Data Envelopment Analysis (DEA)

1
Data Envelopment Analysis(DEA)
2
Which Unit is most productive?
DMU labor hrs. cust. 1 100
150 2 75 140 3
120 160 4 100
140 5 40 50
DMU decision making unit
3
DEA (Charnes, Coopers Rhodes 78)A
multiple-input, multiple-output productivity
measurement tool
Basic intuition (DMU decision making unit)
DMU labor hrs. cust. cust/hr. 1 100
150 1.50 2 75
140 1.87 3 120 160
1.33 4 100 140 1.40 5
40 50 1.25
cust.
200
x
slope 1.87
x
x
DMUs 1,3,4,5 are dominated by DMU 2.
x
100
x
labor hrs.
50
100
4
Extending to multiple outputs ...
Ex Consider 8 M.D.s working at Shouldice
Hospital for the same 160 hrs. in a month. Each
performs exams and surgeries. Which ones are
most productive?
Note 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?
5
Efficient M.D.s These two M.D.s (1 and 6)
define the most efficient trade-off between the
two outputs.
Scatter plot of outputs
6
efficient frontier
1
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).
6
How bad are the inefficient M.D.s and where are
the gaps?
5
Performance gap
73.4 of distance to frontier
Efficiency score 73.4
7
Nearest efficient points define a reference set
and a linear combination of the reference set
inputs and outputs defines a hypothetical
composite unit (HCU)
Reference set for 5 is 1,6
6
5
1
HCU
8
DEA summary so far 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?
9
A real-word example NY Area Sporting Goods
Stores
10
Productivity
Reality if 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
Some approaches

• Operating ratios
• e.g. Labor-hrs/transaction, sales/sq.-ft.
• Good for highly standardized operations
• Problem Does not reflect varying mix of inputs
  and outputs found in more diverse operations
• Financial approach Convert everything to !
• Problems?
• Some inputs/outputs cannot be valued in
  (non-profit)
• Profitability is not the same as operating
  efficiency (e.g. variances in margins and local
  costs matter as well)

Inputs
Outputs
13
Profitability vs. effeciency

• Profitability is a function of 3 elements
• Input prices (costs)
• Output prices
• Technical efficiency (How much input is required
  to generate the firms output.)
• Improving operations requires understanding
  technical efficiency not just overall
  profitability.

14
LP Formulation
Data
Model variables
15
To evaluate a give unit, e, choose nonnegative
weights to solve ...
Which can be formulated
Normalize weighted input of e to one
16
Output analysis
These dual variables can be used to contruct an
efficient hypothetical composite unit (HCU) with
Output j of HCU
Input i of HCU
Satisfying
17
HCU can be used to measure excess use of inputs
and potential increase in outputs
Refer to spreadsheet examples.
18
Using the results Eff.-Profit Matrix
High Profit
Under-performing potential leaders
Best practice comparison group
Low Eff.
High Eff.
Under-performing possibly profitable
Candidates for closure
Low Profit
19
Designing DEA Studies

• Inputs/Ouputs
• K gt 2(NM)
• Ambivalence about inputs and outputs - all
  should be relatively important!
• Approximate similarity among DMUs
• objectives
• technology
• Provides relative efficiency only
• choice of units to include matters
• inclusion of global leader unit may be
  desirable
• Experimenting with different I/O combinations may
  be necessary

20
DEA Summary

• Addresses fundamental productivity measurement
  problems due to ...
• complexity of service outputs
• variability in service outputs
• Takes advantage of service operating environment
• large numbers of similar facilities
• diversity of practices/management/environment
• Provides useful information
• objective measures of productivity
• reference set of comparable units
• excess use of inputs measure
• returns to scale measure

21
DEA Summary (cont.)

• Role of DEA
• data mining to generate hypotheses
• evaluation/measurement
• benchmarking to identify best practice units
• Caveats
• black box - No information on root causes of
  inefficiency
• Be aware of assumptions (e.g. linearity)
• Can be sensitive to selection of inputs/outputs