# Reconciled multiplicative relational two-stage network data envelopment analysis

## TL;DR

This paper introduces a new method for evaluating efficiency in two-stage systems that avoids prioritizing any stage and ensures unique results.

## Contribution

The novel RMR model uses data reconciliation to fairly assess efficiency without bias or non-unique solutions.

## Key findings

- The RMR model provides unique efficiency values for all processes simultaneously.
- It solves the non-uniqueness problem in relational two-stage DEA models.
- The model is useful when no decision-making units are preferred over others.

## Abstract

Relational two-stage network DEA (data envelopment analysis) is an approach for two-stage systems, where all input, output and the intermediate products have same weights regardless of which process they are related. One of the main approaches to relational model is the multiplicative relational approach where main process efficiency is the product of two sub-process efficiencies. A shortcoming of the relational model is that the solution of the sub-process efficiencies may not be unique. Researchers have developed some models to overcome this problem, like prioritizing one sub-process to the other or assessing the sub-process efficiencies first and then the main process efficiency. In this study, a novel methodology is presented for a fairer efficiency assessment, where none of the processes is prioritized.•Reconciled Multiplicative Relational (RMR) model presented in this study uses data reconciliation method to determine maximum efficiency values for all processes simultaneously within the relational constraints.•RMR model has unique efficiency assessment solution, which solves the non-uniqueness problem and useful where none of the DMUs are preferred to another or there is no previous information in that matter.

Reconciled Multiplicative Relational (RMR) model presented in this study uses data reconciliation method to determine maximum efficiency values for all processes simultaneously within the relational constraints.

RMR model has unique efficiency assessment solution, which solves the non-uniqueness problem and useful where none of the DMUs are preferred to another or there is no previous information in that matter.

Graphical Abstract.Image, graphical abstract

Graphical Abstract.