OPSM 405 Service Operations Management Koç University OPSM 405 Service Operations Management Class 24: DEA Zeynep Aksin zaksin@ku.edu.tr

Burger Palace Example Service unit meals sold labor-hrs material dollars 1 100 2 200 2 100 4 150 3 100 4 100 4 100 6 100 5 100 8 80 6 100 10 50

Graphical illustration of solution $ S1 200 150 S2 S4 100 S3 S5 50 S6 2 4 6 8 10 hours

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

Unit 1’s problem max 100 u1 s.t. 100 u1-2 v1-200 v2 < 0

Sensitivity analysis: shadow price The shadow price of a constraint is the unit increase in the optimal objective value per unit increase in the RHS of the constraint. Changing the RHS of a non-binding constraint by a small amount has no impact. The shadow price of the constraint is 0. Range of feasibility: the range over which the RHS value may vary without changing the value and interpretation of the shadow price.

Unit 4’s Sensitivity

If Unit 4 were efficient 0.778*inputs for unit 3 + 0.2222 * inputs for unit 6 = 0.778 (4 labor hours) + 0.222 (10 labor hours) ($100) + ($50) = 5.332 labor hours, $88.9 currently 6 labor hours , $ 100

What does DEA determine? A systematic approach to combine multiple inputs and multiple outputs inputs and outputs don’t need to have clear price or market value the best practice units the inefficient units amount of excess resource used by inefficient units best practice units that inefficient units can be compared against

Attributes and weaknesses suggests alternative paths for improvement gives units benefit of the doubt as long as data is reliable, will give reliable results misspecification of inputs and outputs can be misleading is best practice efficient?

Last case assignment: Due on Monday 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. 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.