Robust approach to DEA technique for supplier selection problem: A case study at Supplying Automative Parts Company (SAPCO)

Document Type : Research Paper


Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran


In many industries such as automotive industry, there are a lot of suppliers dealing with the final products manufacturer. With growing numbers of suppliers, the suppliers’ efficiency measurement often becomes the most significant concern for manufacturers. Therefore, various performance measurement models such as DEA, AHP, TOPSIS, are developed to support supplier selection decisions. After an exhaustive review of the supplier selection methods, we employ data envelopment analysis (DEA) for computing the relative efficiency of the suppliers and introducing the most efficient supplier as a benchmark. In reality, there are large amounts of uncertainty regarding the suppliers’ measurements; therefore, we propose the robust optimization approach to the real application of DEA (RDEA). In this approach, uncertainties about incomes and outcomes of decision making units (DMUs) are involved in the relative suppliers’ efficiencies. The proposed RDEA approach is utilized for the selection of suppliers which manufacture the automotive safety components in Supplying Automotive Parts Company (SAPCO), an Iranian leading automotive enterprise. Numerical example will illustrate how our proposed approach can be used in the real supplier selection problem when considerable uncertainty exists regarding the suppliers’ input and output data.


Albino V, Garavelli AC (1998). A Neural Network Application to Subcontractor Rating in
Construction Firms. International Journal of Project Management, 16: 9-14.
Arunkumar N, Karunamoorthy, L, Anand, S, Babu, TR (2006). Linear Approach for Solving a
Piecewise Linear Vendor Selection Problem of Quantity Discounts Using Lexicographic Method. The
International Journal of Advanced Manufacturing Technology, 28: 1254-1260.
Banker RD (1993). Maximum Likelihood, Consistency and Data Envelopment Analysis: a Statistical
Foundation. Management science, 39: 1265-1273.
Bayazit O (2006). Use of Analytic Network Process in Vendor Selection Decisions. Benchmarking:
An International Journal, 13: 566-579.
Bertsimas D, Sim M (2004). The Price of Robustness. Operations research, 52: 35-53.
Bertsimas D, Sim, M (2003). Robust Discrete Optimization and Network Flows. Mathematical
Programming, 98: 49-71.
Bertsimas D, Sim M (2006). Tractable Approximations to Robust Conic Optimization
Problems. Mathematical Programming, 107: 5-36.
Ben-Tal A, Nemirovski A (2000). Robust Solutions of Linear Programming Problems Contaminated
with Uncertain Data. Mathematical Programming, 88: 411-424.
Bevilacqua M, Petroni A (2002). From Traditional Purchasing to Supplier Management: a Auzzy
Logic-based Approach to Supplier Selection. International Journal of Logistics, 5: 235-255.
Bhutta KS, Huq F (2002). Supplier Selection Problem: a Comparison of the Total Cost of Ownership
and Analytic Hierarchy Process Approaches. Supply Chain Management: An International Journal, 7:
Bradley E, Tibshirani R (1993). An Introduction to the Bootstrap. CRC press, Boca Raton, Florida,
Cakravastia A, Takahashi K (2004). Integrated Model for Supplier Selection and Negotiation in a
Make-to-order Environment. International Journal of Production Research, 42: 4457-4474.
Cebi F, Bayraktar D (2003). An Integrated Approach for Supplier Selection. Logistics Information
Management, 16: 395-400.
Chan, FS (2003). Interactive Selection Model for Supplier Selection Process: an Analytical Hierarchy
Process Approach. International Journal of Production Research, 41: 3549-3579.
Chang SL, Wang RC, Wang SY (2006). Applying Fuzzy Linguistic Quantifier to Select Supply
Chain Partners at Different Phases of Product Life Cycle. International Journal of Production
Economics, 100: 348-359.
Charnes A, Cooper WW, Rhodes E (1978). Measuring the Efficiency of Decision Making
Units. European Journal of Operational Research, 2: 429-444.
Supply Chain Management. International Journal of Production Economics, 102: 289-301.
Choy KL, Lee WB, Lo V (2002). An Intelligent Supplier Management Tool for Benchmarking
Suppliers in Outsource Manufacturing. Expert Systems with Applications, 22: 213-224.
Choy KL, Lee WB (2003). A Generic Supplier Management Tool for Outsourcing
Manufacturing. Supply Chain Management: An International Journal, 8: 140-154.
Choy KL, Lee WB, Lo V (2004). Development of a Case Based Intelligent Supplier Relationship
Management System–Linking Supplier Rating System and Product Coding System. Supply Chain
Management: An International Journal, 9: 86-101.
Cooper WW, Seiford LM, Zhu J (Eds.) (2011). Handbook on Data Envelopment Analysis. Springer
Science+ Business Media.
Dahel NE (2003). Vendor Selection and Order Quantity Allocation in Volume Discount
Environments. Supply Chain Management: An International Journal,8: 335-342.
Degraeve Z, Roodhooft F (1998). Determining Sourcing Strategies: a Decision Model Based on
Activity and Cost Driver Information. Journal of the Operational Research Society: 781-789.
Degraeve Z, Roodhooft F (1999). Improving the Efficiency of the Purchasing Process Using Total
Cost of Ownership Information: The case of heating electrodes at Cockerill Sambre SA. European
Journal of Operational Research,112: 42-53.
Degraeve Z, Roodhooft F (2000). A Mathematical Programming Approach for Procurement Using
Activity Based Costing. Journal of Business Finance & Accounting, 27: 69-98.
Dickson GW (1966). An Analysis of Vendor Selection Systems and Decisions. Journal of
Purchasing, 2: 5-17.
Dulmin R, Mininno V (2003). Supplier Selection Using a Multi-criteria Decision Aid
Method. Journal of Purchasing and Supply Management, 9: 177-187.
Feng DZ, Chen LL, Jiang MX (2005, June). Vendor Selection in Supply Chain System: An Approach
Using Fuzzy Decision and AHP. In Services Systems and Services Management, 2005. Proceedings
of ICSSSM'05. p. 721-5.
Figueira J, Greco S, Ehrgott M (Eds.). (2005). Multiple Criteria Decision Analysis: State of the Art
Surveys. Springer, New York, USA.
Chamodrakas I, Batis D, Martakos D (2010). Supplier Selection in Electronic Marketplaces Using
Satisficing and Fuzzy AHP. Expert Systems with Applications, 37: 490-498.
Ghodsypour S H, O'brien C (1998). A Decision Support System for Supplier Selection Using an
Integrated Analytic Hierarchy Process and Linear Programming. International journal of production
economics, 56: 199-212.
Ghodsypour S H, O'brien C (2001). The Total Cost of Logistics in Supplier Selection, under
Conditions of Multiple Sourcing, Multiple Criteria and Capacity Constraint. International Journal of
Production Economics, 73: 15-27.
Giokas DI, Pentzaropoulos GC (2008). Efficiency Ranking of the OECD Member States in the Area
of Telecommunications: A composite AHP/DEA study. Telecommunications Policy, 32: 672-685.
Guo P, Tanaka H (2001). Fuzzy DEA: a Perceptual Evaluation Method. Fuzzy sets and systems, 119:149-160.
Hajidimitriou YA, Georgiou AC (2002). A Goal Programming Model for Partner Selection Decisions
in International Joint Ventures. European Journal of Operational Research, 138: 649-662.
Ho W, Xu X, Dey PK (2010). Multi-criteria Decision Making Approaches for Supplier Evaluation
and Selection: A Literature Review. European Journal of Operational Research, 202: 16-24.
Holand SM (2008). Principal Components Analysis (PCA), Department of Geology, University of
Georgia, Athens, GA.
Ip WH, Yung KL, Wang D (2004). A Branch and Bound Algorithm for Sub-Contractor Sselection in
Agile Manufacturing Environment. International Journal of Production Economics, 87: 195-205.
Kahraman C, Cebeci U, Ulukan Z (2003). Multi-criteria Supplier Selection Using Fuzzy
AHP. Logistics Information Management, 16: 382-394.
Kameshwaran S, Narahari Y, Rosa CH, Kulkarni DM, Tew JD (2007). Multiattribute Electronic
Procurement Using Goal Programming. European Journal of Operational Research, 179: 518-536.
Kao C, Liu ST (2000). Fuzzy Efficiency Measures in Data Envelopment Analysis. Fuzzy sets and
systems, 113: 427-437.
Karpak B, Kumcu E, Kasuganti RR (2001). Purchasing Materials in the Supply Chain: Managing a
Multi-Objective Task. European Journal of Purchasing & Supply Management, 7: 209-216.
Keeney RL, Raiffa H (1993). Decisions with Multiple Objectives: Preferences and Value Tradeoffs.
Cambridge University Press, Cambridge, UK.
Kumar J, Roy N (2010). A Hybrid Method for Vendor Selection Using Neural
Network. International Journal of Computer Applications, 11: 35-40.
Kumar M, Vrat P, Shankar R (2004). A Fuzzy Goal Programming Approach for Vendor Selection
Problem in a Supply Chain. Computers & Industrial Engineering, 46: 69-85.
Kwong CK, Ip, WH, Chan, JWK (2002). Combining Scoring Method and Fuzzy Expert Systems
Approach to Supplier Assessment: a Case Study.Integrated manufacturing systems, 13: 512-519.
Land KC, Lovell CA, Thore S (1993). Chance‐constrained Data Envelopment Analysis. Managerial
and Decision Economics, 14: 541-554.
Lau HC, Lau PK, Fung RY, Chan FT, Ip, RW (2005). A Virtual Case Benchmarking Scheme for
Vendors' Performance Assessment. Benchmarking: An International Journal, 12: 61-80.
León T, Liern V, Ruiz JL, Sirvent I (2003). A Fuzzy Mathematical Programming Approach to the
Assessment of Efficiency with DEA Models. Fuzzy Sets and Systems, 139: 407-419.
Li CC, Fun, YP, Hung JS (1997). A New Measure for Supplier Performance Evaluation. IIE
transactions, 29: 753-758.
Lin CWR., Chen HYS (2004). A Fuzzy Strategic Alliance Selection Framework for Supply Chain
Partnering under Limited Evaluation Resources. Computers in Industry, 55: 159-179.
Liu FHF, Hai HL (2005). The Voting Analytic Hierarchy Process Method for Selecting
Supplier. International Journal of Production Economics, 97: 308-317.
Mendoza A, Ventura JA (2008). An Effective Method to Supplier Selection and Order Quantity
Allocation. International Journal of Business and Systems Research, 2: 1-15.
Min H (1994). International Supplier Selection: A Multi-attribute Utility Approach. International Journal of Physical Distribution & Logistics Management, 24: 24-33.
Morlacchi P (1999, March). Vendor Evaluation and Selection: the Design Process and a Fuzzyhierarchical
Model. In Proceedings of the 8th IPSERA Conference, Dublin.
Noorul Haq A, Kannan G (2006). Design of an Integrated Supplier Selection and Multi-echelon
Distribution Inventory Model in a Built-to-order Supply Chain Environment. International Journal of
Production Research, 44: 1963-1985.
Nydick, RL, Hill, RP (1992). Using the Analytic Hierarchy Process to Structure the Supplier
Selection Procedure. International Journal of Purchasing and Material Management, 28: 31-36.
Ohdar R, Ray PK (2004). Performance Measurement and Evaluation of Suppliers in Supply Chain: an
Evolutionary Fuzzy-based Approach. Journal of Manufacturing Technology Management, 15: 723-
Olesen OB, Petersen, NC (1995). Chance Constrained Efficiency Evaluation. Management
Science, 41: 442-457.
Petroni A, Braglia M (2000). Vendor Selection Using Principal Component Analysis. Journal of
supply chain management, 36: 63-69.
Pi WN, Low C (2006). Supplier Evaluation and Selection via Taguchi Loss Functions and an
AHP. The International Journal of Advanced Manufacturing Technology, 27: 625-630.
Premachandra IM (2001). A Note on DEA vs Principal Component Analysis: An Improvement to Joe
Zhu's Approach. European Journal of Operational Research, 132: 553-560.
Saaty TL (1990). Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority
Setting Resource Allocation. RWS publications, Pittsburgh, PA.
Saen RF (2007). A New Mathematical Approach for Suppliers Selection: Accounting for Nonhomogeneity
is Important. Applied Mathematics and Computation, 185: 84-95.
Sadjadi SJ, Omrani H (2008). Data Envelopment Analysis with Uncertain Data: An Application for
Iranian Electricity Distribution Companies. Energy Policy, 36: 4247-4254.
Sadjadi SJ, Omrani H (2010). A Bootstrapped Robust Data Envelopment Analysis Model for
Efficiency Estimating of Telecommunication Companies in Iran. Telecommunications Policy, 34:
Saen RF (2007). A New Mathematical Approach for Suppliers Selection: Accounting for Nonhomogeneity
is Important. Applied Mathematics and Computation, 185: 84-95.
Simar L, Wilson PW (1998). Sensitivity Analysis of Efficiency Scores: How to Bootstrap in
Nonparametric Frontier Models. Management science, 44: 49-61.
Simar L, Wilson PW (2000). A General Methodology for Bootstrapping in Non-parametric Frontier
Models. Journal of applied statistics, 27: 779-802.
Sha DY, Che ZH (2005). Supply Chain Network Design: Partner Selection and
Production/Distribution Planning Using a Systematic Model. Journal of the Operational Research
Society, 57: 52-62.
Shyur HJ, Shih HS (2006). A Hybrid MCDM Model for Strategic Vendor Selection. Mathematical
and Computer Modelling, 44: 749-761.
Talluri S, Baker RC (2002). A Multi-phase Mathematical Programming Approach for Effective
Supply Chain Design. European Journal of Operational Research, 14: 544-558.
Tahriri F, Osman MR, Ali A, Yusuff RM (2008). A Review of Supplier Selection Methods in Manufacturing Industries. Suranaree Journal of Science and Technology, 15: 201-208.
Talluri S, Narasimhan R (2003). Vendor Evaluation with Performance Variability: a Max–Min
Approach. European Journal of Operational Research,146: 543-552.
Teixeira de Almeida A (2001). Multicriteria Decision Making on Maintenance: Spares and Contracts
Planning. European Journal of Operational Research, 129: 235-241.
Teixeira de Almeida A (2007). Multicriteria Decision Model for Outsourcing Contracts Selection
Based on Utility Function and ELECTRE Method. Computers & Operations Research, 34: 3569-
Timmerman E (1987). An Approach to Vendor Performance Evaluation. Engineering Management
Review, IEEE, 15: 14-20.
Von Neumann J, Morgenstern O (1946). Theory of Games and Economic behavior (commemorative
edition). Princeton university press, Princeton, USA.
Wang G, Huang SH, Dismukes JP (2004). Product-driven Supply Chain Selection Using Integrated
Multi-Criteria Decision-Making Methodology. International journal of production economics, 91: 1-
Wang G, Huang SH, Dismukes JP (2005). Manufacturing Supply Chain Design and Evaluation. The
International Journal of Advanced Manufacturing Technology, 25: 93-100.
Wang J, Zhao R, Tang W (2008). Fuzzy Programming Models for Vendor Selection Problem in a
Supply Chain. Tsinghua Science & Technology, 13: 106-111.
Weber CA, Current JR, Desai A (2000). An Optimization Approach to Determining the Number of
Vendors to Employ. Supply Chain Management: An International Journal, 5: 90-98.
Weber CA, Current JR, Benton WC (1991). Vendor Selection Criteria and Methods. European
journal of operational research, 50: 2-18.
Wen M, Li H (2009). Fuzzy Data Envelopment Analysis (DEA): Model and Ranking
Method. Journal of Computational and Applied Mathematics, 223: 872-878.
Wong YH, Beasley JE (1990). Restricting Weight Flexibility in Data Envelopment Analysis. Journal
of the Operational Research Society: 829-835.
Xia W, Wu Z (2007). Supplier Selection with Multiple Criteria in Volume Discount
Environments. Omega, 35: 494-504.
Yusuff RM, Yee KP, Hashmi MSJ (2001). A Preliminary Study on the Potential Use of the
Analytical Hierarchical Process (AHP) to Predict Advanced Manufacturing Technology (AMT)
Implementation. Robotics and Computer-Integrated Manufacturing, 17: 421-427.
Zadeh LA (1965). Fuzzy Sets. Information and control, 8: 338-353.
Zeng ZB, Li Y, Zhu W (2006). Partner Selection with a Due Date Constraint in Virtual
Enterprises. Applied Mathematics and Computation, 175: 1353-1365.
Zenz G J, Thompson, GH (1994). Purchasing and the Management of Materials, Wiley, New Jersey,
Zhang Y, Bartels R (1998). The Effect of Sample Size on the Mean Efficiency in DEA with an
Application to Electricity Distribution in Australia, Sweden and New Zealand. Journal of Productivity Analysis, 9: 187-204.
Zhu J (1998). Data Envelopment Analysis vs. Principal Component Analysis: An Illustrative Study of
Economic Performance of Chinese Cities. European Journal of Operational Research, 111: 50-61.
Zhu J (2004). Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile
Telecommunication Company. Operations Research, 52: 323-329.