In this paper, we develop a new mathematical model for the multi-period data envelopment analysis (MDEA) problem that attempts to circumvent the limitations of the existing MDEA models through a global approach. The proposed global MDEA model is based on modifications of some DEA axioms, enabling a decision making unit (DMU), defined with inputs and outputs of period $t,$ to be evaluated within the production possibility set (PPS) of another period $l,~t\neq l.$ Building on the properties of the global MDEA model, we also introduce the Global Progress and Regress index (GPRI) to evaluate the extent of progress or regress of a DMU over multi-period time horizons under variable returns to scale (VRS) assumption, as opposed to known productivity indices that are restricted to two successive periods and constant returns to scale (CRS) production technologies. The most salient features of the new MDEA model as well as the GPRI are highlighted using an application that involves a real-life sample of 25 bank branches considered over 4 years.