Finding efficient assignments: An innovative DEA approach

Finding and classifying all efficient assignments for a Multi-Criteria Assignment Problem (MCAP) is one of the controversial issues in Multi-Criteria Decision Making (MCDM) problems. The main aim of this study is to utilize Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state and prove some theorems to clarify the relationships between DEA and MCAP and then design a new two-phase approach to find and classify a set of efficient assignments. In Phase I, we formulate a new Mixed Integer Linear Programming (MILP) model, based on the Additive Free Disposal Hull (FDH) model, to gain an efficient assignment and then extend it to determine a Minimal Complete Set (MCS) of efficient assignments. In Phase II, we use the BCC model to classify all efficient solutions obtained from Phase I as supported and non-supported. A 4 × 4 assignment problem, containing two cost-type and single profit-type of objective functions, is solved using the presented approach.