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Ko ç Un iversity. OPSM 405 Service Management. Class 23: Performance Evaluation: Introduction to DEA. Zeynep Aksin zaksin @ku.edu.tr. Announcement. Class on Monday May 12 will be held in the lab SOS Z12 Last case assignment due Wednesday May 14: Nashville National Bank.

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opsm 405 service management

Koç University

OPSM 405 Service Management

Class 23:

Performance Evaluation:

Introduction to DEA

Zeynep Aksin

zaksin@ku.edu.tr

announcement
Announcement
  • Class on Monday May 12 will be held in the lab SOS Z12
  • Last case assignment due Wednesday May 14: Nashville National Bank
last case assignment
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.
performance evaluation
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…
slide5

Productivity measurement

  • Operating ratios (e.g. man-hr/transaction)
  • Financial approaches (e.g. conversion to Euros)
slide6

Conceptually ...

Productivity = Outputs

Inputs

Productivity

slide7

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

slide8

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

slide9

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

slide10

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

slide11

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?
slide12

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?

slide13

#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).

slide14

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%

slide15

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?

slide16

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
slide17

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
slide18

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

in words
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
slide20

How do we evaluate these variables ?

LP Formulation:

Data

Model variables

slide21

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