Abstract
This paper investigates the problem of efficiency measurement for parallel systems with two components based on Stackelberg game theory, while some inputs/outputs are fuzzy numbers. Conventional DEA models treat DMUs as “Black Boxes”. While in this paper, we propose a new parallel fuzzy DEA model to calculate the efficiency scores for each DMU’s whole system and its sub-systems. Through the Stackelberg (leader–follower) game theory, the whole system’s efficiency score of each DMU is decomposed into a set of efficiency scores for its sub-systems. This approach is independent of the alpha -cut which reduces the computational efforts. In order to show our method, we use the data from Beasley (J Oper Res Soc 46(4):441–452, 1995) to measure the fuzzy efficiency of the teaching and research efficiencies of chemistry departments in UK universities.
Highlights
Data envelopment analysis (DEA), introduced by Charnes et al (1978), is an approach for identifying best practices of peer decision making units (DMUs), in the presence of multiple inputs and outputs
DEA can evaluate the relative efficiency of a set of DMUs, it cannot identify the sources of inefficiency in the DMUs because conventional DEA models view DMUs as “black boxes” that consume a set of inputs to produce a set of outputs
Parallel processes may not be of important, for example, the parallel processes may have leader–follower relationship. To approach this kind of relationship in fuzzy parallel DEA models, we propose a fuzzy parallel DEA method based on Stackelberg game theory in section
Summary
Data envelopment analysis (DEA), introduced by Charnes et al (1978), is an approach for identifying best practices of peer decision making units (DMUs), in the presence of multiple inputs and outputs. Some processes in parallel systems are not of important, for example, there are usually two functional departments in colleges or universities–teaching and research, which uses general expenditure and equipment expenditure and teachers as inputs. The objective of the paper is to calculate the system and process efficiency for parallel systems in the fuzzy environment based on Stackelberg game theory. 2, calculation of the system and process efficiencies using the conventional parallel DEA model based on Stackelberg game theory is reviewed. 4, we present a case study of measuring the teaching and research efficiencies of 52 chemistry departments in UK universities to explain how the proposed model is applied to measure the fuzzy efficiencies of parallel systems with two components based on Stackelberg game theory.
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