1 The efficiency of fleets in Serbian distribution centres Milan Andrejic, Milorad Kilibarda 2 Faculty of Transport and Traffic Engineering, Logistics Department, University of Belgrade, Belgrade, Serbia 2 Abstract: Due to a dynamic market and environmental changes, distribution centres in Serbia have to realize their activities and processes in an efficient way. This paper is devoted to the analysis of the efficiency of transport subsystem in distribution centres. Transport is logistics subsystem with the highest energy consumption. Efficiency of the transport subsystem affects operating of distribution centres. The main objective of this paper is to develop and to propose model for estimating efficiency of thirteen fleets of distribution centres located in Serbia. Data envelopment analysis model is employed in this paper because it does not require the assumption of functional relationship between input and output variables, and also integrates different variables expressed in different units in a single measure of efficiency. Three input and three output variables are used in the model proposed in this paper. Number of vehicles, fuel costs and total trucks time in operation are used as input, while total distance driven, tons shipped, and trucks utilization are used as output variables. This paper analyses the fleet efficiency of two companies in Serbia, seven from company A, and six from company B. Applying statistical tests, the difference in fleet efficiency of mentioned companies is observed. This model helps managers in decision making and improves the operational efficiency. Keywords: Efficiency, Fleet, Data Envelopment Analysis, Distribution Centres. Introduction In last three decades logistics has been recognized as one of the most important service industries. Logistics has crucial role in supply chains, which reflects in connecting members in supply chains. Distribution centres (DCs) are complex logistics systems which connect producers with other participants in the chain including end-users. Two basic subsystems of DCs are warehouse and transport subsystem. The most important part of transport subsystem refers to fleet. Efficiency as a crucial indicator of companies operational analysis is one of the basic and most frequently used performances. Due to complex structures of DC, estimating its efficiencies is a challenging process. Transport costs represent the largest portion of total costs required for DC s operation. Single ratio indicators have been used to estimate the efficiency of a DC for a long time. A number of authors advocate the use of approaches such as the Data Envelopment Analysis (DEA) method (Min and Joo, 2006, Hamdan and Rogers, 2008). The DEA method is used for estimating the efficiency of homogeneous Decision Making Units (DMUs). The main objective of this paper is to propose model for estimating efficiency of thirteen fleets of distribution centres located in Serbia: thirteen fleets of two companies that operate in Serbia - seven from company A and six from company B.
2 Another objective of this paper is the examination of company management and fleet size influence on the efficiency scores. 2. Review of methods and approaches The distribution of goods today relies heavily on the use of road transport. In the literature, there are different approaches for freight transport performance measurement. McKinnon et al., (999) analyzes KPIs for the food supply chain. They analyze operational efficiency of road freight transport by using several indicators such as degree of empty running, fuel efficiency, deviation from schedule, time utilization and vehicle utilization. McKinnon et al., 2003 defines potential reductions in operating costs, energy consumption and vehicle emissions. Chow et al. (994) examine the definition and measurement of performance in logistics research. Authors defined Distribution effectiveness as adequacy, consistency, accuracy, timeliness, initiative, responsiveness. Donselarr et al. (998) also investigates transport effectiveness. The overall vehicle effectiveness (OVE) measure aims to build upon this by providing for a single operational measure of total vehicle performance. It develops a single measure, which assesses the total effectiveness of vehicles. Developing a complete measure that aggregates overall performance is a fundamental element in the efficiency assessment. The use of a single measure would help co-ordinate government policy with logistics customers and providers business objectives by helping to promote increased vehicle effectiveness (Simons et. al 2004). Cruijssena et al. (200) analyzes freight transportation efficiency in Flanders. They state that total inputs are combination of labor (total wages, drivers experience, total hours worked, number of employees, etc.), equipment (number of trucks, number of trailers, total loading capacity etc.) and intangible assets (market information, customer contacts, goodwill, etc.). Profit and value added are considered as the main output variables. Kim (200) evaluates technical and scale efficiency of individual trucks in logistics. The DEA model for 62 trucks efficiency evaluation is specified with three output categories (transportation distance, transportation amount, and effective transportation distance) and five variable input factors (labor cost, fuel cost, oil cost, supplies cost, tax and insurance, etc). Andrejić and Kilibarda (20) evaluate efficiency logistics processes in products distribution. Proposed model is based on DEA method and game theory. Kilibarda et al (20) analyzes efficiency of the logistics processes in the distribution center of a trading company. Authors proved the different impact of the transport and warehouse subsystems performances upon the overall efficiency of the distribution center, as well as the suitability of applying the MODEA (Multiple Objective Data Envelopment Analysis) approach for measuring the efficiency of the logistics systems. DEA method is one of the most frequently used methods for measuring the efficiency in logistics. In this paper DEA method is used for efficiency evaluation of thirteen fleets. It is a non-parametric linear programming technique which enables the comparison of efficiencies of different DMUs, based on multiple inputs and outputs. (Farrell 957) The efficiency is relative and relates to the set of units within the analysis. Charnes et al. (978) proposed a non-parametric approach for efficiency estimation, where they reduce multiple inputs to a single virtual input and multiple outputs reduced to a single virtual output using weighting coefficients. This method is also used for obtaining information about corrective actions of inefficient DMUs.
3 Obtained efficiencies are relative since they relate only to a set of observed DMUs and they cannot be considered as absolute. The basic CCR (Charnes et al. 978) model presents the basis of all present models. In the original form, this model presents the problem of fractional programming. According to the appropriate transformations, the model is reduced to the linear programming problem. In order to estimate DMU efficiency it is necessary to have data of consumed input and realized output variables. In the process of DEA method application, the CCR model is preferable as the initial model. As in linear programming problems, the CCR model also has two formulations: primal and dual. The following notation is most frequently used in the DEA terminology. A set of DMUs has n DMU (j =, 2,..., n), where each input is characterized by m input (i=, 2,..., m) and s output variables (r =, 2,..., s). The value of i input variable is denoted as x ij, while y rj denotes the value of r output variables of DMU j. Weighting coefficients are related to all inputs and outputs and they are denoted with υ i and u r respectively. They present decision variables. In order to estimate DMU efficiency of the observed set it is necessary to perform n independent estimations where DMU k (k=,,n) presents the DC whose efficiency is measured. Dual formulation (envelopment form) of the original CCR model was used in this paper. There are several benefits of solving the dual problem. Considering the fact that the number of DMUs is higher than the number of inputs and outputs, in practice, due to a computational effort the dual model is mostly solved. Max-slack solution can not be obtained by solving the primal model. The interpretation of the dual model is more straightforward because the solutions are characterized as inputs and outputs that correspond to the original data whereas the multipliers provided by solutions to primal represent evaluations of these observed values (Cooper et al., 2007). CCR dual model is usually solved in two stages: Stage I Min θ () Subject to: Stage II n j= λ y y 0, r =,,...,s (2) j rj rk 2 n ik j ij 2 j= j 0, j =,2,...,n θ x λ x 0, i =,,...,m (3) λ (4) Max e s + m s r + s i r= i= (5) Subject to: n j= + λ j yrj yrk sr = 0, r =, 2,..., s (6) n j= θ xik λ jxij si = 0, i =,2,..., m (7)
4 + j r i = λ, s, s 0, i =,2,...,m,r =,2,...,s, j,2,...,n (8) The variable θ is called the intensity factor, and it shows how it is possible for DMU k to proportionally reduce all output variables. The optimal value θ is obtained in the first phase after which it is used for estimating the efficiency in the second phase. + Variables s r and s i show how is it possible that DMU k individually reduce i input variable and increase r output variable in order to become efficient. These values are called slack variables. If from the set of dual weighting coefficients λ j (j =, 2,..., n) only λ k has a positive value then the intensity factor is θ =, which means that DMU k engaged the minimum amount of input variables and it is the marginal point. If that is not the case, DMU k is inefficient. DMUs with a positive value for the dual weighting coefficients λ j are called peers for DMU k. Therefore, if θ <, then DMU k is relatively inefficient and it should proportionally for ( θ ) 00 percentage reduce all input variables in order to become efficient with the existing level of output variables. Dual formulation of the CCR model was used in this paper. 3. Data and model definition This paper evaluates the efficiency of thirteen fleets of two trading companies which operate in Serbia and have similar sale network, products range and distribution system. In this example, transport subsystem, as one of the most important systems in distribution process, is observed. Every DC has its own fleet. Observed trucks have similar capacity and operating system. The main problem in DEA method application is selection of the input and output variables. This problem is previously recognized in literature (Boussofiane et al, 99). From the standpoint of the processing approach, transport subsystem in DC is a system which uses a number of inputs (resources) in order to generate certain outputs. From the large number of potential variables in this paper, three input and three output variables are selected. Input variables include number of vehicles, fuel costs and total vehicle time in operation, while output variables include total distance driven, tons shipped, and vehicle utilization. These indicators fully describe fleet operating. Figure. Fleet operating variables for observed Companies Inputs Vehicle Fuel costs Total truck time Fleet Outputs Distance driven Shipped tons Vehicle utilization The fleet size is described by the number of vehicles (trucks). Fuel costs are one of the most frequently used indicators of energy consumption. Fuel costs are expressed in monetary units. Time indicators are also important in fleet efficiency
5 analysis. This paper analysis total vehicle time in operation. On the other side, total distance driven as output variable, is expressed in kilometers. Tons shipped are frequently used variable for vehicle efficiency evaluation. The last output variable is vehicle utilization. It is expressed in percentage and represents the ratio of volume of goods and the volume of vehicle cargo space. Descriptive statistics of input and output variables used in this paper is given in Table. Table. Input and output variables for efficiency evaluation Variables Min Max Mean SD Number of vehicle Fuel costs (m.u.) Total trucks time Distance driven (km) Shipped tons (t) Vehicle utilization Results and discussion The efficiency scores of thirteen fleets of two trading companies which operate in Serbia are analyzed in this section. In this research, analysis is carried out by DEA software efficiency measurement system (EMS), developed by the Operations Research Department at the University of Dortmund. Results are shown in Table 2. Seven fleets are efficient while six are inefficient. The average efficiency is about 93%. The proposed model is input oriented, so inefficient fleets can improve their efficiency by reducing the input variables. For example, DMU 9 can increase efficiency by reducing number of vehicles, fuel costs and total vehicle time in operation by 26%. On the other side fifth fleet (DMU 5) can achieve the same total distance driven, tons shipped, and vehicle utilization with 3% less use of vehicles, costs and time. Inefficient fleets can improve efficiency in the similar way. Table 2. Efficiency scores DMU Company Efficiency Benchmarks DMU A (0.25) 7 (0.92) DMU2 A.00 DMU3 A.00 2 DMU4 A.00 0 DMU5 A (0.56) 3 (0.0) 7 (0.54) (0.0) DMU6 A.00 4 DMU7 A.00 2 DMU8 B (0.04) (0.83) 3 (0.20) DMU9 B (0.5) (0.5) 3 (0.88) DMU0 B (0.07) (0.24) 3 (0.72) DMU B.00 5 DMU2 B (0.06) (0.54) 3 (0.48)
6 DMU3 B.00 4 The last column of Table 2 shows benchmarks (peer set) for inefficient units. The fleet (DMU) is the most frequently used benchmark for all inefficient fleets. DMU 6 and DMU 3 are benchmarks for four units. On the other side, inefficient fleets have several benchmarks. For example, DMU 3 and DMU 7 are benchmarks for DMU. Table 2 shows that benchmarks corresponding coefficients are quite different. For DMU, DMU 7 (weight coefficient is 0.92) is more significant than DMU 3 (weight coefficient is 0.25). The similar conclusion can be drawn for other inefficient fleets. DEA method also provides information about potential savings in slack movement. The slack movements, which arise because of the sections of the piecewise linear frontier that run parallel to the axes are reported in Table 3. Table 3. Potential savings in inputs Actual average Average slack Potential reduce Number of vehicle % Fuel costs (m.u.) % Total trucks time % Distance driven (km) % Shipped tons (t) % Vehicle utilization % Analysis of slack values shows a slack in the input variables, as well as in the output variables. Potential improvements are related to the average decrease in the inputs, which stand at.3% for total truck time costs and 5.2% for number of vehicles in fleet. In order to improve efficiency, inefficient DMU should improve vehicle utilization for about.5% on average, and shipped tons for 3.3% on average. This paper also investigates the dependence between the fleet efficiency and the management, as well as differences in efficiencies of fleets with small and large number of vehicles. In that sense, two hypotheses are set in this paper: H: There is a difference in fleet efficiencies between Company A and Company B H2: There is a difference in efficiencies between small and large fleets The hypothesis on the difference in fleet efficiencies of mentioned companies is proven (for significance level of 0%) according the Mann-Whitney test (Table 4). According to test results (U=0, P=0.088), it is concluded that the average fleet efficiency of company A is 97%, while the efficiency of company B is 87%. This suggests that the efficiencies of the fleets are largely affected by fleet management. Table 4. Hypothesis tests statistics H Mann-Whitney U Mann-Whitney U Wilcoxon W Wilcoxon W Z Z Asymp. Sig. (2-tailed) Asymp. Sig. (2-tailed) Exact Sig. [2*(-tailed Sig.)] 0.38 Exact Sig. [2*(-tailed Sig.)] H2
7 For the purposes of the second hypothesis, the observed set is divided according to the number of vehicles in small and large fleets. The critical point is set at eighteen vehicles. Observed set is divided in five big and eight small fleets. The hypothesis of the difference in the fleet efficiencies between small and large fleets is not proven according Mann-Whitney test and significance level is 0% (U=8, P=0.750). In this case, no difference in the efficiency between large and small fleets exists (Table 4). 5. Conclusions This paper illustrates how to evaluate and improve efficiency of fleets in 3 distribution centres in Serbia. The proposed model is based on DEA method. Three inputs (number of vehicles, fuel costs and total trucks time in operation) and three outputs (total distance driven, tons shipped and trucks utilization) are used for estimating fleet efficiency of two trade companies in Serbia. Mentioned variables fully describe fleet operating. According to proposed model, 53% fleets are efficient and 47% are inefficient. Two hypotheses are set in this paper. The first hypothesis refers to the difference in fleet efficiencies between company A and company B, caused by Company s management. The second hypothesis refers to the difference in efficiency scores between small and large fleets. The first hypothesis is confirmed, while the second is rejected. On this basis, the following conclusions are derived. Company s management is very important factor for fleet efficiency. In this example company A has better management. According to the second hypothesis, fleet size does not affect efficiency scores. In this case large fleets have average score of 94%, while small have average score of 92%. However, this difference is not statistically significant. The fleet efficiency is also influenced by a great number of factors upon which the Company s management has no influence: weather conditions, market situation, competition behavior, etc. Mentioned factors are not examined in this paper. In the future models, introducing these indicators would add value to the research. Future models should also include indicators of greenhouse gas emission, and other undesirable outputs. Acknowledgment This work was partially supported by the Ministry of Science and Technological Development of the Republic of Serbia, through the project TR 36006, for the period References Andrejić M, Kilibarda M., (20), "The efficiency of logistics processes of products distribution", National quality festival, Kragujevac, 20. A 237 A 242. Boussofiane A., Dyson R. G., and Thanassoulis E. (99), "Applied Data Envelopment Analysis", European Journal of Operational Research, Vol.52, No., pp. -5. Charnes A., Cooper W.W., and Rhodes E. (978), "Measuring efficiency of decision making units", European Journal of Operations Research, Vol. 2, No. 6, pp
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