| | Reference | NDEA topology | NDEA model | # DMUs | SC sector | Variables (inputs, outputs and intermediate) |
| | Liang et al. [17] | two stages in series | multiplier formulation, average individual stages eff. | 10 | not specified | Labour, Operating cost, Shipping cost, Number # units of product A shipped, # units of product B shipped, Sales, Profit |
| | Alfonso et al. [18] | four stages in series | envelopment formulation, input-oriented NSBM eff. | 5 | leather | Stock of equipment, Equipment’s average years of service, Number of employees, Capital stock, Operational costs, Sales, Return On Investment, Requisitions rate, Average lead time, Orders arrival rate, Average time of the agent’s payment, etc. |
| | Khalili-Damghani and Tavana [19] | convergent multiple stages in series | fuzzy DEA formulation, radial efficiency | 40 | dairy product | Providers of agility in sourcing, Capabilities of agility in sourcing, Performance of sourcing, Providers of agility in making, Capabilities of agility in making, Performance of making, Providers of agility in delivery, Capabilities of agility in delivery, Performance of delivery, Final goals of SC |
| | Tavana et al. [20] | multiple layers in series with parallel processes | envelopment formulation, network epsilon-based model | 10 | semiconductor | On-time delivery standard deviation, supplier’s distance from the manufacturer, Supplier price, Supplier quality, Number of employees, Number of machines, Reciprocal of Work-in-Process, Reciprocal of Flow Time, Flexibility, Cost per dollar revenue, Service level, Customer tenure, Material flow, etc. |
| | Shafiee et al. [21] | four-process complex network topology | multiplier formulation, radial efficiency | 22 | food industry | Production capacity utilization, Average number of on time delivery per year, Total inventory cost, Customer response time, Volume of new goods sold, Volume of qualified delivery goods per year, Return on investment, Gross revenue, Profit before tax, Cost of information sharing, etc. |
| | Mirhedayatian et al. [22] | multiple stages in series | envelopment formulation, output-oriented NSBM eff. | 10 | soft drinks | Material purchase cost, Transportation cost, Staff cost, Cost of quality, Advertising cost, Reliability cost, R&D cost, Facility technology level, Supplier flexibility, Capability of suppliers, Services, Parts per million, Eco-design cost, CO2 emission, Producer reputation, On-time delivery to customers, Customer satisfaction, etc. |
| | Khodakarami et al. [23] | two stages in series | envelopment formulation, SBM and Russell-type eff. | 27 | chemical industry | Annual cost, Annual personnel turnover, Environmental cost, Number of products from supplier to manufacturer, Partnership cost in green production plans, Number of trained personnel in the fields of job, safety, and health, Number of green products, Revenue |
| | Tavassoli et al. [24] | multiple layers in series with parallel processes | envelopment formulation, radial efficiency | 11 | air transport | Labour, Passenger-plane-km, Cargo-plane-km, Passenger-km, Ton-km |
| | Momeni et al. [25] | complex reverse logistics topology | envelopment formulation, multi-objective additive eff. | 10 | automotive | Material purchase cost, Transportation cost, Labour cost, No. of delivered parts for recycling, Transportation cost from supplier to facilities, Investment on required equipment, No. of on-time delivered parts, Percent of intact parts, Rate of customer relationship, etc. |
| | Yousefi et al. [26] | multiple stages in series | envelopment formulation, Tchebycheff eff. | 12 | conferences organization | Service staff, Host staff, Partly-prepared halls and booths, Hosts, Fully-prepared halls and booths, Experts, Extra services, Readiness for holding conference, Guests and inventors, Satisfaction of guests and inventors, Encouraging inventors, Introducing inventions to industry and market |
| | Tajbakhsh and Hassini [27] | multiple layers in series with parallel processes | envelopment formulation, input-oriented radial eff. | 27 | banking | Fixed assets, IT budget, No. of employees, Deposits, Profit, Fraction of loans recovered | | 10 | beverage | Raw material cost, Transportation cost, Supplier defect-free parts per million, Advertising cost, CO2 emission, Average reputation factor, No. of green products, Personnel cost, etc. |
| | Fu et al. [28] | multiple layers in series with parallel processes | envelopment formulation, NSBM eff. | 10 | not specified | Material purchase cost, Fixed asset maintenance cost, Transportation cost, Staff cost, Advertising cost, Gross profit, Pollutant emissions, R&D costs, Service level, No. of on-time delivered products, etc. |
| | Izadikhah and Farzipoor Saen [29] | two stages in series | envelopment formulation, weighted average of individual stages eff. | 29 | Equipment for expendable medical devices | Cost of work safety and labour health, Annual cost, Environmental cost, # units from supplier to manufacturer, No. of ISO certificates, Revenue growth rate, etc. |
| | Omrani and Keshavarz [30] | multiple layers in series with parallel processes | multiplier formulation, ratio efficiency | 4 | maritime transport | Ship purchase cost, Crew cost, Costs of spare parts+provisions+insurance, Costs of repairs, Commercial container operation cost, Commercial passenger operation cost, Lease purchasing by instalments, # of containers carried per year, # of passenger+cars carried per year, Net income, etc. |
| | Tavana et al. [31] | multiple stages in series | multiplier formulation, weighted average of individual stages eff. | 7 | cement | Capital, Cooperation experience, Transport cost, Timely delivery, Technology level, Inventory, Order amount, Order profit |
| | Motevali Haghighi et al. [32] | four stages in series | envelopment formulation, weighted average of individual stages eff. | 40 | plastic recycling | Delivery cost, Supplier rejection rate, Hazardous materials, Flexibility, Health and Safety Staff, No. of green products, Delivery cost, Service quality, on-time delivery, etc. |
| | Yousefi et al. [33] | series, parallel and series-parallel | envelopment formulation, robust fuzzy GP-NDEA | 18 | insulating windows | Eco-design costs, Workplace safety costs, Raw materials costs, Kg glass ready for installation, Profile production, Glass received, Profiles received, Cost of glasses, Cost of profiles, Number of shipped windows, Cost of windows, Transportation cost, Quality of installation, Revenue |
| | Shokri Kahi et al. [34] | series | multiplier formulation, dynamic NDEA | 17 (x3 periods) | tomato products | Environmental costs, Cost of labor safety, Other costs, Revenue from sales of raw tomatoes, Cost of purchasing tomato from farm, Volume of tomato paste, Shipping costs, Uncollected revenue, Unpaid costs, Green R&D costs, Annual profit, Degree of customer satisfaction |
| | Moslemi and Mirzazadeh [35] | four-stage series | multiplier formulation, crossefficiency, interval data | 8 | blood supply chain | Space and facilities, Costs, Intellectual capital, Budget, Waste disposal, Waste management, Loss rate, Revenue, Quality, No. of donors, Patient satisfaction, Inventory management, Social actions, Recording and archiving, Information sharing |
| | Badiezadeh et al. [36] | multi-stage series | multiplier formulation, double frontier | 9 | tomato paste | Material purchasing cost, Environmental cost,
Staff welfare cost, CO2 emission, Number of delivered products, Number of products from supplier to manufacturer, Number of green products, Revenue |
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