The weighted additive distance function

• Published in: European journal of operational research Vol. 254; no. 1; pp. 338 - 346
• Main Authors: Aparicio, Juan, Pastor, Jesus T., Vidal, Fernando
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-10-2016; Elsevier Sequoia S.A
• Subjects: Additives; Computational efficiency; Computing time; Data envelopment analysis; Distance functions; Input output analysis; Mathematical analysis; Mathematical functions; Mathematical models; Numerical analysis; Operational research; Operations research; Profit function; Studies; Vector space; Vectors (mathematics); Weighted additive model; Profit function; Weighted additive model; Data envelopment analysis; Distance functions
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2016.04.006

•The literature on the use of the weighted additive model is reviewed.•The necessity of endowing this model with a distance function structure is remarked.•A new weighted additive distance function is introduced.•The main properties of this distance and the way of implementing it are shown.•The existence of a dual relationship regarding the profit function is proved.
Distance functions in production theory are mathematical structures that characterize the belonging to the reference technology through a numerical value, behave as technical efficiency measures when the focus is analyzing an observed input–output vector within its production possibility set and present a dual relationship with some support function (profit, revenue, cost function). In this paper, we endow the well-known weighted additive models in Data Envelopment Analysis with a distance function structure, introducing the Weighted Additive Distance Function and showing its main properties.