# Assessing Container Terminal Safety and Security Using Data Envelopment Analysis

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2 They developed the CCR model that was an optimization method for measuring relative efficiency by multiple-output/multiple-input cases. [2] They generalized Farrell s (1957) singleoutput/input technical-efficiency measure to a multiple-output/multiple-input case by constructing a single virtual output to a single virtual input relative-efficiency measure. According to Charnes et al. the relative efficiency of any DMU is measured by forming the ratio of a weighted sum of outputs to a weighted sum of inputs, where the weights for both outputs and inputs are to be selected in a manner that calculates the Pareto efficiency measure of each DMU subject to the constraint that no DMU can have a relative efficiency score greater than one. [3] The efficiencies captured by a DEA model are relative because they reflect scope for resource conservation or output augmentation at one unit relative to other comparable benchmark units rather than in some absolute sense. In many practical situations there is also a lack of sufficient information to derive the absolute efficiency. [4] DEA methodology can be utilized in a variety of fields. It has been applied to areas such as universities, warehouses, benchmarking, health care systems, banking, and transportation. DEA, in conjunction with other arithmetic methods, has been applied a number of times to assess the efficiency of container terminals and ports, both from technical and economical standpoints. For instance, Kaisar et al. applied DEA to analyze port productivity in the US. [5] Also, Turner et al. used DEA methodology to measure containerport productivity. [6] The methodology presented here, however, focuses on the safety and security aspect of the port operations to maximize the efficiency when cargo is moved from one mode of transportation to another. 2 Methodology 2.1 DEA Concept DEA is a method to analyze relative efficiency by optimizing on each DMU that is being assessed. The focus of DEA is to optimize on each DMU rather than forming population averages. DMUs that are considered efficient by DEA validate the following; for a given input, X, there is no other facility that gives a higher output, Y. The result from the DEA assessment also provides benchmarks that inefficient DMUs can relate to. Banker, Charnes, and Cooper developed one of the most utilized DEA models these days, i.e. the BCC model. They extended the CCR model that only allow for constant return to scale to the BCC model that accommodates technologies that exhibit variable return to scale (VRS). [2] The BCC model has two main approaches; input-oriented and outputoriented. Both approaches will be applied in this study to identify and analyze the efficiency of the current security systems at container terminals. The input-oriented BCC model focuses on optimizing the efficiency by reduction of the inputs, whereas the output-oriented approach focuses on optimizing the efficiency by increasing the output variables. The primal formulations related to these BCC models are presented next. 2.2 Input-Oriented BCC Primal The BCC DEA model for assessing input efficiency of DMUj is shown in formulation (1). The Input- Oriented BCC Primal model shown in formulation (1) was introduced by Charnes et al. [3] min θ, λ,s, s s.t. θ X o λ θ ε 1 s ε (1) z o = 1 s Y λ s = Y 1 1 λ, s, Xλ s s 0 o = 0 where: zo: efficiency score. θ: scalar variable by which the current input level has to be multiplied with in order to increase efficiency. s, s - : vectors that contain the output and input slacks, respectively. ε: a non-archimedean constant that allows the minimization over θ to preempt the optimization involving the slacks. λ: intensity vector. Y, X: Y is a non-negative output matrix and X a non-negative input matrix, with ith columns Yi and Xi, respectively. The evaluation of each DMUj, j = 1, 2,..., n, are characterized by different parameters. The scalar variable θj, 0 < θj 1 is the proportional reduction applied to all inputs of DMUo. The subscript (o) denotes the DMU whose efficiency is being evaluated. The parameter λj = (λj1, λj2,..., λjn) is a vector describing the percentages of reference to the efficient DMUs. The input-oriented model attempts via θ to minimize the input without increasing the given output level. Since ε allows the ISSN: ISBN:

3 minimization over θ to preempt the optimization involving the slacks, the optimization can be computed in two stages: 1) maximal reduction of inputs being achieved first via θ; and 2) movement onto the efficient frontier via the slack variable s and s -. [3] 2.3 Output-Oriented BCC Primal In the output-oriented approach, the focus shift from minimizing the input to maximizing the output. The BCC DEA model for assessing output efficiency of DMUj is shown in formulation (2). The Output- Oriented BCC Primal model shown in formulation (2) was introduced by Charnes et al. [3] max φ, λ,s, s ε (2) z o = Φ 1 s ε 1 s s.t. ΦY o Yλ s = 0 X λ s = λ 1 = 1 λ, s, s 0 X o where: zo: efficiency score. Φ: scalar variable by which the current output level has to be multiplied with in order to increase efficiency. s, s - : vectors that contain the output and input slacks, respectively. ε: allows the maximization over Φ to preempt the optimization involving the slacks λ: intensity vector. Y, X: Y is a non-negative output matrix and X a non-negative input matrix, with ith columns Yi and Xi, respectively. The output-oriented model attempts via Φ to maximize the output without reducing the given input level. The non-archimedean constant, ε, allows the maximization over Φ to preempt the optimization involving the slacks. Thus, the optimization can be computed in two stages: 1) maximal expansion of outputs being achieved firs via Φ; and 2) movement onto the efficient frontier via the slack variable s and s -. [3] 2.4 Selection of Variables When developing a DEA model, the selection of input and output variables is very important. It is critical to include all inputs that impact the outcome and capture all the considerable outcomes that are to be assessed. Table 1 comprises all the chosen input and output variables together with appropriate short forms. After selecting the variables, the related data must be assembled for the given time period. Data gathering is a complex process because some of the variables consist of sensitive security information. The data for the input variables has been estimated whereas the data for the three output variables are obtained from the Bureau of Transportation Statistics and the American Association of Port Authorities. Table 1 Input and Output Variables Variable # Definition Short Form Inputs 1i Number of security checkpoints for cargo Sec. check. cargo 2i Number of police/law Law enf. off. enforcement officers 3i Number of safety and Incidents security-related incidents 4i Number of safety and Accidents security-related accidents Outputs 1o Millions of short tons Short Tons 2o Total port calls Port Calls 3o Container port traffic in TEU volume TEU 3 Case Study Application For this study, 18 containerport terminals in the United States have been chosen for the assessment of the proposed DEA model. Table 2 shows the selected containerports for this study. These ports are ideal for the study area because they present the major containerport terminals in the US in terms of TEU volume, tons of freight, and port calls. [5] The time period for the study is eight years, from 2000 to This time frame is mainly chosen because of the latest availability of data and statistics. In order to validate the developed DEA model for this study, several scenarios have been applied and investigated. A Microsoft Excel add-in developed by Zhu has been used to measure the relative efficiency of the selected containerport terminals. [7] The DEAFronter measures the following: relative efficiency, targets, slacks, and benchmarks. Both the input-oriented and the output-oriented approaches have been applied in the assessment. ISSN: ISBN:

4 Table 2 Sample of Containerports Port # Port Name 1 Los Angeles 2 Long Beach 3 New York 4 Seattle 5 Tacoma 6 Savannah 7 Houston 8 Norfolk 9 Oakland 10 Charleston 11 Port Everglades 12 Miami 13 Palm Beach 14 Canaveral 15 Tampa 16 Jacsonville 17 Port Manatee 18 San Diego 1 Results and Analysis To develop a DEA model to assess the efficiency of the security systems at containerport terminals, a variety of scenarios have been applied and analyzed. Both the input-oriented and output-oriented DEA approaches have been applied for the assessment. For both approaches, the DMUs receiving efficiency equal to 1 are relative efficient compared to the other DMUs in the model. For the input-oriented approach, the DMUs receiving efficiency less than 1 is inefficient, whereas for the output-oriented approach the DMUs receiving efficiency greater than 1 is inefficient. A scenario presenting the DEA model with the proposed variables and the 18 containerports are presented next. For the presented scenario in this study, an assessment of the 18 seaports together with the selected variables has been carried out for the full time period, A sample of the data collected for 2007 is shown in Table 3. Given the 18 port terminals studied over an eight year period, the maximum sample size would be 144 observations. The availability of data, however, will affect the actual sample size. Because the DEA model requires values greater than zero for all variables, missing data within any observation will result in an exclusion of that observation from the sample. San Diego was therefore not included in the DEA model for 2000 and 2001 because the port did not have any reported TEU volume for these years. Consequently, the number of observations for this scenario was 142. Figure 1 illustrates the efficiency score obtained by the DEA model under input minimization, whereas Figure 2 shows the efficiency score obtained under output maximization. It is apparent from both approaches that several ports can improve the efficiency of their security system by either reducing the input or increasing the output. For example, Port Manatee that stands out as one of the worst performers could either try to enhance their efficiency by reducing their input data, increasing their operations, or a combination of the two. The DEA model also calculates targets and benchmarks that inefficient ports can relate to when trying to improve efficiency. The target will show optimal values for all the input and output variables for each containerport terminal in the assessment. The benchmarks on the other hand will indicate what port/ports an inefficient port should measure itself up to when trying to optimize efficiency. 4 Conclusion There is a need for efficient and current security systems at container terminals to meet the predicted growing market of container traffic and other port services. Improved security solutions will also facilitate economic development and help to keep the United States safe from terrorist attacks and other threats. The contribution of the study is a mathematical model that can measure the efficiency of the security systems at containerport terminals. The resulted DEA methodology can be used to assess the relative efficiency of the security operations at containerport terminals. The mathematical model is general in its framework and can therefore also be applied to other containerport terminals in the United States or globally. The success of the mathematical model, however, depends on the accurate and reliable data from several sources. Since the study involves sensitive security information of large containerport terminals, the accuracy of the estimated data is questionable, in some respects. Availability of data, complimented with the presented DEA methodology will help managers in decision making for enhanced safety and security solutions for containerport terminals. Decision makers, however, need to carefully evaluate different aspects of the terminal operations when considering improving the efficiency level of an inefficient container terminal. Lowering the number of law enforcement officers for example might make the port more efficient because one of the input variables is reduced, but it will also possibly result in more accidents and incidents and consequently lowering the efficiency again. ISSN: ISBN:

5 DMU No. DMU Name Table 3 Data for the Containerport Terminals for 2007 Sec. Check. Cargo Law Enf. Off. Incidents Accidents Short Tons Port Calls (1i) (2i) (3i) (4i) (1o) (2o) (3o) 1 Los Angeles, Long Beach, New York, Seattle, Tacoma, Savannah, Houston, Norfolk, Oakland, Charleston, Port Everglades, Miami, Palm Beach, Canaveral, Tampa, Jacksonville, Port Manatee, San Diego, TEU Efficiency Input-Oriented Approach Year Fig. 1 Input-oriented VRS efficiency for scenario 1. Los Angeles Long Beach New York Seattle Tacoma Savannah Houston Norfolk Oakland Charleston Port Everglades Miami Palm Beach Canaveral Tampa Jacksonville Port Manatee San Diego ISSN: ISBN:

6 Efficiency Output-Oriented Approach Year Fig. 2 Output-oriented VRS efficiency for scenario 1. Los Angeles Long Beach New York Seattle Tacoma Savannah Houston Norfolk Oakland Charleston Port Everglades Miami Palm Beach Canaveral Tampa Jacksonville Port Manatee San Diego References: [1] U.S. DOT (2007). The Maritime Administration and the U.S. Marine Transportation System: A Vision for the 21st Century, Washington, DC, USA. [2] Ray, S.C. Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research, Press Syndicate of the University of Cambridge, UK, [3] Charnes, A., W. W Cooper, A. Y. Lewin, and L. M. Seiford. Data Envelopment Analysis: Theory, Methodology, and Application, Kluwer Academic Publishers, USA, [4] Thanassoulis, E. Introduction to the Theory and Application of Data Envelopment Analysis: A Foundation Text with Integrated Software, Kluwer Academic Publishers, USA, [5] Kaisar, E. I., S. Pathomsiri, and A. Haghani. Efficiency Measurement of US Ports Using Data Envelopment Analysis. National Urban Freight Conference, February 1-3, [6] Turner, H., R. Windle, and M. Dresner. North American containerport productivity: Transportation Research, Part E, 40, 2004, pp [7] Zhu, J. Quantitative Models for Performance Evaluation and Benchmarking; Data Envelopment Analysis with Spreadsheet and DEA Excel Solver, Kluwer Academic Publisher, Boston, USA, ISSN: ISBN:

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