Table 1 Summary of literature on DEA...

Table 1

Summary of literature on DEA adoption in retail industry

Authors	Purpose	Method	Input variables	Output variables	Nr of DMUs
Pestana Barros and Alves (2003)	To analyse the efficiency of retail stores of a Portuguese multi-market hypermarket retailing chain	Output-oriented VRS** DEA	1. Nr of employees; 2. Cost of labour; 3. Absenteeism; 4. Area of outlets; 5. Nr of points of sale; 6. Age of the outlet; 7. Inventory; 8; Other costs	1. Revenues; 2. EBIT	47
Sellers-Rubio and Ruiz (2006)	To estimate the economic efficiency of Spanish supermarket chains	Traditional non-parametric input-oriented CRS* DEA	1. Nr of employees; 2. Nr of outlets in supermarket chain; 3. Capital invested	1. Revenues; 2. Profits	100
Perrigot and Barros (2008)	To analyse the efficiency of the French retailers in order to identify the best-practice reference enterprises. To determine the determinants of retailers' efficiency	Two-step procedure: DEA + Bootstrapped Tobit. Four DEA models are used: CRS; VRS*; cross-efficiency; super-efficiency	1. Nr of employees; 2. Total assets; 3. Total costs	1. Revenues; 2. Profits	11 companies x 5 Years
Mostafa (2009)	To measure the relative efficiency of the US specialty retailers and food consumer	Output-oriented VRS** DEA	1. Nr of employees; 2. Total assets	1. Revenues; 2. Market value; 3. Earnings per share	45
Vaz et al. (2010)	To assess efficiency in stores selling different lines of product	Network DEA. Two-stage analysis at line-of-product ad store-level	1. Floor area. 2. Value of products in stock. 3. Nr of references. 4. Value of products spoiled	1. Revenues	70
Gandhi and Shankar (2014)	To find the “best in class” between Indian retailers. To analyse the pattern of efficiency change over time. To test impacts of environmental factors on efficiency of firms	Input-oriented DEA (CRS* and VRS**); Malmquist Productivity Index, Bootstrapped Tobit Regression	1. Cost of labour; 2. Total assets	1. Profits; 2. Sales	18 companies x 3 Years
Ko et al. (2017)	To measure the efficiency of individual stores. To assess the factors that affect store efficiency	DEA + Bootstrapped Tobit Regression	1. Store size. 2. Nr of employees. 3. Nr of items. 4. Rental costs	1. Revenues. 2. Nr of customers	32
Vyt and Cliquet (2017)	To measure retail performance at store level by taking into account the stores' local market characteristics	Two-step procedure: output-oriented DEA + OLS regression of efficiency scores upon 8 local variables	1. Store size. 2. Nr of employees. 3. Product shelf space allocation	1. Revenues	38
Gong et al. (2019)	To evaluate the retailers' benefits on efficiency coming by sustainable operations. To evaluate under which internal conditions an increase of sustainable operations will determine likely an improvement in operational efficiency	Two-stage DEA (evolution of CRS* model); hierarchical regression analysis; non-linear analysis	Stage 1: Supply chain coordination (4 variables); Sustainability level (compliance, environmental, created sharing values)	Stage 1: Cost competency (4 variables); Flexibility competency (3 variables); Social competency (4 variables); Environmental competency (4 variables)	124
Gong et al. (2019)			Outputs of stage 1 are inputs for stage 2	Stage 2: Business performance (sales growth; profits growth; market share growth; ROI)	124
Huang et al. (2019)	To evaluate the performance of the allocation process in the fashion industry	Multi-stage efficiency model based on dynamic network DEA (CRS*)	1. Initial allocation quantity; 2. Replenishment quantity	1. Sales quantity; 2. Inventory quantity	52
Rouyendegh et al. (2019)	To evaluate efficiency in retail industry by using both quantitative and qualitative data	Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IF-TOPSIS) + CRS* DEA	1. Nr of employees; 2. Parking area for the customers; 3. Average number of customers per m² daily	1. Amount of money per customer trip per m² daily; 2–3. Flexibility and accessibility (qualitative variables)	21
Our contribution	To measure efficiency among a large number of retailers, by taking into account the heterogeneity in store characteristics and in the socio-demographic traits of their catchment area	Tandem Analysis: Data-driven factorial and clustering of DMUs + Output-oriented VRS** DEA	1. Average number of kitchen models presented in the store; 2. Total costs of store setup	1. Sales quantity; 2. Revenues	541

Authors	Purpose	Method	Input variables	Output variables	Nr of DMUs
Pestana Barros and Alves (2003)	To analyse the efficiency of retail stores of a Portuguese multi-market hypermarket retailing chain	Output-oriented VRS** DEA	1. Nr of employees; 2. Cost of labour; 3. Absenteeism; 4. Area of outlets; 5. Nr of points of sale; 6. Age of the outlet; 7. Inventory; 8; Other costs	1. Revenues; 2. EBIT	47
Sellers-Rubio and Ruiz (2006)	To estimate the economic efficiency of Spanish supermarket chains	Traditional non-parametric input-oriented CRS* DEA	1. Nr of employees; 2. Nr of outlets in supermarket chain; 3. Capital invested	1. Revenues; 2. Profits	100
Perrigot and Barros (2008)	To analyse the efficiency of the French retailers in order to identify the best-practice reference enterprises. To determine the determinants of retailers' efficiency	Two-step procedure: DEA + Bootstrapped Tobit. Four DEA models are used: CRS; VRS*; cross-efficiency; super-efficiency	1. Nr of employees; 2. Total assets; 3. Total costs	1. Revenues; 2. Profits	11 companies x 5 Years
Mostafa (2009)	To measure the relative efficiency of the US specialty retailers and food consumer	Output-oriented VRS** DEA	1. Nr of employees; 2. Total assets	1. Revenues; 2. Market value; 3. Earnings per share	45
Vaz et al. (2010)	To assess efficiency in stores selling different lines of product	Network DEA. Two-stage analysis at line-of-product ad store-level	1. Floor area. 2. Value of products in stock. 3. Nr of references. 4. Value of products spoiled	1. Revenues	70
Gandhi and Shankar (2014)	To find the “best in class” between Indian retailers. To analyse the pattern of efficiency change over time. To test impacts of environmental factors on efficiency of firms	Input-oriented DEA (CRS* and VRS**); Malmquist Productivity Index, Bootstrapped Tobit Regression	1. Cost of labour; 2. Total assets	1. Profits; 2. Sales	18 companies x 3 Years
Ko et al. (2017)	To measure the efficiency of individual stores. To assess the factors that affect store efficiency	DEA + Bootstrapped Tobit Regression	1. Store size. 2. Nr of employees. 3. Nr of items. 4. Rental costs	1. Revenues. 2. Nr of customers	32
Vyt and Cliquet (2017)	To measure retail performance at store level by taking into account the stores' local market characteristics	Two-step procedure: output-oriented DEA + OLS regression of efficiency scores upon 8 local variables	1. Store size. 2. Nr of employees. 3. Product shelf space allocation	1. Revenues	38
Gong et al. (2019)	To evaluate the retailers' benefits on efficiency coming by sustainable operations. To evaluate under which internal conditions an increase of sustainable operations will determine likely an improvement in operational efficiency	Two-stage DEA (evolution of CRS* model); hierarchical regression analysis; non-linear analysis	Stage 1: Supply chain coordination (4 variables); Sustainability level (compliance, environmental, created sharing values)	Stage 1: Cost competency (4 variables); Flexibility competency (3 variables); Social competency (4 variables); Environmental competency (4 variables)	124
Gong et al. (2019)			Outputs of stage 1 are inputs for stage 2	Stage 2: Business performance (sales growth; profits growth; market share growth; ROI)	124
Huang et al. (2019)	To evaluate the performance of the allocation process in the fashion industry	Multi-stage efficiency model based on dynamic network DEA (CRS*)	1. Initial allocation quantity; 2. Replenishment quantity	1. Sales quantity; 2. Inventory quantity	52
Rouyendegh et al. (2019)	To evaluate efficiency in retail industry by using both quantitative and qualitative data	Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IF-TOPSIS) + CRS* DEA	1. Nr of employees; 2. Parking area for the customers; 3. Average number of customers per m² daily	1. Amount of money per customer trip per m² daily; 2–3. Flexibility and accessibility (qualitative variables)	21
Our contribution	To measure efficiency among a large number of retailers, by taking into account the heterogeneity in store characteristics and in the socio-demographic traits of their catchment area	Tandem Analysis: Data-driven factorial and clustering of DMUs + Output-oriented VRS** DEA	1. Average number of kitchen models presented in the store; 2. Total costs of store setup	1. Sales quantity; 2. Revenues	541

Note(s): *CRS = constant returns to scale. It is also known as CCR: Charnes, Cooper, Rhodes (1978). **VRS = variable returns to scale. It is also known as BCC: Banker et al., (1984)

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