Expert Systems with Applications 40 (2013) 3926–3933

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Expert Systems with Applications

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Benchmarking distribution centres using Principal Component Analysisand Data Envelopment Analysis: A case study of Serbia

Milan Andrejic ⇑, Nebojša Bojovic, Milorad KilibardaUniversity of Belgrade, Faculty of Transport and Traffic Engineering, Republic of Serbia

a r t i c l e i n f o a b s t r a c t

Keywords:Distribution centresEfficiencyData Envelopment AnalysisPrincipal Component Analysis

0957-4174/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.eswa.2012.12.085

⇑ Corresponding author. Address: Vojvode Stepe 305Serbia. Tel.: +381 11 30 91 304; fax: +381 11 30 96 7

E-mail addresses: m.andrejic@sf.bg.ac.rs (M. AndreBojovic), m.kilibarda@sf.bg.ac.rs (M. Kilibarda).

The efficiency of distribution systems is largely affected by the performances of distribution centres. Themain objective of this paper is to develop and propose a DEA model for distribution centres efficiencymeasuring that can help managers in decision making and improving the efficiency. Due to numerousindicators that describe DCs operating, the main problem is indicators selection. In order to improve dis-criminatory power of classical DEA models PCA–DEA approach is used. This paper analysis the efficiencyof distribution centres of one trading company in Serbia. Proposed models integrate operational, quality,energy, utilisation and equipment warehouse and transport indicators. Several hypotheses are tested inthis paper. The results showed that small distribution centres are more efficient than large.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

In order to survive in the market and achieve profitability, thecompanies need to perform their activities in an efficient way. Effi-ciency is a very important indicator of companies’ operations anal-ysis, and it is one of the basic and the most frequently usedperformances. Measuring, monitoring and improving efficiencyare the main tasks for companies in the 21st century. The impor-tance of efficiency measuring in logistics has been recognised in lit-erature (Chow, Heaver, & Henriksson, 1994; Hackman, Frazelle,Griffin, Griffin, & Vlasta, 2001; Min & Joo, 2006). This process is avery complicated one due to the complex structure of logistics sys-tems. Distribution centres (DCs) are complex logistics systemswhich connect producers with other participants in the chain,including end-users. DCs of trading companies and DCs in generalrepresent complex logistics systems with a very important placeand role in the supply chains. In literature little has been donefor the performance measurement of the distribution side of thesupply chain. This paper analyses in more detail the efficiency ofDCs of the trading company that operates in the region of Serbia.

‘‘Single ratio’’ indicators have been used for estimating theefficiency of DCs for a long time. These indicators do not provideenough information about the system operating. Recently, anincreasing number of authors have advocated the use of ap-proaches such as the Data Envelopment Analysis (DEA) method(Min & Joo, 2006; Toloo & Nalchigar, 2011). Adler and Golany

ll rights reserved.

, 11000 Belgrade, Republic of04.jic), nb.bojovic@sf.bg.ac.rs (N.

(2001), Adler and Golany (2002) have suggested using the PrincipalComponent Analysis (PCA), a methodology that produces uncorre-lated linear combinations of original inputs and outputs, to im-prove discrimination in the DEA with a minimal loss ofinformation. The DEA models often fail when there are an exces-sive number of inputs and outputs in relation to the number ofdecision making units (DMUs).

DC’s operating describes a large number of different indicators,and the problem is how to select relevant indicators which de-scribe DC operating in the best way. Variables selection problemis recognized in literature (Boussofiane, Dyson, & Thanassoulis,1991). Various indicators with different effect on systems, subsys-tems, processes and activities further complicate the selection ofvariables. The main objective of this paper is to develop a modelfor measuring efficiency of DCs of one trading company. Informa-tion obtained from the company management and the author’sexperience is used in the process of model development.

Next section gives a review of indicators used for measuringefficiency in logistics. The third section describes the PCA–DEA ap-proach. Efficiency evaluation system of observed DCs is given inthe fourth section. In section five the results of the proposed modelare described. Several hypotheses are also tested in section five. Atthe end of the paper, the concluding remarks and directions of fu-ture research are presented.

2. Literature review

In the field of logistics, the DEA method is mostly used forefficiency estimation. Different indicators are used for measuringefficiency in logistics (Table 1). Ross and Droge (2002) analyzed102 DCs efficiency, as a part of complex supply chains. They also

Tabl

e1

Effi

cien

cyin

dica

tors

inw

areh

ouse

san

dD

Cs.

Publ

icat

ion

Inpu

tO

utp

ut

Fiel

dIn

dica

tor

type

s

Ch

akra

bort

y,M

aju

mde

r,an

dSa

rkar

(201

1)

Nu

mbe

rof

empl

oyee

s,ge

ner

alex

pen

ses,

spac

e,in

ven

tory

Fill

rate

,sal

e,se

rvic

eti

me

DC

sO

pera

tion

al,

fin

anci

al,q

ual

ity

Hac

kman

etal

.(20

01)

Labo

r,sp

ace,

mat

eria

lh

andl

ing

and

stor

age

equ

ipm

ent

The

pick

ing/

ship

pin

gw

orkl

oad

isdr

iven

byth

en

um

ber

ofor

ders

and

the

nu

mbe

rof

lin

eson

thos

eor

ders

,In

vest

men

tsin

mat

eria

lh

andl

ing

equ

ipm

ent,

The

stor

age

outp

ut

inde

xW

areh

ouse

san

dD

Cs

Equ

ipm

ent,

oper

atio

nal

Ham

dan

and

Rog

ers

(200

8)La

bor

hou

rs,W

areh

ouse

spac

e,te

chn

olog

yin

vest

men

t,M

ater

ials

han

dlin

geq

uip

men

t(M

HE)

Thro

ugh

put,

orde

rfi

ll,s

pace

uti

lisa

tion

War

ehou

ses

and

DC

sO

pera

tion

al,

qual

ity,

uti

lisa

tion

Kor

pela

etal

.(20

07)

Dir

ect

cost

s,in

dire

ctco

sts

Rel

iabi

lity

(tim

e,qu

alit

y,qu

anti

ty),

Flex

ibil

ity

(Urg

ent

deli

veri

es,f

requ

ency

,spe

cial

requ

est,

Cap

acit

y(a

bili

tyto

resp

ond

toch

ange

sin

war

ehou

sin

gca

paci

tyn

eeds

ofa

cust

omer

)W

areh

ouse

sQ

ual

ity,

fin

anci

al

deK

oste

ran

dB

alk

(200

8)N

um

ber

ofdi

rect

full

-tim

eeq

uiv

alen

ts,S

ize

ofth

ew

areh

ouse

,deg

ree

ofau

tom

atio

n,n

um

ber

ofdi

ffer

ent

SKU

sN

um

ber

ofda

ily

orde

rli

nes

pick

ed,T

he

leve

lofv

alu

e-ad

ded

logi

stic

s(V

AL)

acti

viti

esca

rrie

dou

t,N

um

ber

ofsp

ecia

lpr

oces

ses,

Perc

enta

geof

fail

ure

-fre

eor

ders

War

ehou

ses

Ope

rati

onal

,qu

alit

yM

inan

dJo

o(2

006)

Acc

oun

tre

ceiv

able

s,Sa

lari

esan

dw

ages

,Exp

ense

sot

her

than

sala

ries

and

wag

es.

Ope

rati

ng

inco

me

War

ehou

ses

and

DC

sFi

nan

cial

Ros

san

dD

roge

(200

2)A

vera

gela

bor

expe

rien

ce,fl

eet

size

,equ

ipm

ent,

mea

nor

der

thro

ugh

put

tim

e(M

OT)

Prod

uct

sale

svo

lum

eD

Cs

Equ

ipm

ent

(Cap

acit

y),

Ope

rati

onal

M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933 3927

analyzed efficiency change in time. Hamdan and Rogers (2008)used the DEA method for estimating efficiency of 3PL providerswith an emphasis on warehouse operations. The authors comparedthe results of two DEA models with and without weight restric-tions. Hackman et al. (2001) developed a model with multiple in-puts and outputs to evaluate the efficiency of 57 warehouse anddistribution facilities. Among other things, they confirmed conclu-sions concerning the relation between warehouse size, level oftechnology and efficiency. They used labour, space, material han-dling and warehouse equipment inputs, as well as movement,accumulation and storage outputs. De Koster and Balk (2008)benchmarked international warehouse operator’s performances.They used equipment and capacity indicators (size of the ware-house in square meters; degree of automation, etc.), operational(number of daily order lines picked, the level of value-added logis-tics (VAL) activities) and quality indicators (the percentage of fail-ure-free orders shipped; order flexibility) for efficiency evaluation.

Korpela, Lehmusvaara, and Nisonen (2007) advocated the use ofcost indicators as inputs, but also qualitative indicators as outputs.The authors combined the Analytic Hierarchy Process (AHP) andthe DEA model to evaluate the warehouse providers. Min and Joo(2006) measured the efficiency of third party logistics providers.

The distribution of goods today relies heavily on the use of roadtransport (Table 2). In literature there are different approaches forfreight transport performance measurement. In the literature avariety of indicators of transport system are used. Kim (2010)has evaluated technical and scale efficiency of individual trucksin logistics. The DEA model for 62 trucks efficiency evaluation isspecified with three output categories and five costs categorieswhich represent inputs. Cruijssen, Dullaert, and Joro (2010) ana-lysed freight transportation efficiency in Flanders. Simons, Mason,and Gardner (2004) defined Overall Vehicle Effectiveness (OVE)and state that transport efficiency is important at an economic, so-cial and environmental level. The authors defined five transportlosses or wastes: driver breaks, excess loading time, fill loss, speedloss and quality delay. McKinnon (1999) analyses KPIs for the foodsupply chain. They analysed vehicle utilisation and energy effi-ciency. They used several indicators such as the degree of emptyrunning, fuel efficiency and deviations from schedule, time utilisa-tion and vehicle utilisation.

Nowadays, energy efficiency has become a critical issue forlogistics systems. In a situation of increasing global energy de-mands and rising energy costs, conserving energy is becoming avery important issue (Table 2). In literature there are many papersthat investigate indicators of energy efficiency in logistics systems.Kalenoja, Kallionpää, and Jarkko Rantala (2011) studied indicatorsof energy efficiency of supply chains. Authors also noted theimportance of some indicators like: energy consumption, waterand electricity consumption, fuel consumption and material use,habitat improvements and damage due to enterprise operations,quantity of non-product output returned to process or market byrecycling or reuse. The authors also link energy efficiency in supplychains with the requirements of ISO 14301 classical (environmen-tal performance evaluation). Neto, Walther, Bloemhof, van Nunen,and Spengler (2009) recognized the problem of balancing environ-mental and business concerns. A detailed overview of indicatorsfor green supply chain management is given in the paper of Her-vani, Helms, and Sarkis (2005). They give the list of environmentalperformance metrics ranging from air emissions to energy recov-ery and recycling.

Mckinnon, Cullinane, Browne, and Whiteing (2010) in frame-work of assessment for developing sustainability in warehousingdistinguished a micro and a macro-level perspective. Micro levelincludes business and economy with indicators of energy, waterand buildings, while macro level includes environment and societywith indicators of ecology, environment and land use. Kuosmanen

Table 2Efficiency indicators in transport and supply chains.

Publication Indicators Field Indicator types

Cruijssen et al.(2010)

Labor (e.g. total wages, (drivers’) experience, total hours worked, number of employees, etc.),Equipment (e.g. number of trucks, number of trailers, total loading capacity etc.), Intangibleassets (market information, customer contacts, goodwill etc), Added value, Profit

Transportsystems andvehicles

Equipment (Capacity),operational, financial,energy

Hervani et al.(2005)

Ranging from air emissions to energy recovery and recycling: fugitive non-point air emissions,total energy use, total electricity use, total fuel use, other energy use, major environmental,social, and economic impacts associated with the life cycle of products and servicesManagement level to measure - strategic, tactical, operational

Supply chain Energy, environmental

Kalenoja et al.(2011)

Costs, quality, time and flexibility, environmental indicators such as energy consumption orcarbon dioxide emissions, ISO 14031 performances (environmental condition indicators,management performance indicators and operational performance indicators)

Supply chain Financial, energy, quality,environmental

Kim (2010) Labor cost, fuel cost, oil cost, supplies cost, tax, insurance, transportation distance,transportation amount, effective transportation distance

Transportsystems andvehicles

Financial, operational,energy

Kuosmanen andKortelainen(2005)

Road transportation, mileage, fuel consumption, environmental pressures-undesirableoutputs (CO2, CH4,N2O, CO, NOx SO2, emissions...)

Transportsystems andvehicles

Operational, energy,environmental

McKinnon (1999) Vehicle fill, Empty running, Vehicle time utilisation, Deviations from schedule, Fuelconsumption

Transportsystems andvehicles

Energy, utilisation

Neto et al. (2009) Masses entering the treatment system, Output masses that are recycled Logisticsnetwork

Environmental

Sarkis and Talluri(2004)

Quantitative inputs (raw material intake, energy, materials used, employees...) Qualitativeinputs (managerial plans, Green Purchasing program, ISP 14000...) Quantitative outputs(water emissions, air emissions, solid wastes, products, penalties. . .) Qualitative outputs(biodiversity impacts, greenhouse impact, community response...)

Generalorganisation

Environmental, qualitative,operational

Simons et al.(2004)

Operating costs, energy consumption, vehicle emissions, fuel, labour, transport losses orwastes (driver breaks, excess loading time, fill loss, speed loss, quality delay)

Transportsystems andvehicles

Financial, operational,energy, quality

3928 M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933

and Kortelainen (2005) defined main environmental pressures andundesirable outputs that are due to road transport. The authorsalso emphasized the importance of economic variables such asmileage and fuel consumption. Sarkis and Talluri (2004) investi-gated eco-efficiency measurement using the DEA method. Theydistinguished qualitative and quantitative inputs and outputs.

It is evident that in literature there are numerous efficiencyindicators. For DCs warehouse and transport indicators are rele-vant. These indicators are related to the operational, tactical andstrategic decision-making level. Selection of the most appropriateindicators is complex process. In situation of a large number ofindicators and a relatively small number of data, the use of DEAmethod is limited. Namely, the discriminatory power of DEA mod-els decreases. In order to overcome this PCA–DEA approach is usedin this paper. PCA–DEA approach is described in next section.

3. PCA–DEA approach

DEA is a non-parametric linear programming technique whichenables the comparison of different DMUs, based on multiple in-puts and outputs. The efficiency is relative and relates to a set ofunits within the analysis. Charnes, Cooper, and Rhodes (1978) pro-posed a non-parametric approach for efficiency estimation, wherethey reduced multiple inputs to a single virtual input and multipleoutputs reduced to a single virtual output using weighting coeffi-cients. In the set of homogeneous units, the DEA finds the mostefficient DMUs and according to them it defines the efficiency ofother units. In this paper classical BCC DEA output oriented modelis used (Banker, Charnes, & Cooper, 1984).

Originally, the PCA was pioneered as a data reduction techniqueof multivariate data (Beltrami, 1873; Jordan, 1874). PCA explainsthe variance structure of a matrix of data through linear combina-tions of variables, consequently reducing the data to a few princi-pal components (PCs), which generally describe 80–90% of thevariance in the data (Sharma, 1996). If most of the population var-iance can be attributed to the first few components, then they can

replace the original variables with minimum loss of information. Inliterature the PCA is used for improving discrimination in the DEA.

By comparing n units with q outputs denoted by Y and r inputsdenoted by X, the efficiency measure for unit observed unit DMUa

is expressed as in:

minU;V

VXa � va ð1Þ

Subject to:

VX � UY � va P 0 ð2ÞUYa ¼ 1 ð3ÞV P 0 ð4ÞU P 0;vafree ð5Þ

In previous model V and U represent vectors of DMU weights cho-sen by the linear program, va is scalar, Xa and Ya input and outputcolumn vectors for DMUa.

In the PCA the most of the population variance can be attributedto the first few components, so they can replace the original vari-ables with minimum loss of information (Adler & Golany 2001; Ad-ler & Golany 2002). According to Hair, Anderson, Tatham, and Black(1995), a random vector X = [X1,X2, . . . ,Xp] (the p is the number oforiginal inputs/outputs chosen to be aggregated) has the correla-tion matrix C with eigenvalues k1 P k2 P � � �P kp P 0 and normal-ized eigenvectors l1, l2, . . . , lp. Consider the linear combinations,where the superscript t represents the transpose operator:

XPCi¼ lt

i ¼ l1iX1 þ l2iX2 þ � � � þ lpiXp; i ¼ 1;2; . . . ;p ð6ÞVarðXPCI Þ ¼ lti Cli; i ¼ 1;2; . . . ;p ð7ÞCorrelationðXPCI ;XPCK Þ ¼ lt

i Clk; i ¼ 1;2; . . . ;p; k ¼ 1;2; . . . ;p; i–k

ð8Þ

The PCs are the uncorrelated linear combinations ranked by theirvariances in descending order. As mentioned before PCA ranksPCs in descending order of importance. Alder and Golany (2002)set additional constraints that require the weight of PC1 to be at

M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933 3929

least that of PC2, the weight of PC2 to be at least that of PC3 and soon. VPC and UPC represents vector of weights assigned to inputs andoutputs PCs. The PCA–DEA model used in this paper has the follow-ing form:

minUPC ;VPC

VPCXaPC � va ð9Þ

Subject to:

VPCXPC � UPCYPC � va P 0 ð10ÞUPCYa

PC ¼ 1 ð11ÞVPC P 0 ð12ÞUPC P 0; vafree ð13Þ

In this paper PCA is applied to all groups of inputs and outputs sep-arately. Next section describes the efficiency evaluation system inmore details.

4. DC’s efficiency evaluation system

This paper analyzes the efficiency of seven distribution centresof a trading company which operates in Serbia. The efficiencies ofthe observed centres were analyzed during a twelve-month period.The company management has used a variety of indicators to mon-itor the operating of the company. Performances are evaluated by‘‘single ratio’’ indicators such as: distance/driver, order pickingtransaction/order picker, warehouse and vehicle space utilization,etc. which do not provide enough information about the company’soperation. According to various criteria, the indicators in logisticscan be classified in different ways.

From the point of decision-making level there are indicators atthe strategic, tactical and operational level. The DC representscomplex systems with a large number of interconnected subsys-tems, processes and activities, which are all interconnected andinfluence each other. Each of them is characterized by certain indi-cators. The main processes in the DC, among others, are: receiving,shipping, control, packing, warehousing, order picking, order pro-cessing, etc. Each of them is characterized by certain indicators.Transport and warehouse subsystems are basic subsystems in theDC. Consequently, it is possible to define transport efficiency indi-cators and warehouse efficiency indicators. However, there areindicators that cannot be strictly divided into mentioned catego-ries. For example invoices (demands) and turnover are consideredas common variables in DCs.

Depending on the type, logistics indicators can be divided into:equipment and capacity indicators, operational indicators, qualityindicators, energy indicators, environmental (social) indicators,etc. The aforementioned indicators can be qualitative andquantitative.

As mention before in the observed DCs, as well as in most realsystems, performances are evaluated by ‘‘single ratio’’ indicatorswhich are not good indicators of the DC’s efficiency since they donot provide enough information about their operating mode. TheDEA method provides the possibility of integrating a large numberof different indicators into a unified measure of efficiency. For asuccessful DC’s efficiency evaluation in observed period it is neces-sary to choose the most important indicators that best describe theDC’s operating. One way of overcoming this problem is the applica-tion of the PCA method. The PCA method is a popular method usedfor different problems in literature (Adler & Golany 2001; Adler &Golany 2002; Adler & Golany 2007; Liang, Li, & Li, 2009). To thebest of our knowledge there are not enough papers in the literatureconcerning the DCs which uses the PCA–DEA approach for measur-ing efficiency.

List of indicators that are used in observed example are shownin Table 3. They are divided into five groups. Input and outputcategory is indicated in the third column. Warehouse and transport

indicators are marked in the fourth column. Equipment and capac-ity indicators include general indicators frequently used in litera-ture (Ross & Droge 2002; Hamdan and Rogers 2008; Hackmanet al., 2001). The largest group is the operational indicators group.Similar indicators are used in the literature (de Koster & Balk,2008; Kim, 2010; Cruijssen et al., 2010). There are also ‘‘single ra-tio’’ indicators that observed DCs monitor, and to the best ofauthors’ knowledge have not been used in the literature. Driversovertime per driver and order picking transactions per order pickerare some of them. Energy indicators are very important for logisticssystems. Energy consumption costs in DCs have a great share of to-tal costs. Utilization factors greatly influence the operating of thecompany, on total costs, as well as on efficiency (McKinnon,1999). Apart from warehouse and vehicle space utilization this pa-per also analyses time utilization of truck in distribution process.

Failures in the transport and warehouse subsystems representquality indicators which may be the cause of dissatisfaction andcomplaints of the customer. Failures in the warehouse relates tothe mistakes in the order picking process (shortage/excess in thedelivery, articles mix-up, damages), but also to other processessuch as bad inventory management, etc. Failures in transport pri-marily concern the delivery that is falling behind schedule, as wellas the damaging and losing goods in the transport process

Three groups of inputs – equipment, operational and energy,and three groups of outputs – operational, utilisation and qualitycan be observed in Table 3.

The proposed methodology is realizes in two phases. In the firstphase, it is necessary to implement the PCA for each of the groupsof inputs and outputs separately. PCs from the first stage are usedas inputs and outputs in the second phase. PCA–DEA models areused in the second phase for efficiency evaluation. Several modelsare used in this paper for measuring efficiency of observed set: theclassical BCC DEA output oriented model (Eqs. (1)-(5) – Model I),and the four PCA–DEA models. The first PCA–DEA model (ModelII) has additional constraints (Eqs. (14)-(20)) to model ((9)-(13))described in previous section and prioritizes the PCs in descendingorder of importance in each group. For example, the first compo-nent in the group of equipment and capacity indicators is moreimportant than the second one from the same group. In this wayconstraints in all groups of inputs and outputs are set:

VPCequipm1� VPCequipm

2P 0 ð14Þ

VPCenergy3� VPCenergy

4P 0 ð15Þ

VPCoperat5� VPCoperat

6P 0 ð16Þ

VPCoperat6� VPCoperat

7P 0 ð17Þ

UPCutilisat1� UPCutilisat

2P 0 ð18Þ

UPCquality3� UPCquality

4P 0 ð19Þ

UPCoperat5� UPCoperat

6P 0 ð20Þ

In the previous model VPCequipm1

and VPCequipm2

represent weights assign

to PCs from the group of equipment and capacity inputs, VPCenergy3

and

VPCenergy4

PCs from energy inputs group, VPCoperat5

, VPCoperat6

and VPCoperat7

from the operational inputs group. Similar, UPCutilisat1

and UPCutilisat2

are

weights assigned to PCs of utilisation indicators group, UPCquality3

and

UPCquality4

PCs from quality output group, UPCoperat5

and UPCoperat6

PCs from

operational output group.This model does not consider the relationship between the

components of different groups. Therefore additional models areanalysed. In contrast to previous model, Models III, IV and V areadditionally constrained in accordance with the company’s man-agement information and author’s experience (opinion). The basicidea in these models is to favour variables that are most important

Table 3Data for DC’s efficiency measuring.

Type Variables I/Oa W/T b

Equipment and capacity indicators Vehicles I TForklifts I WEmployees in warehouse I WEmployees in transport I TWarehouse area I WPallet places I W

Energy Fuel I TElectricity consumption I WOther energy costs (water, gas) I WUtility costs I W

Operational Invoices (Demands) I W-TWarehouse overtime I WDriver’s overtime I TVehicle maintenance I TDriver’s overtime/driver I TShipped pallets O TDistance O TDeliveries O W-TOrder picking transactions O WTour/driver O TDelivery/driver O TTons/ driver O TPallets/driver O TDistance/driver O TOrder picking trans./order picker O WTurnover O W-T

Utilisation Time truck utilisation O TSpace truck utilisation O TWarehouse space utilisation O W

Quality Failures in warehouse O WFailures in transport O TWrite off expired goods O WTotal failures O W-T

a I-Input; O-Output.b W-Warehouse indicator; T-Transport indicator.

3930 M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933

for the DC’s operating. Managers in the observed company paymore attention to outputs. They also argue that in most cases itis easier to implement corrective actions on inputs rather thanon outputs. Therefore, in subsequent models, restrictions are ap-plied only to the outputs.

Managers in DCs consider that operational variables like turn-over, shipped pallets, distance driven, etc. are major indicators ofsuccessful operating. In that manner Model III favours PCs fromoperational output indicators group. Additional constraints havethe following form:

UPCoperat6� UPCutilisat

1P 0 ð21Þ

UPCoperat6� UPCquality

3P 0 ð22Þ

The importance of utilisation indicators is recognized in literature(McKinnon, 1999). Model IV gives more importance to PCs compo-nents composed of utilisation indicators. In that sense the two newconstraints are:

UPCutilisat2� UPCquality

3P 0 ð23Þ

UPCutilisat2� UPCoperat

5P 0 ð24Þ

There are numerous quality indicators in logistics. The ultimategoal, however, is customer satisfaction. No matter what indicatoris concerned the quality of service greatly affects customer satisfac-tion. Satisfied and loyal customers mean a secure income for thecompany. On the other side unsatisfied customers and customer’scomplaints create additional costs. In this paper, more attention ispaid to the failures in the distribution process. In that sense, Model

V favours PCs of quality indicators in DC. Additional constraints inModel V are:

UPCquality4� UPCutilisat

1P 0 ð25Þ

UPCquality4� UPCoperat

5P 0 ð26Þ

Proposed models are tested on real example in the next section.Several hypotheses are also tested.

5. Case study results

As mention before, the PCA–DEA approach is used for measur-ing efficiency of seven DCs of one trading company in Serbia duringa twelve-month period. Data has been aggregated for the twelvemonths of 2011. Each DC in each month is a separate decision mak-ing unit. Thus, a set of 84 DMUs is observed. (Tulkens & Eeckaut,1995; Cullinane, Ji, & Wang, 2005; Hoff, 2007).

5.1. Principal Component Analysis scores

The first phase of efficiency measuring is the PCA for all groupsof inputs and outputs separately. From each of six groups maincomponents were selected. All extracted components explain min-imum 80% of total variance of each group. All quality indicatorsused in this paper represent some kind of undesirable outputs, sothey are reversed (Liang et al., 2009). The results of Principal Com-ponent Analysis are presented in Table 4.

Two PCs are extracted from equipment and capacity input indi-cators. They explain a vast of the majority of the variance in the

Table 4PCA scores (Correlation between variables and PCs).

Inputs Average St. dev. PC 1 PC 2 PC 3

Vehicles (No) 22.38 8.11 0.901 �0.390Forklifts (No) 51.76 25.18 0.950 0.047Employees in warehouse (No) 71.35 31.84 0.859 �0.468Employees in transport (No) 46.51 21.74 0.984 �0.070Warehouse area (m2) 8173.62 3311.03 0.737 0.501Pallet places (No) 4484.86 1947.72 0.699 0.584

Variance explained 74.19% 90.34%Fuel (103 m.u.) 2528.43 1673.49 0.849 �0.026Electricity consumption (103 m.u.) 481.89 281.53 0.945 0.061Utility costs (103 m.u.) 125.36 249.10 0.689 �0.487Other energy costs (water, gas, etc) (103 m.u.) 167.76 157.78 0.335 0.897

Variance explained 55.02% 81.17%Invoices (Demands) (103) 8505.01 2896.76 0.833 �0.355 0.142Warehouse overtime (h) 373.33 445.21 0.375 �0.660 �0.630Driver’s overtime (h) 450.20 242.33 0.683 0.524 �0.282Vehicle maintenance (103 m.u.) 649.08 431.42 0.747 �0.290 0.508Driver’s overtime/driver (h/driver) 13.82 8.49 0.627 0.641 �0.110

Variance explained 45.05% 71.67% 87.02%OutputsTime truck utilisation (%) 34.38 7.32 0.919 �0.020Space truck utilisation (%) 66.77 15.60 0.847 �0.389Warehouse space utilisation (%) 89.68 13.06 0.381 0.913

Variance explained 56.86% 89.71%Failures in warehouse (103 m.u.) 48.51 46.80 0.836 �0.336Failures in transport (103 m.u.) 174.74 250.89 0.829 �0.185Write off expired goods (103 m.u.) 45.85 68.91 0.601 0.794Total failures (103 m.u.) 480.17 894.63 0.969 �0.045

Variance explained 67.16% 86.67%Shipped pallets (No) 9021.48 4534.55 0.992 �0.088Distance (103 km) 116.01 68.03 0.954 �0.188Deliveries (No) 4270.15 1751.67 0.759 0.435Order picking transactions (103) 188.29 98.94 �0.042 0.913Turnover (106 m.u.) 281.06 178.81 0.955 0.023Tour/driver (No/driver) 27.36 13.64 0.909 �0.084Delivery/driver (No/driver) 112.52 28.06 0.764 0.314Tons/ driver (t/driver) 96.94 60.43 0.982 �0.092Pallets/driver 214.80 107.97 0.992 �0.088Distance/driver (km/driver) 2762.20 1619.86 0.954 �0.188Order picking trans./order picker (No/order picker) 6737.95 999.54 0.166 0.888

Variance explained 69.83% 88.14%

M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933 3931

original data matrices, since they explain more than 90%. From thegroup of energy indicators two PCs are also extracted. In the firstPC which explains 55% of total variance electricity and fuel con-sumption has the greatest influence, while in the second PC otherenergy costs have the greatest influence. Three operational inputPCs explain 87% of variance. On the output side six PCs are ex-tracted. The first relates to utilisation factors in transport (timeand space truck utilisation), while the second relates to warehousespace utilisation. In the quality output group two PCs are domi-nant. The first quality output PC incorporates failures in warehouseand transport, as well as total failures, while the second incorpo-rates write off expired goods. In the last output group two PCsare extracted. Shipped pallets, distance driven and turnover are lar-gely correlated with the first PC. Warehouse indicators (order pick-ing transactions and order picking transactions/order picker) aredominant in second PCs of mention group.

Table 5Efficiency scores according to different models.

Average St.Dev. Efficient Inefficient

Model I (Standard BCC DEA) 0.9999 0.0001 83 (99%) 1 (1%)Model II 0.9466 0.0692 40 (47%) 44 (53%)Model III 0.9001 0.1030 28 (33%) 56 (67%)Model IV 0.9389 0.0751 35 (42%) 49 (58%)Model V 0.8273 0.1244 18 (21%) 66 (79%)

5.2. Efficiency scores

The second phase of efficiency measurement process is thePCA–DEA model for evaluating efficiency. Classical DEA modelscannot be applied in this case. They do not have sufficient discrim-inatory power, considering the fact that almost 99% of DMUs areefficient. Models described in this paper are used for evaluation

of efficiency of observed DCs. Results of proposed models areshown in Table 5.

Certain conclusions can be made according to the results in Ta-ble 5. According to the classical BCC model almost all DMUs all effi-cient. This model does not make differentiation between DMUs.

PCA–DEA models are more appropriate for efficiency evaluation(Table 5). These models make greater differentiation betweenDMUs. Results show that 47% are efficient according to Model II.In this model, there is no relationship between the weights ofPCs from different groups. In Model III additional constraints thatfavour operational indicators are set. Only 33% of observed DMUsare efficient. According Model IV 42% of DMUs are efficient. Resultsin Table 5 show that Model V makes the greatest degree of differ-entiation in the observed set and only 21% of all DMUs are efficient.

3932 M. Andrejic et al. / Expert Systems with Applications 40 (2013) 3926–3933

The author’s assumption that quality indicators are more relevantfor efficiency evaluation is confirmed. This model maximizes dis-crimination with minimal loss of information. According observedexample quality and operational indicators positively affect thediscriminatory power of the model. Utilisation factors have lessimpact on DC’s efficiency scores discrimination.

5.3. Hypotheses testing

This paper also investigates the influence of different factor onthe efficiency scores. Three hypotheses are set:

Hypothesis 1. There is a difference in efficiencies scores of DCsduring ‘‘peak months’’ and other months in the year

Hypothesis 2. There is a difference in efficiency scores of DCslocated in large and small cities

Hypothesis 3. There is a difference in efficiency scores of large andsmall DCs

In order to test previous hypotheses non-parametrical Mann–Whitney and Kolmogorov–Smirnof tests are used. In observedexample tests indicate whether the efficiency scores differ be-tween subgroups. The non-parametrical tests were run insteadvariance analysis, because the tested efficiency scores are not nor-mally distributed. The company has enlarged turnover in August,September and December. Company management considers thesemonths the ‘‘peak months’’. In the first hypothesis efficiency scoresof DCs in ‘‘peak months’’ are compared with efficiency scores inother months. The results are presented in Table 6. The p valueindicates that there are no reasons for rejecting null hypothesiswith significant level of a = 0.05. According Mann–Whitney testthere are no significant differences in efficiency scores of observedDCs in ‘‘peak months’’. Kolmogorov–Smirnof test confirmed previ-ous conclusion, so hypothesis 1 is rejected.

Based on information obtained from the management companysecond hypothesis is set. Namely, management assumption is thatDCs located in large cities are more efficient than DCs located insmall cities. The observed set is divided to two subgroups accord-ing gravity area. The first group consists of DCs located in citieswith more than five hundred thousand people, while the secondconsists of DCs located in smaller cities. According results in Table 6both tests show that there no differences in the efficiency scoresacross small and large catchment’s (gravity) areas. Hypothesis 2is rejected.

Many studies in literature showed that there are differences inefficiency scores between small and large DCs (Hackman et al.,2001; Hamdan & Rogers, 2008). In order to verify this, Mann–Whit-ney and Kolmogorov–Smirnof tests were run. Observed set is di-vided in two groups according to number of pallet places. Thecritical point is set 4400 pallet places. According the tests resultsin Table 6 both test confirmed last hypothesis. There is significant

Table 6Hypotheses tests statistics.

H1 H2 H3

Mann–Whitney (a = 0.05)U 496.000 587.500 404.500Z �1.719 �1.319 �3.140Asymp. Sig. (2-tailed) - p 0.086 0.187 0.002

Kolmogorov–Smirnof (a = 0.05)Z 0.945 1.311 1.829Asymp. Sig. (2-tailed) – p 0.334 0.064 0.002

difference in efficiency of large and small DCs. Small DCs are moreefficient than large DCs.

6. Conclusions

Measuring, monitoring and improving efficiency affect marketsuccess. In this paper a model for measuring DC’s efficiency, basedon different indicators, is developed. The main problem in this pa-per is how to select, from a large number of indicators those thatbest describe the DC operating. PCA is used for improving discrim-inatory power of the model.

The observed company monitors a number of different indica-tors. They are divided into six different groups. The classical DEAmodel does not give good results, so PCA–DEA approach is used.Additional restrictions are set in accordance with the opinion ofthe DC’s management, as well as the author’s opinion and experi-ence. Model results show remarkable importance of additionalconstraints. Relationship between weight coefficients assigned toPCs from different groups greatly affect final results. Differentmodels that favour operational, utilisation and quality indicatorsare tested on the observed set. The highest level of discriminationis achieved with Model V in which the emphasis is on quality indi-cators. The quality of the service affects both customer satisfactionand the company’s revenues. The results show that for efficiencyevaluation operational indicators are more important than utilisa-tion indicators. Management pays more attention to operationalindicators than utilisation, but less than quality indicators.

This paper investigates the influence of different factors on theefficiency scores. Three hypotheses are set in this paper. The influ-ence of the ‘‘peak months’’ on DC’s efficiencies was examined inthe first hypothesis. This hypothesis is rejected. In the secondhypothesis, there was no significant difference in the efficiencyscores of DCs located in large and small cities. The last hypothesisconfirmed assumption from the literature. Namely, there is differ-ence in efficiency scores of small and large DCs.

In literature, there is a lack of case studies that test the PCA–DEA approach on real logistics systems. This fact indicates theinsufficient amount of research in this area. This paper showshow a theoretical model can be applied in practice. The model pro-posed in this paper corresponds to a real situation of the observedtrading company. Proposed methodology represents support in thedecision making process.

Models presented in this paper, with minor adjustments, can beused for measuring and improving the efficiency of providers,warehouses, suppliers, etc. Presented models are a good basis fordevelopment of future models. In the future research, modelsshould include environmental and other quality indicators.

Acknowledgement

This paper was partially supported by the Ministry of Scienceand Technological development of the Republic of Serbia, throughthe projects TR 36006 and TR 36022, for the period 2011–2014.

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