TY - JOUR

T1 - Measurement of returns-to-scale using interval data envelopment analysis models

AU - Hatami-Marbini, Adel

AU - Ghelej Beigi, Zahra

AU - Hougaard, Jens Leth

AU - Gholami, Kobra

N1 - Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2018/3/1

Y1 - 2018/3/1

N2 - The economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterised by intervals. For instance, the heat losses of the Combined production of Heat and Power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study.

AB - The economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterised by intervals. For instance, the heat losses of the Combined production of Heat and Power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study.

KW - Data envelopment analysis

KW - Interval data

KW - Returns-to-scale

UR - http://www.scopus.com/inward/record.url?scp=85042942736&partnerID=8YFLogxK

U2 - 10.1016/j.cie.2017.12.023

DO - 10.1016/j.cie.2017.12.023

M3 - Article

AN - SCOPUS:85042942736

VL - 117

SP - 94

EP - 107

JO - Computers and Industrial Engineering

JF - Computers and Industrial Engineering

SN - 0360-8352

ER -