Statistics

Entropy (arrow of time)

Combinatorics

Physics

Data mining

Engineering

Normalization (sociology)

Sociology

Demography

Rank (graph theory)

Anthropology

Process management

Balanced scorecard

Data envelopment analysis

Population

Mathematics

Computer science

Operations research

Relational database

Quantum mechanics

Grey relational analysis

Evaluation and Program Planning

Various approaches are used to measure the firms’ performance. Grey relational analysis is one of the multiple attribute decision-making methods and data envelopment analysis is used to calculate the efficiency. Regarding the importance of water and wastewater companies’ services, the present study, evaluates the performance and rank these companies by using grey relational analysis and data envelopment analysis approaches based on balanced scorecard criteria. Besides, balanced scorecard considers all levels of organization. In this research, statistical population includes thirty-five municipal water and wastewater companies in Iran for the year 2017. In order to ascertain grey relational grade, fuzzy normalization method was used then by subtracting normalized numbers from one, reference sequences obtained and in the next step, grey relational coefficient was calculated and finally, grey relational grade was determined by multiplying relative weight from Shannon entropy to relational coefficients. In order to assess companies’ efficiency in data envelopment analysis, after ascertaining input and output indices, with the assumption of constant returns to scale and output-oriented viewpoint, the efficiency scores were calculated. Also, to rank efficient units Anderson-Petersen model implemented. Results demonstrated that, grey relational analysis is a more accurate method to measure the performance of water and wastewater companies.

Improving performance evaluation based on balanced scorecard with grey relational analysis and data envelopment analysis approaches: Case study in water and wastewater companies