A general series network slacks-based measure approach for non-controllable inputs and undesirable outputs in mixed integer data envelopment analysis: An application to airport operations

Efficiency evaluation of many production systems often faces three main issues, which are: (i) how can undesirable outputs accompanied with desirable outputs be treated, (ii) how can inputs that are beyond the control (i.e., non-controllable) of the decision-making units (DMUs) be handled, and (iii) how can data that only takes integer values be handled. Additionally, the internal network structure of DMUs may be ignored in some production systems. To consider the internal network structure of DMUs, a novel network slacks-based measure (NSBM) approach was first proposed by Tone and Tsutsui (2009), which assumes disproportionate changes in inputs and outputs. However, Tone and Tsutsui's (2009) approach did not handle these three issues. This research thus proposes a mixed integer NSBM approach in non-controllable inputs and undesirable outputs for general series network systems. The proposed approach has been applied for modelling and benchmarking the operations of 39 Spanish airports. To validate the impact of proposing non-controllable inputs and undesirable outputs in mixed integer values into the existing NSBM approach, a comparative analysis between the existing approach and the proposed approach has been applied. The comparison indicates that the proposed factors have properly been integrated into the existing approach. The proposed approach is quite general and can be harmonised with different series network topologies and returns to scale technologies.