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DEA Based Approaches and Their Applications in Supply Chain Management Dr. Sri Talluri Professor of Supply Chain Management Presentation at the Helsinki University of Technology 1 Course Outline Introduction to Data Envelopment Analysis (DEA) DEA Models and Approaches Application Papers in Supply Chain Management 2 Introduction to DEA DEA evaluates relative efficiencies of a homogenous set of decision making units (DMUs) in the presence of multiple input and output factors Efficiency is defined as the ratio of weighted sum of outputs to weighted sum of inputs A DMU is considered efficient if it achieves a score of 1.00 DEA identifies necessary improvements required in making inefficient DMUs efficient DEA has extensively been applied in a variety of business and decision making environments that include banking, healthcare, transportation, and supply chain management 3 Some DEA Models and Approaches CCR Model (Primal and Dual) BCC Model Super Efficiency Model DEA Models with Weight Restrictions Cross-Efficiency Models in DEA Benchmarking in DEA DEA Windows Analysis DEA with Ordinal and Cardinal Factors 4 CCR Ratio Model: Primal Form s v k 1 m max u j 1 k j y kp s k 1 x jp s.t k 1 m s.t u j 1 j u x j 1 1, i x ji v k , u j 0 k , j k m s vk y ki v max s v k 1 j jp y kp 1 m k y ki u j x ji 0, i j 1 v k , u j 0 k , j where: p is the unit being evaluated; s represents the number of outputs; m represents the number of inputs; yki is the amount of output k provided by unit i; xji is the amount of input j used by unit i; vk and uj are the weights given to output k and input j, respectively. 5 CCR Ratio Model (Input-Oriented): Dual Form min x s.t x jp i ji ki y kp j i y i k i i 0 i where: represents the efficiency score of unit p; s represent the dual variables that identify the benchmarks for inefficient units. 6 CCR Ratio Model (OutputOriented): Dual Form max x s.t i ji x jp j i y i ki y kp k i i 0 i 1 Efficiency = 7 Graphical Depiction of DEA C D O1/I B1 A E Efficient Frontier B F O2/I 8 CCR Model: Illustration DMU 1 2 3 Input 1 5 8 7 Input 2 14 15 12 Output 1 Output 2 Output 3 9 4 16 5 7 10 4 9 13 Maximize 9v1 4v 2 16v3 s.t. 5u1 14u 2 1 9v1 4v 2 16v3 5u1 14u 2 0 5v1 7v 2 10v3 8u1 15u 2 0 4v1 9v 2 13v3 7u1 12u 2 0 v1 , v 2 , v3 , u1 , u 2 0 9 CCR Model: Illustration Results DMU 1 and DMU 3 are efficient (efficiency of 1.00 with no slacks) DMU 2 is inefficient (efficiency < 1.00) DMU 2 can utilize DMU 1 and DMU 3 as benchmarks for improvement See EXCEL file: DEA_Example_HUT 10 Selection of Inputs, Outputs, and units in DEA Inputs: resources (examples: workers, machines, operating expenses, budget, etc.) Outputs: actual number of products produced to a host of performance and activity measures (examples: quality levels, throughput rates, lead-time, etc.) If there are m inputs and s outputs then potentially ms DMUs can be efficient. Thus, to achieve discrimination we need substantially more units than ms 11 BCC Model CCR model considers constant returns to scale (CRS) whereas the BCC model considers variable returns to scale (VRS) min x s.t x jp i ji ki y kp i y i i i k j new constraint (convexity) 1 i i 0 i 12 Super Efficiency Model Super efficiency model allows for effective ranking of efficient DMUs s v max k 1 m u s.t j 1 s v k 1 j k y kp x jp 1 The DMU being evaluated is removed from the constraint set thereby allowing its efficiency score to exceed a value of 1.00 m k y ki u j x ji 0, i p j 1 v k , u j 0 k , j 13 DEA Model with Weight Restrictions Unrestricted weight flexibility in DEA can be resolved through weight restrictions Weight restrictions also allow for the incorporation of managerial input into DEA models Methods such as AHP and ANP can be utilized for identifying weight restriction constraints in DEA 14 DEA Model with Weight Restrictions s max v k y kp k 1 m s.t u j x jp 1 j 1 s v k 1 m k y ki u j x ji 0i j 1 j u1 u j 0, j 2,3,...,m j u1 u j 0, j 2,3,...,m a k v1 v k 0,k 2,3,...,s bk v1 v k 0,k 2,3,...,s v k ,u j 0 vk is the weight given to output k, uj is the weight given to input j, and , , a, b are nonnegative scalars. 15 Cross Efficiencies in DEA Cross efficiency in DEA allows for effective discrimination between niche performers and good overall performers Cross efficiency score of a DMU represents how well the unit is performing with respect to the optimal weights of another DMU A DMU that achieves high cross efficiency scores is considered to be a good overall performer 16 Cross Efficiency Models: Aggressive and Benevolent Approaches min v k y ki k 1 i p m s.t u j x ji 1 j 1 i p max v k y ki k 1 i p m s.t u j x ji 1 j 1 i p s s Aggressive s v k 1 m k y ki u j x ji 0, i p j 1 s v k 1 m k y kp p u j x jp 0 j 1 v k , u j 0 k , j Benevolent s v k 1 m k y ki u j x ji 0, i p j 1 s v k 1 m k y kp p u j x jp 0 j 1 v k , u j 0 k , j Where p is the relative efficiency score of DMU p obtained from the CCR model 17 Cross Efficiency Matrix DMU 1 2 3 N 1 Θ11 Θ21 Θ31 ΘN1 2 Θ12 Θ22 Θ32 ΘN2 3 Θ13 Θ23 Θ33 ΘN3 N Θ1N Θ2N Θ3N ΘNN Efficiency score of DMU 2 when evaluated with the optimal weights of DMU 1 18 Benchmarking in DEA We discussed traditional DEA benchmarking in the illustrative example Benchmarks may not be inherently similar to inefficient DMUs Virtual benchmarks do not exist in practice Benchmarking can also be performed based on the cross efficiency matrix. Use of cluster analysis on cross efficiencies 19 Windows Analysis in DEA Evaluating the performance of a DMU over time by treating it as a different entity in each period A DMU is compared to itself over time 20 Ordinal and Cardinal Factors in DEA Discuss Model in Class Sarkis and Talluri (1999)- IJPR 21 Applications in Supply Chain Management Supplier Evaluation and Rationalization (CCR DEA Model) System Performance Evaluation (Super Efficiency Model with Weight Restrictions) Strategic Sourcing (Cross-Efficiencies with Nonparametric Methods) Benchmarking of Manufacturing Cells (Clustering Methods) NPD Project Performance (BCC Model) Buyer-Supplier Negotiations (DEA Based Approach) 22 Questions 23