Efficiency analysis is widely employed to evaluate decision making units (DMUs) which convert input resources into outputs. In this paper, we develop models for allocating these resources to DMUs in order to maximize the overall efficiency of the portfolio formed by these DMUs. Our models do not require complete preference information about how valuable the inputs and outputs are relative to each other. Rather, based on incomplete preference information and explicit assumptions about the DMUs’ production possibilities, they determine all efficient DMUs portfolios which are then analyzed to provide robust decision recommendations on how much resources should be allocated to each DMU. We illustrate our models by revisiting earlier case studies and show that the use of conventional efficiency analysis in guiding resource allocation decisions can cause inefficiencies.