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Unformatted text preview: the problem as “There are too few servers.“ "There aren't
enough tables.” or “The servers need to work faster.“ The
real problem was identiﬁed correctly as "The customers must
wait too long.” Another concept that has been difﬁcult for study teams
l5 localization. which Is a process of focusing on smaller and
smaller vital pieces oi the problem. This concept initially
proved difﬁcult because team members had not yet intemal
izedtheideathatlrnprovementshouldbedﬁvenbyctntomer Chimera Proscm traumasmt 203 theyfelttobelrrelevant. Insomecases, membershadto leanl
new skills. such as how to obtain information in a nonthreat
ening way from workers in the system. Finally, organizational
problems such as arranging meeting times and getting sup
portlromco—vvorltershadtoberesohredaswell. Questions
1. How is SSM different from Deming's PDCA cycle? 2. Prepareacame—and—eﬁectorﬁshbonediagramioraproblem such as "Why customers have long waits for coiiee.“ Your
ﬂshbone diagram should be similar to that in Figure 8.17,
using the main sources oi cause: policy. procedure. people,
and physical environment. How would you resolve the difﬁculties that study teams
have experienced when applying 55M? r' requirements.
Somesmdyteamshaveexperiencedanassortmentoi other difﬁculties. Occasionally, team when could not see the benefit oi collecting data accurately. or they did not under . stand how baseline data would be used to validate a solu 3. r tion. Some members had trouble keeping an open mind and. ' consequently. resisted itwestlgating the effects of variables . Chapter 8 Supplement Data Envelopment Analysis (DEA) How can corporate management evaluate the productivity of a fast~food outlet. a branch
. bank. a health clinic. or an elementary school? The difﬁculties in measuring productivity
'. arc threefold. First. what an: the appropriate inputs to the system (c.g.. labor hours. mate
rial dollars) and the measures ofthosc inputs? Second. what are the appropriate outputs
of the system (e.g.. checks cashed. certiﬁcate of deposits) and the measures of those out
puts? Third. what are the appropriate ways of measuring the relationship between these
inputs and outputs? Measuring Service Productivity The measure of an organization‘s productivity. if viewed from an engineering perspec
tive, is similar to the measure of a system‘s efﬁciency. It can be stated as a ratio of out
puts to inputs (c.g.. miles per gallon for an automobile). To evaluate the operational efﬁciency of a branch bank. for example. an account
ing ratio such as cost per teller transaction might be used. A branch with a high ratio
in comparison with those of other branches would be considered less efﬁcient. but
the higher ratio could result from a more complex mix of transactions. For example.
I a branch opening new accounts and selling CDs would require more time per trans action than another branch cngagcd only in simple transactions such as accepting
deposits and cashing checks. The problem with using simple ratios is that the mix of
outputs is not considered explicitly. This some criticism also can be made concerning
the mix of inputs. For example, some branches might have automated teller machines
in addition to live tellers. and this use of technology could achct the cost per teller
transaction. Broadbased measures such as proﬁtability or return on investment are highly rel
evant as overall perfomtancc measures. but they are not sufﬁcient to evaluate the oper—
ating efﬁciency of a service unit. For instance. one could not conclude that a proﬁtable
branch bank is necessarily efﬁcient in its use of personnel and other inputs. A higher
thanaverage proportion of revenuegenerating transactions could be the explanation
rather than the costefﬁcient use of resources. The DEA Model Fortunately. a technique has been developcd with the ability to compare the efﬁciency
of multiple service units that provide similar services by explicitly considering their use 204 Part Two Bridging the Service Enterprise of multiple inputs ti.e.. resources] to produce multiple outputs {i.e.. services}. The tech
nique. which is referred to as data envehrpmem unoftsis (DEA). circumvean the need to
develop standard costs for each service. because it can incorporate multiple inputs and
multiple outputs into both the numerator and the denmninalor of the efficiency ratio with
out the need for conversion to a common dollar basis. Thus. the DEA measure of chi
cieney explicitly accounts for the mill of inputs and outputs and. consequently. is more
comprehensive and reliable than a set of operating ratios or proﬁt measures. DEA is a linear programming model that attempts to maximize a service unit's
efﬁciency. expressed as a ratio of outputs to inputs. by comparing a particular unit's
efficiency with the performance of a group of similar service units that are delivering the
same service. In the process. some units achieve 100 percent efﬁciency and are referred
to as the relativeb' efficient units. whereas other units with efﬁciency ratings of less than
IOU percent are referred to as inefficient units. Corporate management thus can use DEA to compare a group of service units to
identify relatively ineﬂicient units, measure the magnitude of the inefﬁciencies. and
by comparing the inefﬁcient with the eﬁicient ones. discover ways to reduce those
inefﬁciencies. The DEA linear programming model is formulated according to Chartres. Cooper. and
Rhodes. and is referred to as the CCR Model. Deﬁnition of Mirfables
Let E... with l = l. 2. . . . . K. be the efﬁciency ratio of unit it. where K is the total number
of units being evaluated. Let uj. with} = l. 2. . . . . M. be a coefﬁcient for output}. where M is the total number
of output types considered. The variable u] is a measure of the relative decrease in eff
ciency with each unit reduction of output value. Let vi. with r‘ = l. 2. . . . . N. be a coefﬁcient for input r'. where N is the total number of
input types considered. The variable v. is a measure of the relative increase in efﬁciency
with each unit reduction of input value. Let 0].. be the number of observed units of output j generated by service unit It during
one time period. Let I... be the number of actual units of input i used by service unit It during one time
period. Objective Function The objective is to find the set of coefﬁcient u's associated with each output and of‘ v's
associated with each input that will give the service unit being evaluated the highest pos
sible efficiency. EM (1) maxi? :
f Vl’lr + ”232. + + Vain. where e is the index of the unit being evaluated. This function is subject to the constraint that when the same set of input and output
coefﬁcients (uj’s and ,rg’s) is applied to all other service units being compared. no service
unit will exceed 100 percent efﬁciency or a ratio of 1.0. Comm were k=ll...K (2)
VJ” + ugly. + + ”slat , ' ' where all coefficient values are positive and nonzero.
To solve this fractional linear programming model using standard linear program
ming software requires a reformulation. Note that both the objective function and all t Example 8.1
Burger Palace TABLE 8.6 Summary of Output!
and Inputs for Burger
Palace (Jupiter's Pam: (maamt 205 constraints are ratios rather than linear ﬁrnetions. The objective function in equation (1) is restated as a linear function by arbitrarily scaling the inputs for the unit under evalua~
tion to a sum of Lt]. max 5. = "Ion + "202: ‘l' + "MON: (3) subject to the constraint that Viln + ”21:: + + Velab = I (4) For each service unit. the constraints in equation (2) are similarly reformulated: ”[0” + "202* + ”' + "MQ‘H‘ _ (“In “F VII}; + "' + “9’51, 5 0 k = l,2....,K (5) where 3
IV W e r:
‘0 HI
H in 3 "‘ Sample Size A question of sample size often is raised concerning the number of service units that are
required compared with the number of input and output variables selected in the analysis.
The following relationship relating the number of service traits K used in the analysis and
the number of input N and output M types being considered is based on empirical find
ings and the experience of DEA practitioners: K :2 2(N + M) (6) An innovative driveinonly burger chain has established six units in several different cities.
EachunitislocatedinastripshopphtgcenterparkingloLOnlyastandardmealcomlstlngof
aburger.fries.andadrinltisavailable. ManagementhasdecldedtouseDEAtoinrprovepro
ductivity by identifying which units are using their resources most efﬁciently and "ten sharing
their experience and knowledge with the less efficient locations. Table 8.6 surnman'zes data
for two inputs: laborhours and material dollars consumed during a typical lunch hour period
to generate an output of 100 meals sold. Nonnatly. output will vary among the service units,
but‘rnthisexample.wehavemadetheoutputsequaltoallowloragraphlcal presentationof
the units' productivity. As Figure 8.19 shows. service units 5;. $3. and S. have been joined to
form anefﬁcientproductlon frontierol altemativemethodsof using laborhoursmdmate
rialresourcestogeneratelOOmeals.Ascanbeseen.theseefﬂdentunhshmdeﬁnedan
envelope that contains all the inefﬁcient units—thus the reason for calling the process ”data
envelopment analysis.“ Servlcellnlt MealsSold LaborHans MaterlllDollIrs
1 100 2 200
2 100 4 150
3 100 4 100
4 too 6 100
5 100 8 80
6 100 10 0 206 Part Two kaigning the Service Enterprise FIGURE 8.19
Productivity Frotier of
Berger Palace It!) '2 ill] Material dollnn 50 For this simple example, we can identify efﬁcient units by inspection and see the excess
inputs being used by inefficient units (e.g., S; would be as efﬁcient as S; if it used 550 less in
materials). To gain an understanding of DEA, however, we will proceed to formulate the linear
programming problems for each unit, then solve each of them to determine efﬁciency ratings
and other information. We begin by illustrating the LP formulation for the first service unit, 5., using equations (3).
(4), and (5). max 513.) = «.100 subjectto ull00  v12 _
H.100  v.4 — v2150 5
u1l00  v.4  1'3100 ‘5 ullﬂﬂ — v.6 _ H.100 — v.8  1380 S u.l00 — tall] — v150 '5
v12 + V3200 = Similar linear programming problems are formulated (or, better yet, the S1 linear program
ming problem is edited) and solved for the other service units by substituting the appropriate
output function for the objective function and substituting the appropriate input function for
the last constraint. Constraints 1 through 6, which restrict all units to no more than 100 per
cent elficiency. remain the same in all problems. This set of six linear programming problems was soived with Excel Solver 7.0 in fewer than
ﬁve minutes by editing the data ﬁle between each run. Because the output is 100 meals for all
units, only the last constraint must be edited by substituting the appropriate labor and mate
rial input values from Table 8.6 for the unit being evaluated. The data ﬁle for unit 1 of Burger Palace using a linear programming Excel addin is shown
in Figure 8.20. The linear programming results for each unit are shown in Table 8.7 and sum
marized in Table 8.8. In Table 8.7. we find that DEA has identified the same units shown as being efficient in
Figure 8.18. Units 5;, S4. and 55 all are inefﬁcient in varying degrees. Also shown in Table 8.7
and associated with each inefficient unit is an efﬁciency reference set. Each inefficient unit will
have a set of efficient units associated with it that deﬁnes its productivity. As Figure 8.18 shows
for inefﬁcient unit 5‘. the efﬁcient units 53 and 5. have been ioined with a line deﬁning the
efﬁciency frontier. A dashed line drawn from the origin to Inefﬁcient unit 54 cuts through this if Chapterﬂ Pmss from: 207 TABLE 8.7 LP Solution for DEA Study of Burger Palace Summarized results for unit 1 + 33.333336 V2 4 .00333333 +60.000000
51 0 +33.333336 0
S2 +16.666670 Maximized objective function = 100 Summarized results for unit 2 No. 1 + .35714287 2 V1 +.142857'5 +28.57143O 3 V2 +.002857i4 +51.428574 0
4 $1 0 + 71 .428574 0
5 +14.23571 7 Maximized objective function = 85.71429 Summarized results for unit 3 Maximized objective function = 100 Summarized results for unit 4 No. 1 + 38888890
2 V1 +.05555556
3 V2 + .00666667
4 $1 + 55.555553
5 + 33.333340 V'I +.05681818 +11.363637
V2 +.00681818 +9.0909100
S'I +56.318180 UlbWN" + 34.09091 6
Maximized objective function = 90.90909 208 Part Tm Designing the Sender Enterprise TABLE 8.7 (concluded) FIGURE 8.20
Excel Data File hr DEAAulyslaofBuuer
Palaoellaltl Summarized results for unit 6 frontier and, thus, deﬁnes unit 54 as inefficient. In Table 8.8, the value in parentlieses that is
associated with each member of the efﬁciency reference set (i.e., .7778 for 5; and .2222 for
sarepresentsdierelawweightassignedtomatefﬁdentunhhrcakulaﬁng theelﬁciencyrat
ingfor S..Theserelativeweightsaretheshadowpricesthatareassociatedwiththerespective
efficientunit constraints In the linear programming soiution. (Note in Table 8.7 that for unit 4,
these ‘htsappearasopportunitycostsforS;andS..) . Them for v. and v; that are associated with the inputs of laborhours and matenais,
respectively. measure the relative increase in efﬁciency with each unit reduction of input value.
For unit 5., each unit decrease in laborhours results in an efficiency increase of 0.0555. For
unit 5.. tobecorne efﬁcient, itmust increaseitsefﬁciencyrating by0.111 points. This can be
accomplished by reducing labor used by 2 hours (l.e., 2 hours x 0.0555 = 0.111). Note that
with this reduction in laborhours, unit 5.. becomes identical to efﬁcient unit 5,. An alternative
approach would be a reduction in materials used by 516.57 (i.e., 0.111100067 = 16.57). Any
linear combination of these two measures also would move unit 5.. to the productivity frontier
deﬁned the line segment joining efficient units 53 and 5.. Tablebsyﬂ contains the calculations for a hypothetical unit C, 1which is a composite reference
unit defined bytheweighted inputs of the reference set 53 and 5,. As figure 8.18 shows, this
compositeunit Chiocatedatdieintersection oftlieproductivityfronoerand thedashedline
drawn from the origin to unit 54. Thus, compared with this reference unit C. inefficient unit 5..
is using excess inputs in the amounts of 0.7 laborhour and 11.1 material dollars. \ . .. . .  _ ‘ ' Alli.)
sin: to 0 m run out 0: w an we:
'aIi ...&ﬁ 4.21.;[112 . ... .
El .l I rll'JJ‘II'.‘
‘ A a c 0 g  r 0 a I r v E
1 vanities U? ‘0'] 'J'
2‘ m 001 mm: 0003333 _ 2.
3 'Dbrtlur
when 51203.. 100"“ CECIL _.
Itwurmv {:Ihe "HS
11" our 100 :11) — 0 0
12 um: :02 4 450  0 ram: .. r.
:3 In: I00 .4 101 = 0 0
u um i :03 .0 .101.) = 0 33335 « . .0
15 we :00 a m = 05 0
is (has 100 1r. 50 033333 .1 0
i7 lllptllt 0 J :00  i = .
la‘mu‘ne I 0 0  001 u: (I
new... 0 I 0  curses: 0
”well" 0 0 'I =. nmsm .= a
21w; . ms
3 ﬁatum 111 [3.3
3. mm r. B, r‘ no “yard: F that .. _ _'__‘_
25 omm —J .
g Input: 3 a... I a
3 woocavern.» w l
3 H11 «lam ’9 I I
I) #313 40:3? '
'I'I(e )
it“! mu r—Ilsu ————!M “In I tl_ 353233? .1 on i TABLE 8.8
Sanitary ol‘ DEA
Results TABLE 8.9
Calculation of Excess
Inputs Used by Unit 5'. FIGURE 8.21
DEA Strategic MaoIs Clupters Prim Jaimieincur 209 Efﬂdency Efﬁciency Relative Labor Relative Material
Service Unit Rating (E) Reference Set Hour Value (V1) Value (V2)
51 1.000 NA. 0.1667 0.0033
52 0.857 5, (0.2057) 0.1428 0.0028
53 (0.7143)
5, 1.000 N A 0.0625 0.0075
54 0.889 5; (0.7778) 0.0555 0.0067
5. (0.2222)
5, 0.901 5, (0.4545) 0.0568 0.0068
56 (0.5454)
5. ‘i .000 NA. 0.0625 0.0075
Composite Excess
Reference Inputs
Outputs and Reference Set Unit C Used
Inputs 53 55 54
Meals (0.7773) x 100 + (0.2222) x 100 = 100 100 0
Laborhours (0.7778) x 4 + (0.2222) x 10 = 5.3 e 0.7
Material (5) (0.7773) x 100 + (0.2222) x 50 = 33.9 100 11.1 DEA offers many opportunities for an Inefﬁcient unit to become efﬁcient regarding its ref erence set of efﬁcient units. In practice, management would choose a particular approach
on the basis of an evaluation of its cost. practicality, and feasibility; however; the motivation for change is clear (i.e., other units actually are able to achieve similar outputs with fewer
resources). DEA and Strategic Planning When combined with proﬁtability. DEA efﬁciency analysis can be mild in strategic
planning for services that are delivered through multiple sites (0.3.. hour] chains). Figure 8.2l presents a matrix of four possibilities that arise from combining efﬁciency
and proﬁtability. Considering the topleft quadrant of this matrix (i.c.. underpcrl'orming potential stars)
reveals that units operating at a high proﬁt may be operating inefﬁciently and. thus. have
unrealized potential. Comparing these with similar efﬁcient units could suggest measures
that would lead to even greater proﬁt through more efﬁcient operations. Star performers can be found in the topright quadrant (l.e.. benchmark group). These
efficient units also are highly proﬁtable and. thus. serve as examples for others to emulate
in both operations efﬁciency and marketing success in generating high revenues. for divestiltm: Low 11'
Efﬁciency 15h ...
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 Fall '09

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