A slacks-based Measure of Efficiency for Parallel and Series Production Systems

Abstract

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision making units (DMUs) that convert multiple inputs into multiple outputs. In many cases, production systems may have internal or network structures, such as series and parallel structures, which are composed of several processes interacting with each other. In the last two decades, several authors have proposed DEA models which usually utilize the radial measure to calculate the efficiency of the DMUs with internal structure. In this paper, we first introduce a non-radial DEA model in the slacks-based measure (SBM) framework for evaluating the overall efficiency of parallel production systems by considering the parallel relationship between sub-processes. We will, then extend the methodology to series production systems. A numerical experiment is used to demonstrate and compare the results with obtained using new methods and show the application of the proposed approach.

Key words and phrases. Data envelopment analysis (DEA); Decision making unit (DMU); Efficiency; Series and parallel production systems; Slacks-based measure (SBM).

2010 Mathematics Subject Classification. 90C05