Interior point methods in DEA to determine non‐zero multiplier weights

This is a study on the generation of non‐zero weights in DEA using interior point methods. The purpose is to generate these weights efficiently and in a manner that can be replicated independently. There is a clear demand for non‐zero multiplier weights in DEA for use to price the attributes. We introduce new LP formulations specifically designed to provide access to the full set of multiplier weights at the DMU being scored. Multiplier weights in DEA are obtained by solving any one of several multiplier linear programs (LPs). These weights are a fundamental aspect of DEA and have many uses and interpretations including determining marginal rates of substitution. Obtaining usable values from multiplier weights can be problematic due to the way DEA LPs are formulated and solved. For example, extreme efficient DMUs generate multiple optima in standard multiplier LPs. This is also true of any efficient or virtual DMU on a face of the production possibility set with less than full dimension. Another problem arises when the LP generates optimal solutions where one or more of the multipliers are zero. An important class of interior point algorithms for LP known as ‘path‐following’ methods addresses these two issues about finding optimal multiplier weights in DEA: (1) reproducibility, that is, the optimal solution is independent of a starting point since it is generated by applying a well‐defined optimization criterion; (2) non‐zero multipliers, whereby the multiplier weights associated with an optimal solution for a point in the efficient frontier are never zero. In the process of exploring these methods for DEA we introduce the ‘multiplier generator’ DEA LP formulated to provide access to all multiplier vectors for points on the efficient frontier. Our results provide prescriptions and recommendations for using path‐following solvers in DEA.