Data Envelopment Analysis (DEA)

Which Unit is most productive? DMU = decision making unit DMU labor hrs. #cust

DEA 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 #cust. labor hrs. x x x x x slope = 1.87 DMU’s 1,3,4,5 are dominated by DMU 2.

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?

Scatter plot of outputs: Efficient M.D.’s: These two M.D.’s (#1 and #6) define the most efficient trade-off between the two outputs. efficient frontier #6 #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).

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

Reference set for #5 is {1,6} #1 #6 “Nearest” efficient points define a reference set and a linear combination of the reference set inputs and outputs defines a hypothetical composite unit (HCU) HCU

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

A real-word example: NY Area Sporting Goods Stores

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

Operating Units Differ l Mix of customers served l Availability and cost of inputs l Facility configuration l Processes/practices used l 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?

Some approaches l 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 l Financial approach: Convert everything to $$$! l 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

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

LP Formulation: Data Model variables

To evaluate a give unit, e, choose nonnegative weights to solve... Which can be formulated Normalize weighted input of e to one

Output analysis These dual variables can be used to contruct an efficient hypothetical composite unit (HCU) with Input i of HCU Output j of HCU Satisfying

HCU can be used to measure excess use of inputs and potential increase in outputs Refer to spreadsheet examples.

Using the results: Eff.-Profit Matrix High Profit Low Profit Low Eff. High Eff. Under-performing potential leaders Best practice comparison group Under-performing possibly profitable Candidates for closure

Designing DEA Studies l #Inputs/Ouputs K > 2(N+M) l “Ambivalence” about inputs and outputs - all should be relatively important! l “Approximate similarity” among DMUs – objectives – technology l Provides relative efficiency only – choice of units to include matters – inclusion of “global leader” unit may be desirable l Experimenting with different I/O combinations may be necessary

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

DEA Summary (cont.) l Role of DEA – “data mining” to generate hypotheses – evaluation/measurement – benchmarking to identify “best practice” units l 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