Optimal solutions of multiplier DEA models

Abstract

Conventional models of data envelopment analysis (DEA) are based on the constant and variable returns-to-scale production technologies. Any optimal input and output weights of the multiplier DEA models based on these technologies are interpreted as being the most favorable for the decision making unit (DMU) under the assessment when the latter is benchmarked against the set of all observed DMUs. In this paper we consider a very large class of DEA models based on arbitrary polyhedral technologies, which includes almost all known convex DEA models. We highlight the fact that the conventional interpretation of the optimal input and output weights in such models is generally incorrect, which raises a question about the meaning of multiplier models. We address this question and prove that the optimal solutions of such models show the DMU under the assessment in the best light in comparison to the entire technology, but not necessarily in comparison to the set of observed DMUs. This result allows a clear and meaningful interpretation of the optimal solutions of multiplier models, including known models with a complex constraint structure whose interpretation has been problematic and left unaddressed in the existing literature.

Research of the economic positioning of the Western Balkan countries using the LOPCOW and EDAS methods

“…Permanent control of key factors is a basic assumption for improving the economic performance of the economies of the Western Balkans. In addition to the application of ratio analysis, statistical analysis, and DEA analysis (Amini et al, 2019;Chen et al, 2021a, Chang et al, 2020Fenyves, & Tarnóczi, 2020;Guo, & Cai, 2020;Lee et al, 2011;Lin , 2020;Pendharkar, 2021;Podinovski et al, 2021;Rostamzadeh et al, 2021;Tone, 2002;Tsai et al, 2021), and the use of multi-criteria decision-making methods, including the LOPCOW-EDAS method, a significant role is played in this. About the classical analysis, their integrated application gives more accurate results of the achieved economic performance of the economy of the Western Balkan countries as a basis for improvement in the future by applying adequate measures.…”

Performance Measurement using DEA-Multipliers Method: A Case Study of Clean Water Companies in Indonesia

“…Traditional designs of data envelopment analysis (DEA) method consists of constant and variable returns-to-scale production techniques. In the multiplier DEA method, each optimal input and output weight built on these techniques is defined as very profitable for the decision-making unit (DMU) in the evaluation when the last is compared to the aggregate of entire supervised DMUs [4]. The industrial field's role is important for the development of the national economy in Indonesia.…”

Analysis of Determinants of Corporate Cash Holding of Listed Manufacturing Companies on the Macedonian Stock Exchange

“…It is very challenging to study the cost efficiency, ie the overall efficiency of all companies, which means trade, based on DEA ( Data Envelopment Analysis) models, as well as the method of multi-criteria decision making . The literature devoted to the development of the DEA model is very rich (Andersen, 1993;Banker, 1984;Chen, 2021, Chang, 2020Guo, 2020;Lee, 2011;Lin, 2020;Pendharkar, 2021;Tone, 2002;Dobrovich, 2021;Podinovski , 2021;Rostamzadeh, 2021). Also, an increasing number of papers are dedicated to the specifics of the analysis of the efficiency of commercial enterprises based on the DEA model (Ko, 2017;Baviera-Puig, 2020;Fenyves, 2020;Shuangyan, 2018;Pachar, 2021).…”