1. OPSM 405 Service Operations Management
Koç University
OPSM 405 Service Operations Management
Class 24:
DEA
Zeynep Aksin

2. Burger Palace Example
Service unit meals sold labor-hrs material dollars

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

4. 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

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

6. 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.

7. Unit 4’s Sensitivity

8. If Unit 4 were efficient
0.778*inputs for unit * inputs for unit 6 =
0.778 (4 labor hours) (10 labor hours)
($100) ($50)
= labor hours, $88.9
currently
6 labor hours , $ 100

9. 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

10. 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?

11. 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.