# Measuring Service Productivity

Data Envelopment Analysis (DEA) Identifying Efficient Decision Making Units Measuring Service Productivity Branch Bank Example 1. ACCOUNTING RATIO: COST PER TELLER TRANSACTION HIGHER RATIO WOULD BE INEFFICIENT RELATIVE TO OTHERS, BUT COULD BE EXPLAINED BY: 1. MIX OF OUTPUTS (SELLING CDS VS SIMPLE DEPOSITS) 2. MIX OF INPUTS (USE OF ATMS AND LIVE TELLERS) 2. BROAD BASED MEASURE: RETURN ON INVESTMENT OVERALL IMPORTANT BUT NOT SUFFICIENT TO EVALUATE OPERATING EFFICIENCY OF INDIVIDUAL DECISION MAKING UNIT (DMU) FOR EXAMPLE: A PROFITABLE BRANCH COULD BE THE RESULT OF HIGHER-THAN-AVERAGE PROPORTION OF REVENUE GENERATING TRANSACTIONS RATHER THAN COST-EFFICIENT USE OF RESOURCES. THE DEA MODEL Fractional Form O b je c tiv e F u n c tio n u 1O 1e u 2 O 2 e u M O M e m ax E e v 1 I 1e v 2 I 2 e v N I N e C o n s tr a in ts u 1O 1k u 2 O 2 k u M O M k 1 .0 v 1I1k v 2 I 2 k v N I N k j 0 j =1,2,,M i 0 i= 1,2,,N k 1 , 2 , , K DEA in Standard LP Form (Scaling inputs to sum to 1.0) S T A N D A R D m a x E L P F O R M ( s c a lin g in p u t s t o s u m e

u 1O 1 e u 2O u 2 e M O M e v N o f 1 .0 ) S U B JE C T T O : v1I u 1O 1 e 1 k v 2 I 2 e u 2O v 2 k N I N e u

M O 1 M k v 1 I 1 k v 2 I 2 k I N k w h e re : u v j 0 j 1 , 2 , , M i 0 i 1 , 2 , , N R E C O M M E N D E D S A M P L E S IZ E : K 2 N

M 0 k 1 , 2 , , K Burger Palace Example S U M M A R Y O F O U T P U T S A N D IN P U T S F O R B U R G E R P A L A C E S e r v ic e u n it 1 2 3 4 5 6 M e a ls s o ld 100 100 100 100 100 100 L a b o r -h o u rs 2 4 4 6 8 10 M a te r ia l d o lla r s 200 150 100 100 80 50 L P M O D E L F O R E V A L U A T IO N O F S E R V IC E U N IT 1 m a x E ( S1 ) u11 0 0

s u b je c t to : u11 0 0 v1 2 v 2 2 0 0 u11 0 0 v1 4 v 2 1 5 0 u11 0 0 v1 4 v 2 1 0 0 u11 0 0 v1 6 v 2 1 0 0 u11 0 0 v1 8 v 2 8 0 u11 0 0 v11 0 v 2 5 0 v1 2 v 2 2 0 0 u1 , v1 , v 2 0 0 0 0 0 0 1 0 Burger Palace Productivity Frontier Material dollars 200 S1 (2,200) 150 S2 (4,150) 100 S3 (4,100) S4 (6,100) S5 (8,80) C (5.3, 88.9) 50 S6 (10,50) 0 0 2 4

6 Labor hours 8 10 Summary of DEA Results SUMMARY OF DEA RESULTS Service unit Efficiency rating (E) Efficiency reference set Relative labor-hour value v1 Relative material value v2 S1 S2 1.000 0.857 .1667 .1428 .0033 .0028 S3 S4 1.000 0.889 .0625 .0555 .0075 .0067 S5

0.901 .0568 .0068 S6 1.000 N.A. S1 (.2857) S3 (.7143) N.A. S3 (.7778) S6 (.2222) S3 (.4545) S6 (.5454) N.A. .0625 .0075 CALCULATION OF EXCES INPUTS USED BY UNIT S4 Outputs and inputs Composite reference unit C Reference set S3 Meals Labor-hours Material \$ (.7778) (.7778) (.7778) 100 + 4 + 100 +

S6 (.2222) (.2222) (.2222) 100 = 10 = 50 = Excess inputs used S4 100 5.3 88.9 100 6 100 0 0.7 11.1 DEA and Strategic Planning High Profit Low Under-performing potential stars Problem Branches Low Benchmark group Candidates for divestiture Efficiency High

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