The master Malmquist index measurement using DEA-based weighted average efficiency

The Malmquist index, based on data envelopment analysis (DEA) models, is the prominent index for measuring the relative productivity change of decision-making units (DMUs) in multiple time periods. This study presents new insight into the Malmquist index for measuring the productivity change of a master unit (master-DMU) that encompasses a set of units, its sub-DMUs, in multiple time periods. This is achieved by providing a framework for measuring productivity changes at the master level for the master-DMU regarding productivity changes at the sub-level for all sub-DMUs. The suggested index is illustrated by means of a real-world example from banking.