ARTICLE IN PRESS

0261-5177/$ - se

doi:10.1016/j.to

�CorrespondE-mail add

joseplluis.marti

(F.P. Buffa).

Tourism Management 28 (2007) 262–270

www.elsevier.com/locate/tourman

Research Paper

Improving resource utilization in multi-unit networked organizations:The case of a Spanish restaurant chain

Vıctor M. Gimenez-Garcıaa,�, Jose Luis Martınez-Parrab, Frank P. Buffac

aDepartament d’Economia de l’Empresa and Escola Universitaria de Turisme i Direccio Hotelera, Universitat Autonoma de Barcelona,

08193 Bellaterra (Barcelona), SpainbDepartament d’Economia de l’Empresa, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain

cDepartment of Information and Operations Management, Mays Business School, Texas A&M University, 301N Wehner Building,

College Station, TX 77843-4217, USA

Received 24 May 2005; accepted 1 December 2005

Abstract

In this paper, a three-step data envelopment analysis model is used to reallocate resources in an organizational network. First, the

model identifies the excess resources of inefficient units; then reallocates these resources to and sets revised output-oriented production

goals for efficient units. Finally, the model recalculates improvement targets for the inefficient units based on the revised remaining

resources. The procedure is applied to the analysis of 54 restaurant locations belonging to a Spanish fast-food chain. The results show

that originally efficient restaurants can improve their output by an average of 4.20% after a reallocation of inputs, and that this

reallocation is beneficial for the entire restaurant chain.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Tourism service industry; Data envelopment analysis; Resource allocation

1. Introduction

To achieve and maintain competitive advantage, anetworked organization of multiple units must achievethe highest possible overall system efficiency in how itmeasures individual unit efficiency and how it allocatesorganizational resources among its various business units.The methodology described here is especially suitable forcompanies with multiple business units for the followingreasons. It simultaneously accounts for all input andoutput levels of each unit analyzed (Thanassoulis, Bousso-fiane, & Dyson, 1996). It uses data from each business unit,identifying those units that are efficient and those that arenot. It sets improvement objectives for inefficient unitsbased on the achievements of efficient units. As a resultcentral management can benchmark its individual units

e front matter r 2006 Elsevier Ltd. All rights reserved.

urman.2005.12.021

ing author. Tel.: +3493 581 1209; fax: +34 93 581 2555.

resses: victor.gimenez@uab.es (V.M. Gimenez-Garcıa),

nez@uab.es (J.L. Martınez-Parra), f-buffa@tamu.edu

using information internal to the organization and withoutmaking any theoretical assumption.A data envelopment analysis (DEA) procedure is

presented to optimize the resource assignments amongdifferent business units in order to maximize the overallnetwork efficiency. The procedure determines the resourcesthat are being wasted by inefficient units, reallocates theseresources to the efficient units and also revises outputexpectations for inefficient units based on the resourcesremaining after the reallocation. By reallocating organiza-tional resources to efficient units, central management canimprove overall network productivity by establishing newand higher production goals for efficient units. Revisingoutput values for the inefficient units helps them focus onoperational issues that require process improvement andthat can eventually support higher network productivity.The procedure is applied to the case of a Spanish

restaurant chain of 54 centrally managed units, but caneasily be adapted in other organizations where multipleunits are involved, regardless of the industry or country.The motivation for this study was central management’s

ARTICLE IN PRESSV.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270 263

need for an internal data based method for setting revenueand cost goals for the managers whose restaurants wereefficiently operated. Central management wanted to offeradditional staff and extra advertising support to themanagers of efficient restaurants in order to motivate themto achieve improved goal. At central management’s requestfor illustrative purposes, only the summary results of themodel application are presented in order to disguise thespecific results related to bonus plans, actions taken, andeffects of these actions on individual unit operations.

The contents of this article are organized as follows.Section 2 presents a literature review of the DEA modelsrelated to this study. Section 3 presents the DEA model forresource reallocation and a description of the applicationof the procedure using data from a group of 54 restaurantunits belonging to a well-known Spanish chain. Section 4summarizes the main results and discusses the managerialimplications of these results. Section 5 summarizes theconclusions of the study, references how the procedure isapplicable to other resource reallocation problems in otherindustries, and offers directions for further research.

2. Literature review

DEA models measure overall operating efficiency andare useful for establishing objectives for efficiency im-provement. In addition, these models have been used toestablish potential input reductions or output increases toimprove efficiency. A comprehensive explanation of DEAmethodology can be found in Cooper, Seiford, and Tone(2000).

DEA models are examples of frontier models that have along record of applications. They have typically been usedto identify efficient units (best practices) and to facilitatethe learning of the inefficient units by setting targets toimprove outputs and/or reduce inputs (Andersen &Petersen, 1993; Athanassopoulos & Shale, 1997; Banker,Charnes, & Cooper, 1984; Beasley, 1990; De Borger,Ferrier, & Kerstens, 1998; Pedraja-Chaparro, Salinas-Jimenez, & Smith, 1999; Seiford, 1997; Thanassoulis &Dyson, 1992; Wagstaff, 1989). This paper focuses in thislearning process and contributes to the literature bydemonstrating how to also set output improvement goalsfor efficient units after they receive resource reallocationsfrom inefficient units.

Studies similar to this application have been reported inthe literature. Fare, Grabowski, Grosskopf, and Kraft(1997) allocated tracks of land for different kinds ofcultivation, using a resource allocation process. Athanas-sopoulos (1995) allocated resources among differentdecision-making units using a linear goal-programmingmodel that optimized a system-wide objective after firstsetting individual goals for each unit. But, when reallocat-ing resources he did not set higher priorities on the efficientunits nor increase their improvement goals.

This paper presents an alternative model to the Fareet al. (1997) and Athanassopoulos (1995) models that were

applied in different scenarios. The model reported herediffers from the Fare model because it deals withreallocating inputs among different units. The Fare modelreallocated one input among competing outputs of thesame business unit. The Athanassopoulos model also dealtwith reallocating inputs among units, but used a goal-programming approach. His model was focused on how toallocate a scarce resource among different units that hadpredetermined, desired targets for the resource amount tobe received. The model reported here maximizes overallsystem efficiency, without setting previous goals, afteridentifying remaining resources from inefficient units andthen resetting output goals for the efficient units. Resettingoutput goals has not been addressed in the reportedliterature.Frontier models, like DEA, have also been applied to the

service sector, particularly tourism-related services like therestaurant industry. Morey and Dittman (1995) evaluatedthe performance of hotel general managers through a DEAmodel application that minimized input resources whilemaintaining outputs levels. Morey and Dittman (1997) alsoapplied DEA as a selection model for hotel properties.Their procedure combined DEA and regression analysis toaddress both operations management and marketingissues. Anderson, Fish, Xia, and Michello (1999) employeda stochastic frontier technique to estimate managerialefficiency levels in the hotel industry. Reynolds andThompson (2002) described a DEA process used tocompare restaurants’ efficiencies and to examine their bestpractices.

3. The reallocation model

3.1. Problem setting

The DEA model was applied to a Spanish fast-foodrestaurant chain. Data were collected from a sample of 54chain units that were located in shopping centers andowned and directly operated by the firm’s central manage-ment. Operating data were collected from the sampledunits during the period from October 2001 to May 2002.Central management required that its name be heldconfidential and that any reported data be transformedso that the data would not be available to its competitors.Given the small number of similar size chains in Spain,central management wanted to avoid any risk that itscompetitors would have access to this information. Anabbreviated set of results is reported here to avoid thedisclosure of the identity of the chain.The data collected by chain management and used in the

model represented a small but reliable set. There areprevious works on the effects of using small samples inDEA. Banker, Gadh, and Gorr (1993) and Bifulco andBretschneider (2001) argued that when samples are smalland no measurement error exists, DEA probably forms aproduction frontier with mostly inefficient observations,and thus underestimates inefficiency in these cases.

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Table 1

Descriptive statistics for outputs and inputs

Variable Mean Std. Dev. Max. Min.

Sales (h) 561,904.87 309,047.20 1412,437.32 205,678.78

Quality index 82.45 11.05 91.87 69.54

Total Server staff 9.34 2.61 21.00 7.00

Number of seats 105.38 41.74 214.00 62.00

Location index 89.77 7.63 94.6 82.34

Average ticket per customer (h) 7.87 0.89 8.56 6.87

Number of competitors 12.26 3.98 17 8

Restaurant “k”

Sales ( )

Quality index

Wait and kitchen staff

Number of seats

Number of server counters

Loc

atio

n

Num

ber

ofco

mpe

titor

s

Ave

rage

bill

amou

nt ti

cket

Inputs Outputs

Context variables

Fig. 1. Inputs, outputs and context variables.

V.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270264

Similarly, Zhang and Bartels (1998) stated that thediscriminatory capability of DEA models increases withsample size. Consequently, a risk of underestimatinginefficiency exists in this application as a result of itssample characteristics. However, the utilization of DEA isjustifiable because it provides, even with small samples,more accurate efficiency indexes than other parametricmethodologies such as corrected ordinary least squares(Banker et al., 1993).

The researchers presented to central management a listof the most used output and input attributes identified inthe literature. After several interviews, guided by theresearchers, and taking into account the available informa-tion, the following variables were selected as the mostrepresentative of the productive process for this chain.Outputs factors included sales (expressed in million euros)and a quality index for each restaurant unit. The qualityindex is a range from 0 to 100 that is based on qualityquestionnaires filled out freely at each restaurant bycustomers, internal service quality audits, and dataprovided by mystery shoppers. The only input factor thatcould be reallocated among the restaurant units was thetotal number of wait and kitchen staff measured in full timeequivalents. Also, wait and kitchen staffs were interchange-able due to the short training required to hold eitherposition. Non-reallocable input factors included thenumber of seats and the number of server counters thatboth provide information about the size and servingcapacity of each unit.

Both the researchers and central management agreedthat specific unit characteristics like site location, thenumber of restaurant competitors at the shopping centerlocation, and the average bill amount per customer ticketcan also affect final sales. Central management used aninternal location index ranking from 0 to 100 to estimatethe sales potential for each restaurant unit. This indexcombines the number of shopping center customers peryear and a subjective measure for the relative site locationof the restaurant unit within the shopping center. Theunit’s average bill amount per consumer ticket was used toaccount for possible differences in sales-mix among therestaurant units. Depending on the sales-mix, two restau-rant units serving the same number of customer per yearcould yield different total sales. Since sales-mix is a variabledependent on market characteristics at each location, only

restaurants with similar average bill amounts werecompared. The number of competitors refers to thenumber of restaurants with similar average-ticket amountsin the same shopping center. Pearson’s correlation coeffi-cient showed that the sales per available seat were greaterin shopping centers with a higher number of competitors(r ¼ 0.768, with significant at level 0.05). The likely reasonfor this is the attraction power that a wide variety ofrestaurants may exert on customers. Other restaurantsefficiency studies using DEA have also used sales, numberof seats, and competition environment (Reynolds &Thompson, 2002). Table 1 presents a statistical summaryof input and output factors and Fig. 1 is a schematicdiagram of the input, output, and context variables.The environmental context variables—location, number

of restaurant competitors at the shopping center andaverage bill amount per customer ticket—were modelled asnon-adjustable inputs that central management did notcontrol. Lozano-Vivas, Pastor, and Hasan (2001) andLozano-Vivas, Pastor, and Pastor (2002) refer to thesenon-adjustable factors as non-discretionary factors. Pre-vious research reported in the literature described differentalternative ways to account for these environment factorswhen dealing with efficiency evaluation. In DEA models,the alternative approaches include: frontier division(Banker & Morey, 1986a; Brockett & Golany, 1996;Charnes, Cooper, & Rhodes, 1981); one-step models

ARTICLE IN PRESSV.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270 265

(Banker & Morey, 1986b; Charnes, Cooper, Lewin, &Seiford, 1994); multi-step mixed models (Ray, 1991) andmodels of consecutive step corrections in the slackvariables or the initial input or output variables (Fried,Schmidt, & Yaisawarng, 1999). A detailed summary ofthese alternatives can be found in Muniz (2002). But, thereis still no consensus as to what is the best way to reflectthese factors in DEA models.

Regarding the number of inputs and outputs selected,the proposed model satisfies the heuristic that the numberof analyzed units should be at lease three times the totalnumber of inputs and outputs factors (Charnes, Cooper,Divine, Ruefli, & Thomas, 1989).

3.2. Stage I model (1)

Each unit in the sample is evaluated on R outputmeasures and is provided I different input resources. Letyk ¼ ðy1k; . . . ; yRkÞ be the output measures vector for R

different outputs and xk ¼ ðx1k; . . . ;xIkÞ be the inputresources vector for I different inputs for the kth unit.The input resource set contains two subsets i � if [ iv

where inputs iv can be reallocated and inputs if cannot. Letcipjbe the cost of reallocating one unit of input (i 2 iv) fromthe pth unit to the jth unit. Central management of therestaurant chain places restrictions on reallocating inputresources. Let dipj 2 f0; 1g, where dipj ¼ 1 when the ithinput resource can be reallocated from the pth unit to thejth unit, and dijp ¼ 0 when it cannot.

The model in Stage I identifies both the efficient andinefficient units and determines the amount of unusedinput resources for each inefficient unit. The Stage 1 Modeldiffers from traditional DEA models in that efficiencycoefficients are obtained using a single linear programmingmodel instead of solving a different model for eachanalyzed unit. A similar formulation has been previouslyused by Athanassopoulos (1995).

The Stage I Model is

MinXK

k¼1

yk� e

XK

k¼1

XI

i¼1

siki þ

XK

k¼1

XR

r¼1

sokr

!

st:

XK

j¼1

lkj yrj � sok

r ¼ yrk 8r; k,

XK

j¼1

lkj xij þ sik

i ¼ ykxik; i 2 iv;8k,

XK

j¼1

lkj xij þ sik

i ¼ xik; i 2 if ;8k,

XK

j¼1

lkj ¼ 1 8k,

ykp1; lkj X0,

I � I f [ Iv, ð1Þ

where lk1 ; . . . ; l

kK are the intensity variables for the kth unit,

yrk is the rth output measure for the kth unit, xik is the ithinput resource for the kth unit, sok

1 ; . . . ; sokR are the slacks

variables for output measures for the kth unit, sik1 ; :::; sik

I

are the slacks variables for input resources for the kth unit,yk is the input oriented radial efficiency coefficient for thekth unit, and e 4 0 is a non-arquimedean infinitesimalparameter introduced in order to obtain efficient solutionsin the Koopmans’ sense (Koopmans, 1951).For solving this linear programming model, a two-step

model is used to avoid the computational problems thatinvolve assigning a numerical value to epsilon (Ali, 1994).Variable returns to scale (VRS) are assumed for technol-ogy. Removing or changing the last restrictions on theintensity vectors could also introduce other technologicalassumptions. (See Cooper et al. (2000) for more details)When yk

¼ 1, the kth unit is efficient and there are nounused input resources, while when yk o 1, the unit isinefficient and there are unused input resources. Here(1� yk) represents the maximum achievable reduction inall inputs for the kth unit that can be reallocated to otherunits. Let k1 be the set of efficient units and k2 the set ofinefficient units, where k � k1 [ k2. Let remk

i be theremaining or unused amount of the ith input resource forthe kth unit, where

remki ¼ ð1� yk

Þxik þ siki ; i 2 Iv.

The total unused amount of the ith resource input acrossall units is given by

remi ¼XK

k¼1

remki ; i 2 Iv.

3.3. Stage II model (2)

The next step is to reallocate remi among efficient units(k1). Central management imposed specific restrictions onstaff reallocation among restaurant units. It was consideredundesirable to move staff more than 20 km from theircurrent location. Central management felt it was importantto share staff among different restaurant units in order tomore efficiently use available resources, but the firm’shuman resources department felt strongly that Spanishworkers are not accustomed to reallocating over longdistances. The 20-km limit represented an acceptablecompromise and is similar to the reallocation limits foremployees used in some Spanish banks. Also, for practicalreasons central management wished to avoid reallocatingvery small quantities of full-time equivalents (FTEs)among different units. Thus, an additional restrictionimposed in Model (2) is that any staff reallocation be inmultiples of 0.5 FTE.Model (2) maximizes the overall system efficiency subject

to the imposed constraints while minimizing the cost ofreallocating staff among the restaurant units. A surrogatemeasure for the cost of the movement is the distance thatan input unit is moved. The total cost of reallocation is

ARTICLE IN PRESSV.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270266

defined as the sum of the products of units moved timesdistance for all reallocations:X

k1

Xk2

Xiv

qivk2k1civk2k1

.

This approach satisfies central management’s desire tokeep movements at a minimum and to make a move onlywhen a relative improvement in overall system efficiencyresults.

It should be highlighted that Model (2) only includesrestaurant units that are efficient in Model (1) and arethe only ones eligible to receive unused resources from theinefficient units in Model (1). Note that for forming theefficient frontier in Model (2) only the initial amounts ofinputs from Model (1) are considered. This ensures that theefficient frontier does not change and that the improvedoutput goals are technologically feasible after the realloca-tion of additional inputs.

Model (2) is as follows:

MaxX

k1

fk1 � eX

k1

Xk2

Xiv

qivk2k1civk2k1

!

st:

XK

j¼1

lk1

j yrj � sok1r ¼ fk1yrk1

8r; k1;

XK

j¼1

lk1

j xij þ sik1

j ¼ xik1þX

k2

qik2k1; i 2 iv;8k1,

XK

j¼1

lk1

j xij þ sik1

j ¼ xik1; i 2 if ; 8k1,

Xk1

qik2k1premk2

i ; i 2 iv;8k2,

qik2k1pMdik2k1

; i 2 iv;8k1; k2,

qik2k1¼ 0:5gik2k1

; i 2 iv; 8k1; k2,XK

j¼1

lk1

j ¼ 1 8k1,

fkX1; lk

j ; sok1r ; sik1

j ; qik2k1X0,

gik2k12 N

M !1, ð2Þ

where fk1 is the output efficiency of the k1th unit that isachieved after receiving reallocated inputs, qivk2k1

isreallocated amount of the ivth input from unit k2 to k1,dik2k1

¼ 1 if the distance between unit k2 and k1 is less than20 km, and 0 otherwise, gik2k1

is an instrumental binaryvariable equal to 0 if dik2k1

¼ 0, and any natural value ifdik2k1

¼ 1, e40 is a non-arquimedean infinitesimal para-meter.

In Model (2) only efficient units determined in Model(1) are evaluated in order to determine how resource inputscan be reallocated to expand the maximum efficiency of thechain. The objective function maximizes the outputefficiency coefficients fk1and, in the case of alternative

optimal solutions, selects those that minimize the inputreallocation cost. This meets central management’s re-quirement that allows for the least possible movement ofstaff when alternatives exist. The efficiency coefficientsfk1determined by Model (2) can be greater than or equal toone since some units may receive additional inputs. Also,units found to be efficient in Model (1) may now becomeinefficient after the input reallocation. Thus, fk1 representsthe revised output efficiency achieved after obtaining thenew inputs.Model (2) and Model (1) differ as follows. In the three

first sets of constraints Model (2) allows for an increase inresource inputs of

Pk2

qik2k1above the initial amount for

cases where reallocations are allowed. The fourth set ofconstraints assure that the total increase of the ith resourceinput for all efficient units must be less than or equal to thetotal available amount to be reallocated from inefficientunits (remk2

i ). The fifth constraint set assures that onlyfeasible reallocations are permitted. The next constraint setensures that feasible reallocations of resource inputs mustbe made in multiples of 0.5 that avoids relatively smallreallocates of staff among different units. The last groupsof restriction are standard in the literature for assumingVRS (Cooper et al., 2000).Model (2) does not require that all available resource

inputs from inefficient units in Model (1) be reallocatedamong the efficient units. Note that the total of requiredinputs for efficient units to achieve their maximum outputefficiency in Model (2) could be smaller than the totalresource inputs available for reallocation from Model (1).The fifth and sixth constrain sets allow that not allavailable resource inputs need be reallocated.A special feature of Model (2) is that it does not use the

marginal contribution that each resource input makestoward the output efficiencies of the restaurant units. Thesecontributions are the shadow prices obtained in Model (1).A microeconomic view would prescribe that the realloca-tion of remaining inputs to efficient units be made tomaximize the marginal contributions on output efficiencies.However, one well-known feature of DEA models is themultiplicity of marginal rates or virtual weights for theefficient units. This is because DEA models developempirical production functions that are continuous butnot derivable. In spite of this, different methods to get themaximum and minimum values of the marginal rates areknown (Rosen, Schaffnit, & Paradi, 1998; Sueyoshi,Ohnishi, & Kinase, 1999).A second characteristic of Model (2), also derived from

the efficient frontier concept, is the variation along thefrontier of the maximum and minimum marginal ratevalues. This would involve calculating validity rangesand using them as resource reallocation criterion. Model(2) reallocates the remaining resource inputs to the efficientunits in an implicit way while maximizing the marginalcontribution on output efficiencies, without the need tocalculate them explicitly. To achieve this effect, Model(2) introduces a criterion to choose among the various

ARTICLE IN PRESSV.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270 267

implicit marginal rates. Central management of therestaurant chain chose this criterion by requiring that insituations of alternative optimal solutions, that it preferredthe solution that allows for the least movement orrelocation of staff resources. This criterion is reflected inthe second term of the objective function in Model (2).

3.4. Stage III Model (3)

Once the reallocation procedure has been completed, thethird and last step determines the revised output targets forthe Model (1) inefficient units in set k2. These revisedtargets are based on the reduction and transfer of inputresources from these units and the reallocation of theseresources made in Model (2). Model (3) below provides thenew outputs targets. It is similar to Model (1) but dealsonly with setting revised output targets for the inefficientrestaurant units. In this case, again the initial efficientfrontier from Model (1) is maintained:

MaxX

k2

fk2 þ eXI

i¼1

sik2

i þXR

r¼1

sok2r

! !

st:

XK

j¼1

lk2

j yrj � sok2r ¼ fk2yrk2

8r; 8k2,

XK

j¼1

lk2

j xij þ sik2

i ¼ xik2�X

k1

qik2k1; i 2 iv;8k2,

XK

j¼1

lk2

j xij þ sik2

i ¼ xik2; i 2 if ;8k2,

XK

j¼1

lk2

j ¼ 1 8k2,

lkj X0; i � if [ iv. ð3Þ

Here, k2 is the set of inefficient units and the objectivefunction and constraints address only units in set k2. Thesecond constraint set formalizes the adjustment forreallocated units.

4. Results

Table 2 presents the results of Model (1) that determinesthe efficiency coefficients for both the efficient andinefficient units and the excess amounts, or unusedresources, of the inefficient units. The efficiency coefficientsare yk

¼ 1 for efficient restaurant units and yko1 forinefficient units. The percent of the current staff that eachinefficient restaurant unit could transfer given its efficiencycoefficient is ð1� yk

Þ � 100. Table 2 presents the staffeligible for potential transfer in FTEs for each inefficientunit. Model (1) determined that 57.4% of the units areinefficient and can contribute to the reallocation process.Recall that central management required that inputresources be efficiently reallocated. Thus, the amount of

resources transferred to efficient units might be less thanthe amount available for reallocation.Model (2) reallocated resources among the efficient

restaurant units and Model (3) set revised output targetsfor all units. The units receiving reallocated inputs, butmaintaining original output levels, would then becomeinefficient. The acquired inefficiency can be interpreted as anew output target for each unit base on the additionalresources the restaurant unit receives. Table 2 summarizesthe revised output goals after resource reallocations asdetermined by Models (2) and (3). Table 2 shows newoutput improvement targets for Model (1) efficient unitsand the initially inefficient ones after resources have beenreallocated. Note that previously efficient restaurant unitsthat received new output targets are highlighted in boldfont. These are units 13, 15, 17, 45, and 52.Table 2 identifies four different patterns that resulted

from the reallocation of resource inputs and the re-evaluation of output efficiency for each unit.

�

Model (1) inefficient units converted to Model (3) efficient

ones—units 6,16, and 43: For example, consider restau-rant unit 43. Initially, its efficiency coefficient was 0.60,but after resource reallocation its output efficiencycoefficient was 1.00. These units (6, 16, and 43) hadremaining resource inputs identified in Model (1), butafter input reallocation have become efficient. In thesecases, all remaining inputs have been reallocated toother units and, consequently, these units are now leftwith the optimum amount of inputs for their respectiveoutput level.

� Model (1) and Model (3) inefficient units—all Model (1)

inefficient units except for units 6, 16, and 43: Forexample, consider restaurant unit 50 which had anoutput efficient coefficient of 0.92 before resourcereallocation and 1.11 after. In this case, either an excessof resource inputs remained for the observed output, oran insufficient level of output resulted with the availableresources. Model (2) pointed out that this unit couldimprove its outputs by 11%, on average, since remain-ing resources were not reallocated in full to other units.Thus, it was still inefficient based on the amount of itsoutput efficiency determined by Model (M3).

� Model (1) and Model (3) efficient units—all Model (1)

efficient units except for units 13, 15, 17, 45 and 52: Theseunits were initially efficient, did not receive anyadditional reallocated resources, and remained efficientin Model (3). Restaurant unit 10 is an example of thissituation.

� Model (1) efficient units and Model (3) inefficient—units

13, 15, 17, 45 and 52: This group consisted of initiallyefficient units that have received additional reallocatedresources in Model (2) together with higher revisedoutput targets in Model (3). The average increase inoutput efficiency that these units could achieve was4.2%, with a maximum increase of 8% for restaurantunit 17. By providing additional resources central

ARTICLE IN PRESS

Table 2

Results: Model (1), Model (2), Model (3)

Rest. (k) Model (1)

efficiency

coefficient

Staff eligible for

transfer (FTE)

Model (3)

efficiency

coefficient—

revised target

Rest. (k) Model (1)

efficiency

coefficient

Staff eligible for

transfer (FTE)

Model (3)

efficiency

coefficient—

revised target

1 0.51 1.47 1.02 28 1.00 1.00

2 0.51 1.48 1.03 29 0.71 0.57 1.02

3 0.54 1.86 1.04 30 0.18 4.89 1.08

4 0.45 1.64 1.02 31 1.00 1.00

5 1.00 1.00 32 0.35 1.95 1.06

6 0.99 0.02 1.00 33 0.49 1.52 1.19

7 1.00 1.00 34 0.58 1.47 1.01

8 1.00 1.00 35 0.56 1.10 1.01

9 0.73 0.55 1.04 36 0.94 0.09 1.02

10 1.00 1.00 37 1.00 1.00

11 1.00 1.00 38 1.00 1.00

12 0.73 0.55 1.01 39 0.68 0.96 1.01

13 1.00 1.05 40 1.00 1.00

14 1.00 1.00 41 0.75 0.50 1.00

15 1.00 1.01 42 0.48 1.56 1.01

16 0.74 0.52 1.00 43 0.60 1.19 1.00

17 1.00 1.08 44 1.00 1.00

18 0.70 0.60 1.01 45 1.00 1.05

19 0.40 1.49 1.09 46 0.35 1.96 1.11

20 0.47 1.58 1.02 47 1.00 1.00

21 0.36 2.89 1.02 48 0.42 1.74 1.06

22 0.40 2.11 1.03 49 0.45 1.66 1.03

23 1.00 1.00 50 0.92 0.11 1.11

24 0.93 0.26 1.02 51 0.93 0.11 1.16

25 1.00 1.00 52 1.00 1.02

26 1.00 1.00 53 0.46 1.61 1.03

27 1.00 1.00 54 1.00 1.00

Table 3

Detailed reallocation matrix

From/To 13 15 17 45 52 Total

V.M. Gimenez-Garcıa et al. / Tourism Management 28 (2007) 262–270268

management can provide incentives and can work withunit managers to achieve higher output targets for theseunits.

2 1.00 1.00

4 0.50 0.50

16 0.50 0.50

20 0.50 0.50

21 0.50 0.50

30 1.00 1.00

35 1.00 1.00

41 0.50 0.50

48 0.50 0.50

Total 1.00 1.00 0.50 2.00 1.50 6.00

Table 3 presents the reallocation schedule for inputresources from inefficient units to efficient ones. Only sixFTE’s input resources were reallocated across the wholesystem taking into account the constraints placed bycentral management. Only 30% of the initial inefficientrestaurant units provided resources to be reallocated tofive efficient ones. All movements from inefficient unitsinvolved no more than one FTE, while at most two FTEswere received by any one of the efficient units. Unit 45received a total of two FTEs from units 2, 20 and 21.

The model results reflect central management’s require-ment that staff be shared among restaurants in closeproximity. Since the chain owns all restaurant units, centralmanagement plans and allocates staff and other resourcesfor all units. Thus, there are no potential conflicts based onresource allocation that could arise if, for example, thesewere franchise operations. Also, potential employee-rela-tions problems were avoided because central managementset a maximum distance for reallocating staff from theirinitial location and required reallocations in multiples of

0.5 FTEs, or a half workday, that simplified the workforcescheduling for both workers and unit managers.Convincing unit managers of efficient units to increase

output expectations and increase sales could be difficult todo. Unit managers might argue that in practice they havevery limited tools to increase sales and expand theirmarkets. The majority of fast-food chains hire unitmanagers for their operating skills, while limitingtheir marketing and sales responsibilities, which areretained by central management. But, unit managers

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should understand the impact that reallocated resourcesand the increased output goals would have on improve-ment in service quality. Zeithaml and Bitner (1996)highlighted the importance of people, facilities andprocesses in achieving service quality. Thus, with addi-tional server staff, higher levels of service quality forcustomers in the form of faster and more accurateexecution of order taking, serving, and bill processing arepossible. Quality improvement can and should lead toincreased sales that in turn make the achievement of highersale objectives easier. Thus, central management and unitmanagers should recognize that proper administration ofadditional input resources can lead directly to meetingincreased output goals.

5. Summary and conclusions

This paper describes a non-parametric, efficient frontier,three-stage DEA method used to allocate resources amonga set of restaurant units belonging to a networked, centrallymanaged Spanish fast-food chain. Specifically, the model-ling procedure identified inefficient units and their remain-ing resources, reallocated these resources among theefficient units, and set new improvement targets for boththe efficient and inefficient units. After the work reportedhere, the Spanish fast-food chain used the model to designa bonus system and to improve the management of therestaurant units. This application demonstrates the model’sutility and capability to improve the management ofnetworked organizations.

Model results pointed out that it is not necessary toreallocate large amounts of resources that might provedisruptive for the restaurant chain. But, initial allocation ofresources can be adjusted to achieve significant improve-ment in output. In this case, resource reallocation led torevised output goals averaging an increase of 4.2% (salesand service quality) for the efficient restaurant units.This improvement in output goals was first reflected inimproved service quality for the units since service qualityis directly related to available staff.

There are broader managerial implications for using thismodelling procedure. It provides internal benchmarks onwhich to evaluate units and an objective means to identifyand reallocate resources to efficient units. Central manage-ment benefited by having an objective justification to re-enforce and communicate its confidence in efficient unitmanagers and to provide incentives for the potentialgrowth for these units. In addition, central managementhas objective model results to use to identify, address, andeliminate situations that might accommodate mediocreperformance in inefficient units and to emphasize the needto value scarce resources and use them efficiently.

Finally, this modelling procedure can be used in non-service-related situation where resources inputs are tied tooutput goals. For example, consider the case of formulat-ing supplier relationship management plans in manufactur-ing. These plans start with the evaluation of a portfolio of

suppliers based on multiple performance criteria thatmeasure various output attributes in the way suppliers fillorders from a manufacturer. The manufacturer providesresource inputs in the form of orders to the suppliers. Overtime and at predetermined intervals the manufacturer mustevaluate the relative performance of each supplier andmake decisions regarding future orders to each supplierand how the relationship with each supplier might evolve.The modelling procedure described here can be of use: toperform an evaluation of suppliers, identifying those thatare efficient and those that are inefficient, to identify howorders might be reallocated among the suppliers, and toadjust output goals for each supplier.

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