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MGS 8770
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Service Operations Management
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Data Envelopment Analysis
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Learning Objectives
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Understanding the basics of data envelopment analysis (DEA) Solve simple DEA problems
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Data Envelopment Analysis (DEA)
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DEA is a linear programming method for comparing the relative productivity (or efficiency) of multiple service units
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Difficulties in evaluating the relative performance of organizational units
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Service businesses typically have a very large number of facilities or units that perform similar tasks. There are multiple inputs and outputs. Accounting/financial ratios are often not sufficient.
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MGS8770 – Service Operations Management
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1
Service Companies with Multi-Site Operations Company Auto-Related AAMCO Transmissions Budget Rent-a-Car Jiffy Lube Meineke Car Care Midas (brake/muffler repair) Novus Auto Glass Repair Banks Bank of America Wachovia Bank
Number of Sites > 700 3,240 2,156 891 2,777 > 2,200
4,495 2,626
Cleaning Coverall Cleaning Concepts Jani-King Mitex Indoor Hygenics
7,085 > 9,500 > 4,000
Desserts Baskin-Robbins (ice cream) Dunkin' Donuts Tim Horton's (doughnuts) TCBY (frozen yogurt) Yogen Fruz Worldwide, Inc.
3,460 4,736 1,893 2,006 > 5,000
Fast Food Burger King Domino's Pizza
Company McDonald's Subway
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Number of Sites 31,129 17,500
Hair Styling Fantastic Sam's Supercuts
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1,350 1,778
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Lodging Choice Hotels Marriott Super 8 Motels
> 5,000 2,600 > 2,000
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Other Carlson Wagonlit Travel Associates Dollar General (discount stores) GNC (nutrition) Heel Quik! (shoe repair) Kumon Math and Reading Centers Kwik Kurb (concrete services) Merle Norman Cosmetics Studios Miracle Ear (hearing aids) Pearl Vision (eyecare) Radio Shack Snap-On (tools) Wal-Mart (discount stores)
1,121 6,700 4,811 732 1,272 > 1,250 2,006 1,103 811 7,113 4,680 4,800
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8,246 5,996
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Issues with Simple Ratios
________________________________________ 1.Accounting ratio: cost per teller transaction
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Higher ratio would be inefficient relative to others, but could be explained by: (1) Mix of outputs transactions (selling CD’s vs simple deposits); (2) Mix of inputs (use of ATM’s plus live tellers)
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2.Broad based measure: return on investment
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Is not sufficient to evaluate operating efficiency of individual decision making unit (DMU). For example: A profitable branch could be the result of higher-thanaverage proportion of revenue generating transactions rather than cost-efficient use of resources. 5
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Advantages of DEA
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DEA can handle multiple inputs and multiple outputs. Inputs and outputs can have very different units. DEA provides a single comprehensive measure of performance. It doesn't assume any specific functional form relating inputs to outputs. DEA provides valuable information for less efficient DMUs on how to improve. For each inefficient DMU, DEA also provides a peer bestpractice group for reference purposes. 6
MGS8770 – Service Operations Management
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2
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Efficiency Measure in DEA Efficiency =
=
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Re sults Obtained Weighted Sum of Outputs = Resources Used Weighted Sum of Inputs
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u1O1 j + u2O2 j +L
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v1 I1 j + v2 I 2 j +L
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Where u1 = weight given to output 1, O1j = amount of output 1 from unit j v1= weight given to input 1 I1j = amount of input 1 used by unit j
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The DEA Model —Fractional Form Objective Function max E e =
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u1O1e + u2 O2 e + L + u M OMe v1 I1e + v2 I 2 e + L + v N I Ne
Constraints u1O1k + u2 O2 k + L + u M OMk ≤ 10 . v1 I1k + v2 I 2 k + L + v N I Nk u
j
≥ 0
vi ≥ 0
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k = 1, 2,K , K
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j = 1 , 2 , ..., M
i = 1 , 2 , ..., N
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Ek = efficiency ratio of unit k, k=1,2,…,K, K = total # of units uj = weight given to output j, j=1,2,…,M, M = total # of outputs vi = weight given to input i, i=1,2,…,N, N = total # of inputs Ojk = amount of output j from service unit k Iik = amount of input i used by service unit k e = index of the unit being evaluated
8
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Scaling inputs to sum to 1.0
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DEA in Standard LP Form
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Objective Function:
max
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E e = u 1O1e + u 2 O 2 e +L + u M O Me
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Subject to:
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u1O1k + u 2 O 2 k +L+ u M O Mk − v1 I 1k − v 2 I 2 k −L− v N I Nk ≤ 0
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k = 1, 2 , K, K
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v1 I 1e + v 2 I 2 e +L+ v N I Ne = 1
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u j ≥ 0 j = 1, 2 , ..., M vi ≥ 0 i = 1, 2 , ..., N 9
MGS8770 – Service Operations Management
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3
________________________________________ Example
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Burger Palace
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Burger Palace is a drive-in-only chain that has six units. Only standard meal (burger, fries, and drink) is available. The inputs are labor-hours and material dollars and the output is 100 meals sold. Service unit 1 2 3 4 5 6
Meals sold 100 100 100 100 100 100
Labor-hours 2 4 4 6 8 10
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Material dollars 200 150 100 100 80 50
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Burger Palace
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Productivity Frontier
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Burger Palace
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LP Model for Service Unit 1
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Objective Function:
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max E ( S1 ) = u1100 Subject to:
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u1100 − v1 2 − v2 200 ≤ 0 u1100 − v1 4 − v2 150 ≤ 0
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u1100 − v1 4 − v2 100 ≤ 0 u1100 − v1 6 − v2 100 ≤ 0
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u1100 − v1 8 − v2 80 ≤ 0
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u1100 − v110 − v2 50 ≤ 0 v1 2 + v2 200 = 1
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u1 , v1 , v2 ≥ 0 12
MGS8770 – Service Operations Management
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4
________________________________________ Burger Palace
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LP Model for Service Unit 2
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Objective Function:
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Subject to:
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Burger Palace
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Excel Formulation for Unit 1 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
B
C
D
V1 1
V2 1
E
F
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G
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Burger Palace Variables Value
U1 1
Objective Function
100
Constraints Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Inputs
100 100 100 100 100 100 0
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=100*B4 -2 -4 -4 -6 -8 -10 2
-200 -150 -100 -100 -80 -50 200
LHS -102 -54 -4 -6 12 40 202
