Introduction to DEA for Performance Evaluation in Service Management

1. Koç University OPSM 405 Service Management Class 23: Performance Evaluation: Introduction to DEA Zeynep Aksin zaksin@ku.edu.tr

2. Announcement • Class on Monday May 12 will be held in the lab SOS Z12 • Last case assignment due Wednesday May 14: Nashville National Bank

3. Last case assignment • Answer the questions: • Do you agree with Ann’s analysis? Why or why not? • If you were to redesign the analysis, what inputs and outputs would you use? Why? Explain specifically. You can also suggest new alternatives. • What are the strengths and weaknesses of this analysis? • Now take an appropriate subset of the inputs and outputs used by Ann and perform a DEA analysis using Excel Solver. Report efficiencies of the units and values of the optimal input and output weights you have chosen.

4. Performance Evaluation • Services are provided through multiple sites • Each site provides similar services • Example: branches of a bank, Starbucks stores • As managers we want to understand • How each site is performing… • Who performs better… • Who performs worse…

5. Productivity measurement • Operating ratios (e.g. man-hr/transaction) • Financial approaches (e.g. conversion to Euros)

6. Conceptually ... Productivity = Outputs Inputs Productivity

7. A graphical view: who is efficient? 3 4 6 2 7 5 Inputs Outputs 1 2 1 2 4 5 3 7 7 4 9 7 5 5 3 6 10 6 7 4.5 4.5 1

8. Traditional efficiency: who is efficient? 3 4 6 2 7 5 1 Inputs Outputs Ratio 1 2 1 0.5 2 4 5 1.25 3 7 7 1.0 4 9 7 0.77 5 5 3 0.6 6 10 6 0.6 7 4.5 4.5 1.0

9. Frontier efficiency: who is efficient? 3 4 2 6 7 5 Inputs Outputs 1 2 1 2 4 5 3 7 7 4 9 7 5 5 3 6 10 6 7 4.5 4.5 1

10. Conceptually ... Productivity = Outputs Inputs Productivity Reality is more complex ... Inputs Outputs Technology + Decision Making equipment #type A cust. facility space #type B cust. server labor quality index mgmt. labor $ oper. profit

11. Operating Units Differ • Mix of customers served • Availability and cost of inputs • Facility configuration • Processes/practices used • Examples • bank branches, retail stores, clinics, schools, etc. Questions: • How do we compare productivity of a diverse set of operating units serving a diverse set of markets? • What are the “best practice” and under-performing units? • What are the trade-offs among inputs and outputs? • Where are the improvement opportunities and how big are they?

12. Extending to multiple outputs ... Ex: Consider 8 M.D.’s working at an hospital for the same 160 hrs. in a month. Each performs exams and surgeries. Which ones are most “productive”? There is some “efficient” trade-off between the number of surgeries and exams that any one M.D. can do in a month, but what is it?

13. #6 #1 Scatter plot of outputs: efficient frontier These points are dominated by #1 and #6. “Pareto-Koopman efficiency” along the frontier - cannot increase an output (or decrease an input) without compensating decrease in other outputs (or increase in other inputs).

14. Performance “gap” 73.4% of distance to frontier How bad are the inefficient M.D.s and where are the gaps? #5 Efficiency score = 73.4%

15. DEA uses an efficient frontier to define multiple I/O productivity • Frontier defines the (observed) efficient trade-off among inputs and outputs within a set of DMUs. • Relative distance to the frontier defines efficiency • “Nearest point” on frontier defines an efficient comparison unit (hypothetical comparison unit (HCU)) • Differences in inputs and output between DMU and HCU define productivity “gaps” (improvement potential) How do we do this analysis systematically?

16. DEA: basic assumptions • Multiple units • Common inputs and outputs • can be quantitative or qualitative measures • do not need to have market valuation • however need consistency • include environmental factors to capture differences… • … yet not too many to ensure effective discrimination

17. DEA: the basic idea • One input, one output: • efficiency = output / input • multiple inputs, multiple outputs: • efficiency = weighted sum of outputs / weighted sum of inputs • how do you determine the weights • ad-hoc techniques • DEA: LP; assume each unit has its own value system • a strictly relative notion of efficiency

18. How does it work? For each unit solve: max my unit’s efficiency st. efficiency score for all other units < 1 by varying my weights on inputs and outputs where: efficiency = sum of weighted outputs sum of weighted inputs

19. In words • Imagine your own unit • You are searching over all possible weights • You stop either when your own unit’s efficiency is 1: you are efficient • Or when with the selected weights one or more of the other units have reached efficiency 1: you are inefficient • In latter case: the other units with efficiency 1 constitute your peer (reference) group • Linear programming is a systematic way of performing the above described search

20. How do we evaluate these variables ? LP Formulation: Data Model variables

21. Another way of saying the same thing max my unit’s weighted outputs st. weighted outputs < weighted inputs or (weighted outputs - weighted inputs < 0) my weighted sum of inputs = 1 by varying my weights on inputs and outputs where: efficiency = sum of weighted outputs sum of weighted inputs

22. More formally

23. Remember: next class in SOS Z12!