linear programming (BILP). Data envelopment analysis (DEA) is an effective method for classifying all portfolios into efficient and inefficient subgroups. In this paper, we focus on the single input and output case and use DEA as a tool to solve the two-objective BILP. The inherent relationships between output–input ratios of projects, and DEA portfolio efficiencies are presented in this paper. These findings enable the efficient and inefficient portfolios to be identified by ratio analysis. Moreover, if project with non-positive input and/or output is included in the decision set, our method is also valid through changing variables from the original model.