CAR-DEA: Context-Dependent Assurance Regions in DEA

Assurance region (AR) restrictions on multipliers in data envelopment analysis (DEA) have been applied extensively in many performance measurement settings. They facilitate the derivation of multiplier values that reflect the reality of the problem situation under study. In measuring the operational efficiency of bank branches, for example, output multipliers would generally represent unit processing times for branch transactions such as deposits. AR restrictions on these multipliers are intended to ensure that the (multiplier) values assigned to the various outputs are relatively of the proper size. Current AR-DEA models presume that multiplier restrictions apply uniformly across all decision-making units (DMUs) in the analysis set. Such models can have severe shortcomings, however, in those situations where different circumstances prevail for some DMUs than for others. In the context of bank branches, for example, two sets of branches, whose transaction times are known to be different from each other, would generally require different sets of AR restrictions. This paper presents a methodology for incorporating multiple sets of AR restrictions, with each reflecting the context for a particular subset of DMUs. The resulting modified DEA model, referred to as CAR-DEA, evaluates performance in a manner that more accurately captures the circumstances in which the DMUs operate.