Development of two-stage parallel-series system with fuzzy data: A fuzzy DEA approach
- PDF / 464,358 Bytes
- 21 Pages / 595.276 x 790.866 pts Page_size
- 53 Downloads / 168 Views
METHODOLOGIES AND APPLICATION
Development of two-stage parallel-series system with fuzzy data: A fuzzy DEA approach Alka Arya1 · Sanjeet Singh2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We consider a two-stage parallel-series system having three sub-systems. The independent two sub-systems of the first stage are linked in parallel and then linked to the third sub-system of the second stage in series. The deterministic two-stage parallelseries system approach is extended to uncertain/imprecise environment where the data are represented as fuzzy numbers. Using the Zadeh extension principle, we develop a fuzzy two-stage parallel-series system to determine the lower and upper bound fuzzy efficiencies of the decision-making units with the help of α− cut and rank the DMUs using the ranking index approach. The proposed methodology is illustrated using the case of Taiwan’s non-life insurance companies. Keywords Data envelopment analysis · Two-stage parallel-series system · Fuzzy two-stage parallel-series system · Lower and upper bounds fuzzy efficiencies
1 Introduction Data Envelopment Analysis (DEA) is a linear programming based nonparametric technique for measuring the relative performance of decision-making units (DMUs) that utilize multiple inputs to produce multiple outputs. Charnes et al. (1978) first proposed the DEA models to determine the relative efficiencies of DMUs. The CCR DEA model defined the efficiency of the D MUk as the ratio of its weighted sum of inputs to weighted sum of outputs, and this ratio was maximized subject to the condition that the ratio of the weighted sum of outputs to the weighted sum of inputs of every DMU was less than or equal to one (Charnes et al. 1978). In CCR model, the efficiency of D MUk is denoted by E k and defined
Communicated by V. Loia.
B
Alka Arya [email protected] Sanjeet Singh [email protected]
1
Operations Management and Decision Sciences Area, Indian Institute of Management Kashipur, Kundeshwari, Uttarakhand 244713, India
2
Decision Sciences Area, Indian Institute of Management Lucknow, Prabandh Nagar, IIM Road, Lucknow, U.P. 226013, India
as (Charnes et al. 1978) max E k = subject to
s r =1 s
m yr k vr k / xik u ik i=1 m yr j vr k / xi j u ik ≤ 1,
r =1
j = 1, 2, 3, . . . , n,
i=1
u ik , vr k ≥ ε, ∀i, r , where u ik and vr k are the weights corresponding to ith input and r th output, respectively, for D MUk and ε is the nonArchimedean infinitesimal constant. In classical DEA models, the internal structure and operations of DMUs are not considered, and DMUs are called black box. In network structures, the system operations are divided into more than two sub-systems (processes) such as parallel, series and mixture of parallel and series structures. DEA determining the performance of DMUs using networks is called network DEA. In network DEA, DMUs are taken as system consisted of sub-system networks. The system having two networks (internal structure) in DEA is called two-stage DEA (Färe and Grosskopf 2000). In the firs
Data Loading...
