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

Expert Systems with Applications 40 (2013) 3926–3933

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Benchmarking distribution centres using Principal Component Analysis and Data Envelopment Analysis: A case study of Serbia Milan Andrejic´ ⇑, Nebojša Bojovic´, Milorad Kilibarda University of Belgrade, Faculty of Transport and Traffic Engineering, Republic of Serbia

a r t i c l e

i n f o

Keywords: Distribution centres Efficiency Data Envelopment Analysis Principal Component Analysis

a b s t r a c t The efficiency of distribution systems is largely affected by the performances of distribution centres. The main objective of this paper is to develop and propose a DEA model for distribution centres efficiency measuring that can help managers in decision making and improving the efficiency. Due to numerous indicators that describe DCs operating, the main problem is indicators selection. In order to improve discriminatory power of classical DEA models PCA–DEA approach is used. This paper analysis the efficiency of 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 in this paper. The results showed that small distribution centres are more efficient than large. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction In order to survive in the market and achieve profitability, the companies need to perform their activities in an efficient way. Efficiency is a very important indicator of companies’ operations analysis, and it is one of the basic and the most frequently used performances. Measuring, monitoring and improving efficiency are the main tasks for companies in the 21st century. The importance of efficiency measuring in logistics has been recognised in literature (Chow, Heaver, & Henriksson, 1994; Hackman, Frazelle, Griffin, Griffin, & Vlasta, 2001; Min & Joo, 2006). This process is a very complicated one due to the complex structure of logistics systems. Distribution centres (DCs) are complex logistics systems which connect producers with other participants in the chain, including end-users. DCs of trading companies and DCs in general represent complex logistics systems with a very important place and role in the supply chains. In literature little has been done for the performance measurement of the distribution side of the supply chain. This paper analyses in more detail the efficiency of DCs of the trading company that operates in the region of Serbia. ‘‘Single ratio’’ indicators have been used for estimating the efficiency of DCs for a long time. These indicators do not provide enough information about the system operating. Recently, an increasing number of authors have advocated the use of approaches such as the Data Envelopment Analysis (DEA) method (Min & Joo, 2006; Toloo & Nalchigar, 2011). Adler and Golany ⇑ Corresponding author. Address: Vojvode Stepe 305, 11000 Belgrade, Republic of Serbia. Tel.: +381 11 30 91 304; fax: +381 11 30 96 704. E-mail addresses: [email protected] (M. Andrejic´), [email protected] (N. Bojovic´), [email protected] (M. Kilibarda). 0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2012.12.085

(2001), Adler and Golany (2002) have suggested using the Principal Component Analysis (PCA), a methodology that produces uncorrelated linear combinations of original inputs and outputs, to improve discrimination in the DEA with a minimal loss of information. The DEA models often fail when there are an excessive number of inputs and outputs in relation to the number of decision making units (DMUs). DC’s operating describes a large number of different indicators, and the problem is how to select relevant indicators which describe DC operating in the best way. Variables selection problem is recognized in literature (Boussofiane, Dyson, & Thanassoulis, 1991). Various indicators with different effect on systems, subsystems, processes and activities further complicate the selection of variables. The main objective of this paper is to develop a model for measuring efficiency of DCs of one trading company. Information obtained from the company management and the author’s experience is used in the process of model development. Next section gives a review of indicators used for measuring efficiency in logistics. The third section describes the PCA–DEA approach. Efficiency evaluation system of observed DCs is given in the fourth section. In section five the results of the proposed model are described. Several hypotheses are also tested in section five. At the end of the paper, the concluding remarks and directions of future research are presented. 2. Literature review In the field of logistics, the DEA method is mostly used for efficiency estimation. Different indicators are used for measuring efficiency in logistics (Table 1). Ross and Droge (2002) analyzed 102 DCs efficiency, as a part of complex supply chains. They also

Equipment (Capacity), Operational

Warehouses and DCs DCs

Operational, quality Financial

Labor hours, Warehouse space, technology investment, Materials handling equipment (MHE) Direct costs, indirect costs

Number of direct full-time equivalents, Size of the warehouse, degree of automation, number of different SKUs Account receivables, Salaries and wages, Expenses other than salaries and wages. Average labor experience, fleet size, equipment, mean order throughput time (MOT)

Hamdan and Rogers (2008) Korpela et al. (2007)

de Koster and Balk (2008) Min and Joo (2006)

Ross and Droge (2002)

Product sales volume

The picking/shipping workload is driven by the number of orders and the number of lines on those orders, Investments in material handling equipment, The storage output index Throughput, order fill, space utilisation Labor, space, material handling and storage equipment

Reliability (time, quality, quantity), Flexibility (Urgent deliveries, frequency, special request, Capacity (ability to respond to changes in warehousing capacity needs of a customer) Number of daily order lines picked, The level of value-added logistics (VAL) activities carried out, Number of special processes, Percentage of failure-free orders Operating income

Warehouses

Equipment, operational Operational, quality, utilisation Quality, financial Warehouses and DCs Warehouses and DCs Warehouses

Operational, financial, quality Fill rate, sale, service time

Chakraborty, Majumder, and Sarkar (2011) Hackman et al. (2001)

DCs

Output Input

Number of employees, general expenses, space, inventory

Publication

Table 1 Efficiency indicators in warehouses and DCs.

Field

Indicator types

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analyzed efficiency change in time. Hamdan and Rogers (2008) used the DEA method for estimating efficiency of 3PL providers with an emphasis on warehouse operations. The authors compared the results of two DEA models with and without weight restrictions. Hackman et al. (2001) developed a model with multiple inputs and outputs to evaluate the efficiency of 57 warehouse and distribution facilities. Among other things, they confirmed conclusions concerning the relation between warehouse size, level of technology and efficiency. They used labour, space, material handling 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 warehouse in square meters; degree of automation, etc.), operational (number of daily order lines picked, the level of value-added logistics (VAL) activities) and quality indicators (the percentage of failure-free orders shipped; order flexibility) for efficiency evaluation. Korpela, Lehmusvaara, and Nisonen (2007) advocated the use of cost indicators as inputs, but also qualitative indicators as outputs. The authors combined the Analytic Hierarchy Process (AHP) and the 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 road transport (Table 2). In literature there are different approaches for freight transport performance measurement. In the literature a variety of indicators of transport system are used. Kim (2010) has evaluated technical and scale efficiency of individual trucks in logistics. The DEA model for 62 trucks efficiency evaluation is specified with three output categories and five costs categories which represent inputs. Cruijssen, Dullaert, and Joro (2010) analysed 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, social and environmental level. The authors defined five transport losses or wastes: driver breaks, excess loading time, fill loss, speed loss and quality delay. McKinnon (1999) analyses KPIs for the food supply chain. They analysed vehicle utilisation and energy efficiency. They used several indicators such as the degree of empty running, fuel efficiency and deviations from schedule, time utilisation and vehicle utilisation. Nowadays, energy efficiency has become a critical issue for logistics systems. In a situation of increasing global energy demands and rising energy costs, conserving energy is becoming a very important issue (Table 2). In literature there are many papers that investigate indicators of energy efficiency in logistics systems. Kalenoja, Kallionpää, and Jarkko Rantala (2011) studied indicators of energy efficiency of supply chains. Authors also noted the importance of some indicators like: energy consumption, water and 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 by recycling or reuse. The authors also link energy efficiency in supply chains with the requirements of ISO 14301 classical (environmental performance evaluation). Neto, Walther, Bloemhof, van Nunen, and Spengler (2009) recognized the problem of balancing environmental and business concerns. A detailed overview of indicators for green supply chain management is given in the paper of Hervani, Helms, and Sarkis (2005). They give the list of environmental performance metrics ranging from air emissions to energy recovery and recycling. Mckinnon, Cullinane, Browne, and Whiteing (2010) in framework of assessment for developing sustainability in warehousing distinguished a micro and a macro-level perspective. Micro level includes business and economy with indicators of energy, water and buildings, while macro level includes environment and society with indicators of ecology, environment and land use. Kuosmanen

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Table 2 Efficiency 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.), Intangible assets (market information, customer contacts, goodwill etc), Added value, Profit 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 services Management level to measure - strategic, tactical, operational Costs, quality, time and flexibility, environmental indicators such as energy consumption or carbon dioxide emissions, ISO 14031 performances (environmental condition indicators, management performance indicators and operational performance indicators) Labor cost, fuel cost, oil cost, supplies cost, tax, insurance, transportation distance, transportation amount, effective transportation distance

Transport systems and vehicles Supply chain

Equipment (Capacity), operational, financial, energy Energy, environmental

Supply chain

Financial, energy, quality, environmental

Transport systems and vehicles Transport systems and vehicles Transport systems and vehicles Logistics network General organisation

Financial, operational, energy

Hervani et al. (2005)

Kalenoja et al. (2011) Kim (2010)

Kuosmanen and Kortelainen (2005) McKinnon (1999)

Road transportation, mileage, fuel consumption, environmental pressures-undesirable outputs (CO2, CH4,N2O, CO, NOx SO2, emissions...) Vehicle fill, Empty running, Vehicle time utilisation, Deviations from schedule, Fuel consumption

Neto et al. (2009)

Masses entering the treatment system, Output masses that are recycled

Sarkis and Talluri (2004)

Quantitative inputs (raw material intake, energy, materials used, employees...) Qualitative inputs (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...) Operating costs, energy consumption, vehicle emissions, fuel, labour, transport losses or wastes (driver breaks, excess loading time, fill loss, speed loss, quality delay)

Simons et al. (2004)

and Kortelainen (2005) defined main environmental pressures and undesirable outputs that are due to road transport. The authors also emphasized the importance of economic variables such as mileage and fuel consumption. Sarkis and Talluri (2004) investigated eco-efficiency measurement using the DEA method. They distinguished qualitative and quantitative inputs and outputs. It is evident that in literature there are numerous efficiency indicators. For DCs warehouse and transport indicators are relevant. These indicators are related to the operational, tactical and strategic decision-making level. Selection of the most appropriate indicators is complex process. In situation of a large number of indicators and a relatively small number of data, the use of DEA method is limited. Namely, the discriminatory power of DEA models decreases. In order to overcome this PCA–DEA approach is used in this paper. PCA–DEA approach is described in next section. 3. PCA–DEA approach DEA is a non-parametric linear programming technique which enables the comparison of different DMUs, based on multiple inputs and outputs. The efficiency is relative and relates to a set of units within the analysis. Charnes, Cooper, and Rhodes (1978) proposed a non-parametric approach for efficiency estimation, where they reduced multiple inputs to a single virtual input and multiple outputs reduced to a single virtual output using weighting coefficients. In the set of homogeneous units, the DEA finds the most efficient DMUs and according to them it defines the efficiency of other units. In this paper classical BCC DEA output oriented model is used (Banker, Charnes, & Cooper, 1984). Originally, the PCA was pioneered as a data reduction technique of multivariate data (Beltrami, 1873; Jordan, 1874). PCA explains the variance structure of a matrix of data through linear combinations of variables, consequently reducing the data to a few principal components (PCs), which generally describe 80–90% of the variance in the data (Sharma, 1996). If most of the population variance can be attributed to the first few components, then they can

Transport systems and vehicles

Operational, energy, environmental Energy, utilisation

Environmental Environmental, qualitative, operational

Financial, operational, energy, quality

replace the original variables with minimum loss of information. In literature the PCA is used for improving discrimination in the DEA. By comparing n units with q outputs denoted by Y and r inputs denoted by X, the efficiency measure for unit observed unit DMUa is expressed as in:

minVX a  v a

ð1Þ

U;V

Subject to:

VX  UY  v a P 0

ð2Þ

UY a ¼ 1

ð3Þ

V P0

ð4Þ

U P 0; v a free

ð5Þ

In previous model V and U represent vectors of DMU weights chosen by the linear program, va is scalar, Xa and Ya input and output column vectors for DMUa. In the PCA the most of the population variance can be attributed to the first few components, so they can replace the original variables with minimum loss of information (Adler & Golany 2001; Adler & Golany 2002). According to Hair, Anderson, Tatham, and Black (1995), a random vector X = [X1, X2, . . . , Xp] (the p is the number of original inputs/outputs chosen to be aggregated) has the correlation matrix C with eigenvalues k1 P k2 P    P kp P 0 and normalized eigenvectors l1, l2, . . . , lp. Consider the linear combinations, where the superscript t represents the transpose operator: t

X PC i ¼ li ¼ l1i X 1 þ l2i X 2 þ    þ lpi X p ; VarðX PC I Þ ¼

t li Cli ;

i ¼ 1; 2; . . . ; p

CorrelationðX PC I ; X PC K Þ ¼

t li Clk ;

i ¼ 1; 2; . . . ; p

ð6Þ ð7Þ

i ¼ 1; 2; . . . ; p; k ¼ 1; 2; . . . ; p; i–k ð8Þ

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

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least that of PC2, the weight of PC2 to be at least that of PC3 and so on. VPC and UPC represents vector of weights assigned to inputs and outputs PCs. The PCA–DEA model used in this paper has the following form:

min V PC X aPC  v a

U PC ;V PC

ð9Þ

Subject to:

V PC X PC  U PC Y PC  v a P 0

ð10Þ

U PC Y aPC ¼ 1

ð11Þ

V PC P 0 U PC P 0;

ð12Þ

v a free

ð13Þ

In this paper PCA is applied to all groups of inputs and outputs separately. Next section describes the efficiency evaluation system in more details. 4. DC’s efficiency evaluation system This paper analyzes the efficiency of seven distribution centres of a trading company which operates in Serbia. The efficiencies of the observed centres were analyzed during a twelve-month period. The company management has used a variety of indicators to monitor the operating of the company. Performances are evaluated by ‘‘single ratio’’ indicators such as: distance/driver, order picking transaction/order picker, warehouse and vehicle space utilization, etc. which do not provide enough information about the company’s operation. According to various criteria, the indicators in logistics can be classified in different ways. From the point of decision-making level there are indicators at the strategic, tactical and operational level. The DC represents complex systems with a large number of interconnected subsystems, processes and activities, which are all interconnected and influence each other. Each of them is characterized by certain indicators. The main processes in the DC, among others, are: receiving, shipping, control, packing, warehousing, order picking, order processing, etc. Each of them is characterized by certain indicators. Transport and warehouse subsystems are basic subsystems in the DC. Consequently, it is possible to define transport efficiency indicators and warehouse efficiency indicators. However, there are indicators that cannot be strictly divided into mentioned categories. For example invoices (demands) and turnover are considered as common variables in DCs. Depending on the type, logistics indicators can be divided into: equipment and capacity indicators, operational indicators, quality indicators, energy indicators, environmental (social) indicators, etc. The aforementioned indicators can be qualitative and quantitative. As mention before in the observed DCs, as well as in most real systems, performances are evaluated by ‘‘single ratio’’ indicators which are not good indicators of the DC’s efficiency since they do not provide enough information about their operating mode. The DEA method provides the possibility of integrating a large number of different indicators into a unified measure of efficiency. For a successful DC’s efficiency evaluation in observed period it is necessary to choose the most important indicators that best describe the DC’s operating. One way of overcoming this problem is the application of the PCA method. The PCA method is a popular method used for different problems in literature (Adler & Golany 2001; Adler & Golany 2002; Adler & Golany 2007; Liang, Li, & Li, 2009). To the best of our knowledge there are not enough papers in the literature concerning the DCs which uses the PCA–DEA approach for measuring efficiency. List of indicators that are used in observed example are shown in Table 3. They are divided into five groups. Input and output category is indicated in the third column. Warehouse and transport

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indicators are marked in the fourth column. Equipment and capacity indicators include general indicators frequently used in literature (Ross & Droge 2002; Hamdan and Rogers 2008; Hackman et 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 ratio’’ indicators that observed DCs monitor, and to the best of authors’ knowledge have not been used in the literature. Drivers overtime per driver and order picking transactions per order picker are some of them. Energy indicators are very important for logistics systems. Energy consumption costs in DCs have a great share of total costs. Utilization factors greatly influence the operating of the company, on total costs, as well as on efficiency (McKinnon, 1999). Apart from warehouse and vehicle space utilization this paper also analyses time utilization of truck in distribution process. Failures in the transport and warehouse subsystems represent quality indicators which may be the cause of dissatisfaction and complaints of the customer. Failures in the warehouse relates to the mistakes in the order picking process (shortage/excess in the delivery, articles mix-up, damages), but also to other processes such as bad inventory management, etc. Failures in transport primarily concern the delivery that is falling behind schedule, as well as 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 quality can be observed in Table 3. The proposed methodology is realizes in two phases. In the first phase, it is necessary to implement the PCA for each of the groups of inputs and outputs separately. PCs from the first stage are used as inputs and outputs in the second phase. PCA–DEA models are used in the second phase for efficiency evaluation. Several models are used in this paper for measuring efficiency of observed set: the classical BCC DEA output oriented model (Eqs. (1)-(5) – Model I), and the four PCA–DEA models. The first PCA–DEA model (Model II) has additional constraints (Eqs. (14)-(20)) to model ((9)-(13)) described in previous section and prioritizes the PCs in descending order of importance in each group. For example, the first component in the group of equipment and capacity indicators is more important than the second one from the same group. In this way constraints in all groups of inputs and outputs are set:

V PC equipm  V PC equipm P 0

ð14Þ

V PC energy  V PC energy P 0

ð15Þ

V PC operat  V PC operat P 0

ð16Þ

V PC operat  V PC operat P 0

ð17Þ

U PC utilisat  U PC utilisat P 0

ð18Þ

U PC quality  U PC quality P 0

ð19Þ

U PC operat  U PC operat P 0

ð20Þ

1

3

5

6

1

3

5

2

4

6

7

2

4

6

In the previous model V PCequipm and V PC equipm represent weights assign 1

2

to PCs from the group of equipment and capacity inputs, V PCenergy and 3

V PC energy PCs from energy inputs group, V PC operat , V PC operat and V PC operat 4

5

7

6

from the operational inputs group. Similar, U PC utilisat and U PCutilisat are 1

2

weights assigned to PCs of utilisation indicators group, U PC quality and 3

U PC quality PCs from quality output group, U PC operat and U PCoperat PCs from 4

5

6

operational output group. This model does not consider the relationship between the components of different groups. Therefore additional models are analysed. In contrast to previous model, Models III, IV and V are additionally constrained in accordance with the company’s management information and author’s experience (opinion). The basic idea in these models is to favour variables that are most important

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Table 3 Data for DC’s efficiency measuring. Type

Variables

I/Oa

W/T

Equipment and capacity indicators

Vehicles Forklifts Employees in warehouse Employees in transport Warehouse area Pallet places

I I I I I I

T W W T W W

Energy

Fuel Electricity consumption Other energy costs (water, gas) Utility costs

I I I I

T W W W

Operational

Invoices (Demands) Warehouse overtime Driver’s overtime Vehicle maintenance Driver’s overtime/driver Shipped pallets Distance Deliveries Order picking transactions Tour/driver Delivery/driver Tons/ driver Pallets/driver Distance/driver Order picking trans./order picker Turnover

I I I I I O O O O O O O O O O O

W-T W T T T T T W-T W T T T T T W W-T

Utilisation

Time truck utilisation Space truck utilisation Warehouse space utilisation

O O O

T T W

Quality

Failures in warehouse Failures in transport Write off expired goods Total failures

O O O O

W T W W-T

a b

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

for the DC’s operating. Managers in the observed company pay more attention to outputs. They also argue that in most cases it is easier to implement corrective actions on inputs rather than on outputs. Therefore, in subsequent models, restrictions are applied only to the outputs. Managers in DCs consider that operational variables like turnover, shipped pallets, distance driven, etc. are major indicators of successful operating. In that manner Model III favours PCs from operational output indicators group. Additional constraints have the following form:

U PC operat  U PC utilisat P 0

ð21Þ

U PC operat  U PC quality P 0

ð22Þ

6

6

1

3

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

U PC utilisat  U PC quality P 0

ð23Þ

U PC utilisat  U PC operat P 0

ð24Þ

2

2

b

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

U PC quality  U PC utilisat P 0

ð25Þ

U PC quality  U PC operat P 0

ð26Þ

4

4

1

5

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 measuring efficiency of seven DCs of one trading company in Serbia during a twelve-month period. Data has been aggregated for the twelve months of 2011. Each DC in each month is a separate decision making unit. Thus, a set of 84 DMUs is observed. (Tulkens & Eeckaut, 1995; Cullinane, Ji, & Wang, 2005; Hoff, 2007). 5.1. Principal Component Analysis scores

3

5

There are numerous quality indicators in logistics. The ultimate goal, however, is customer satisfaction. No matter what indicator is concerned the quality of service greatly affects customer satisfaction. Satisfied and loyal customers mean a secure income for the company. On the other side unsatisfied customers and customer’s complaints create additional costs. In this paper, more attention is paid to the failures in the distribution process. In that sense, Model

The first phase of efficiency measuring is the PCA for all groups of inputs and outputs separately. From each of six groups main components were selected. All extracted components explain minimum 80% of total variance of each group. All quality indicators used in this paper represent some kind of undesirable outputs, so they are reversed (Liang et al., 2009). The results of Principal Component Analysis are presented in Table 4. Two PCs are extracted from equipment and capacity input indicators. They explain a vast of the majority of the variance in the

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

Average

St. dev.

PC 1

PC 2

Vehicles (No) Forklifts (No) Employees in warehouse (No) Employees in transport (No) Warehouse area (m2) Pallet places (No)

22.38 51.76 71.35 46.51 8173.62 4484.86

8.11 25.18 31.84 21.74 3311.03 1947.72

0.901 0.950 0.859 0.984 0.737 0.699

0.390 0.047 0.468 0.070 0.501 0.584

Variance explained Fuel (103 m.u.) Electricity consumption (103 m.u.) Utility costs (103 m.u.) Other energy costs (water, gas, etc) (103 m.u.)

2528.43 481.89 125.36 167.76

1673.49 281.53 249.10 157.78

74.19% 0.849 0.945 0.689 0.335

90.34% 0.026 0.061 0.487 0.897

Variance explained Invoices (Demands) (103) Warehouse overtime (h) Driver’s overtime (h) Vehicle maintenance (103 m.u.) Driver’s overtime/driver (h/driver)

8505.01 373.33 450.20 649.08 13.82

2896.76 445.21 242.33 431.42 8.49

55.02% 0.833 0.375 0.683 0.747 0.627

81.17% 0.355 0.660 0.524 0.290 0.641

0.142 0.630 0.282 0.508 0.110

45.05%

71.67%

87.02%

Variance explained Outputs Time truck utilisation (%) Space truck utilisation (%) Warehouse space utilisation (%)

34.38 66.77 89.68

7.32 15.60 13.06

0.919 0.847 0.381

0.020 0.389 0.913

Variance explained Failures in warehouse (103 m.u.) Failures in transport (103 m.u.) Write off expired goods (103 m.u.) Total failures (103 m.u.)

48.51 174.74 45.85 480.17

46.80 250.89 68.91 894.63

56.86% 0.836 0.829 0.601 0.969

89.71% 0.336 0.185 0.794 0.045

Variance explained Shipped pallets (No) Distance (103 km) Deliveries (No) Order picking transactions (103) Turnover (106 m.u.) Tour/driver (No/driver) Delivery/driver (No/driver) Tons/ driver (t/driver) Pallets/driver Distance/driver (km/driver) Order picking trans./order picker (No/order picker)

9021.48 116.01 4270.15 188.29 281.06 27.36 112.52 96.94 214.80 2762.20 6737.95

4534.55 68.03 1751.67 98.94 178.81 13.64 28.06 60.43 107.97 1619.86 999.54

67.16% 0.992 0.954 0.759 0.042 0.955 0.909 0.764 0.982 0.992 0.954 0.166

86.67% 0.088 0.188 0.435 0.913 0.023 0.084 0.314 0.092 0.088 0.188 0.888

69.83%

88.14%

Variance explained

original data matrices, since they explain more than 90%. From the group of energy indicators two PCs are also extracted. In the first PC which explains 55% of total variance electricity and fuel consumption has the greatest influence, while in the second PC other energy costs have the greatest influence. Three operational input PCs explain 87% of variance. On the output side six PCs are extracted. The first relates to utilisation factors in transport (time and space truck utilisation), while the second relates to warehouse space utilisation. In the quality output group two PCs are dominant. The first quality output PC incorporates failures in warehouse and transport, as well as total failures, while the second incorporates write off expired goods. In the last output group two PCs are extracted. Shipped pallets, distance driven and turnover are largely correlated with the first PC. Warehouse indicators (order picking transactions and order picking transactions/order picker) are dominant in second PCs of mention group.

5.2. Efficiency scores The second phase of efficiency measurement process is the PCA–DEA model for evaluating efficiency. Classical DEA models cannot be applied in this case. They do not have sufficient discriminatory power, considering the fact that almost 99% of DMUs are efficient. Models described in this paper are used for evaluation

PC 3

of efficiency of observed DCs. Results of proposed models are shown in Table 5. Certain conclusions can be made according to the results in Table 5. According to the classical BCC model almost all DMUs all efficient. This model does not make differentiation between DMUs. PCA–DEA models are more appropriate for efficiency evaluation (Table 5). These models make greater differentiation between DMUs. Results show that 47% are efficient according to Model II. In this model, there is no relationship between the weights of PCs from different groups. In Model III additional constraints that favour operational indicators are set. Only 33% of observed DMUs are efficient. According Model IV 42% of DMUs are efficient. Results in Table 5 show that Model V makes the greatest degree of differentiation in the observed set and only 21% of all DMUs are efficient.

Table 5 Efficiency scores according to different models.

Model Model Model Model Model

I (Standard BCC DEA) II III IV V

Average

St.Dev.

Efficient

Inefficient

0.9999 0.9466 0.9001 0.9389 0.8273

0.0001 0.0692 0.1030 0.0751 0.1244

83 40 28 35 18

1 (1%) 44 (53%) 56 (67%) 49 (58%) 66 (79%)

(99%) (47%) (33%) (42%) (21%)

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The author’s assumption that quality indicators are more relevant for efficiency evaluation is confirmed. This model maximizes discrimination with minimal loss of information. According observed example quality and operational indicators positively affect the discriminatory power of the model. Utilisation factors have less impact on DC’s efficiency scores discrimination. 5.3. Hypotheses testing This paper also investigates the influence of different factor on the efficiency scores. Three hypotheses are set: Hypothesis 1. There is a difference in efficiencies scores of DCs during ‘‘peak months’’ and other months in the year Hypothesis 2. There is a difference in efficiency scores of DCs located in large and small cities Hypothesis 3. There is a difference in efficiency scores of large and small DCs In order to test previous hypotheses non-parametrical Mann– Whitney and Kolmogorov–Smirnof tests are used. In observed example tests indicate whether the efficiency scores differ between subgroups. The non-parametrical tests were run instead variance analysis, because the tested efficiency scores are not normally distributed. The company has enlarged turnover in August, September and December. Company management considers these months the ‘‘peak months’’. In the first hypothesis efficiency scores of DCs in ‘‘peak months’’ are compared with efficiency scores in other months. The results are presented in Table 6. The p value indicates that there are no reasons for rejecting null hypothesis with significant level of a = 0.05. According Mann–Whitney test there are no significant differences in efficiency scores of observed DCs in ‘‘peak months’’. Kolmogorov–Smirnof test confirmed previous conclusion, so hypothesis 1 is rejected. Based on information obtained from the management company second hypothesis is set. Namely, management assumption is that DCs located in large cities are more efficient than DCs located in small cities. The observed set is divided to two subgroups according gravity area. The first group consists of DCs located in cities with more than five hundred thousand people, while the second consists of DCs located in smaller cities. According results in Table 6 both tests show that there no differences in the efficiency scores across small and large catchment’s (gravity) areas. Hypothesis 2 is rejected. Many studies in literature showed that there are differences in efficiency scores between small and large DCs (Hackman et al., 2001; Hamdan & Rogers, 2008). In order to verify this, Mann–Whitney and Kolmogorov–Smirnof tests were run. Observed set is divided in two groups according to number of pallet places. The critical point is set 4400 pallet places. According the tests results in Table 6 both test confirmed last hypothesis. There is significant

difference in efficiency of large and small DCs. Small DCs are more efficient than large DCs. 6. Conclusions Measuring, monitoring and improving efficiency affect market success. In this paper a model for measuring DC’s efficiency, based on different indicators, is developed. The main problem in this paper is how to select, from a large number of indicators those that best describe the DC operating. PCA is used for improving discriminatory power of the model. The observed company monitors a number of different indicators. They are divided into six different groups. The classical DEA model does not give good results, so PCA–DEA approach is used. Additional restrictions are set in accordance with the opinion of the DC’s management, as well as the author’s opinion and experience. Model results show remarkable importance of additional constraints. Relationship between weight coefficients assigned to PCs from different groups greatly affect final results. Different models that favour operational, utilisation and quality indicators are tested on the observed set. The highest level of discrimination is achieved with Model V in which the emphasis is on quality indicators. The quality of the service affects both customer satisfaction and the company’s revenues. The results show that for efficiency evaluation operational indicators are more important than utilisation indicators. Management pays more attention to operational indicators than utilisation, but less than quality indicators. This paper investigates the influence of different factors on the efficiency scores. Three hypotheses are set in this paper. The influence of the ‘‘peak months’’ on DC’s efficiencies was examined in the first hypothesis. This hypothesis is rejected. In the second hypothesis, there was no significant difference in the efficiency scores of DCs located in large and small cities. The last hypothesis confirmed assumption from the literature. Namely, there is difference 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 the insufficient amount of research in this area. This paper shows how a theoretical model can be applied in practice. The model proposed in this paper corresponds to a real situation of the observed trading company. Proposed methodology represents support in the decision making process. Models presented in this paper, with minor adjustments, can be used for measuring and improving the efficiency of providers, warehouses, suppliers, etc. Presented models are a good basis for development of future models. In the future research, models should include environmental and other quality indicators. Acknowledgement This paper was partially supported by the Ministry of Science and Technological development of the Republic of Serbia, through the projects TR 36006 and TR 36022, for the period 2011–2014. References

Table 6 Hypotheses tests statistics. H1

H2

H3

Mann–Whitney (a = 0.05) U Z Asymp. Sig. (2-tailed) - p

496.000 1.719 0.086

587.500 1.319 0.187

404.500 3.140 0.002

Kolmogorov–Smirnof (a = 0.05) Z Asymp. Sig. (2-tailed) – p

0.945 0.334

1.311 0.064

1.829 0.002

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