1 Introduction

The economic development of all countries depends to a large extent on the development of ports and the growth of freight traffic in ports. Nevertheless, port activities cause negative impacts on air, water, soil and sediments (Marti Puig et al., 2015). Fossil fuels, as the main energy source for shipping, are high-carbon and less refined, and air pollutant emission standards are less stringent (ITF, 2018). Consequently, shipping is considered a significant source of air pollutants. According to the fourth study by the International Maritime Organization (IMO) (IMO, 2020), shipping generates 1,076 (data for 2018, which significate a 9.6% increase from 2012) million tonnes of greenhouse gas (GHG) emissions. The IMO’s fourth study showed that GHG emissions from all shipping (international shipping, domestic or inland shipping and fisheries) increased by 9.6% from 977 million tonnes in 2012 to 1,076 million tonnes in 2018. Emissions are projected to increase from about 90% of 2008 emissions in 2018 to 90–130% of 2008 emissions by 2050 (IMO, 2020). Therefore, significant efforts have been made in the last decade to reduce air pollution from shipping by setting various standards, new supporting policies and measures (Abbasov et al., 2019). Also at sea, GHG emissions are the main source of air pollution from shipping in most ports (ITF, 2018). In addition to shipping, loading and unloading facilities and trucks on the landside of ports are also significant sources of air pollution (Joon-Ho Na et al., 2017).

Nowadays, air quality at the ship–port interface is the biggest environmental problem (IMO, 2015). Decarbonization of maritime transport can be achieved by implementing various solutions to reduce GHG emissions at the port–ship interface (ITF, 2018). The European Union (EU) has recognized the environmental problem and is focusing on the collection and reporting of GHG emissions from international shipping in the IMO. Therefore, as of 2018, the EU has adopted legislation to monitor, report, and verify emissions (Commission, 2016). In addition, the European Commission (EC) supports further investigation of measures and best practices to reduce air emissions and improve overall efficiency in the port sector (IMO, 2015; Commission, 2016).

In the context of interconnected global trade, supply chains, production processes, and economies of countries with well-functioning port systems, it is increasingly important to monitor and measure the environmental performance of ports in addition to their operational, financial, economic and social performance (UNCTAD, 2018). In the literature, based on a review article (Markovits-Somogyi, 2011) and other published to date, the DEA method has received considerable attention in assessing port efficiency. For this purpose, various Data Envelopment Analysis (DEA) models have been used to measure the overall efficiency of ports or their parts. The evaluation of port efficiency considering the port’s environmental performance has attracted considerable attention from scholars and port experts (Sun et al., 2017), but none two-stage DEA model was used since now.

The literature review indicates that previous studies of port efficiency have used one-stage models DEA. The use of one-stage DEA models to evaluate the environmental efficiency (EE) of the ports examined in this study can also be found in the literature. However, the one-stage DEA models treat decision-making units (DMUs) as a "black box" and ignore the sources of inefficiency and the internal relationships between the stages of the system (Liu et al., 2015). Due to this limitation of the one-stage models, two-stage DEA models have been used to evaluate efficiency by using the results (i.e., outputs) of the first stage as inputs to the second stage (Cook et al., 2010), (Mahdiloo et al., 2016). Two-stage models can be used to separately evaluate the performance of DMUs and their sub-processes to identify the source of inefficiency (Kao, 2014). However, in the literature and to the authors’ knowledge, there are no two-stage DEA models for measuring port EE.

Therefore, the main objective of our paper is to demonstrate the suitability of the two-stage non-radial DEA model (NRDEA) (Djordjević et al., 2018) for the assessment of the entirety of ports EE. For this purpose, using the available data for the port of Koper and the port of Dublin, this study compares the results of the one-stage and the two-stage DEA models. The EE of these two ports were measured using environmental indicators that consider desirable and undesirable inputs and outputs.

It is expected that this study will make an important contribution to the research community, especially in the field of decision making. Monitoring port efficiency using environmental indicators at different points in time—i.e., annually, monthly, or daily—with these models can guarantee good port performance and ensure that stakeholders continue to support port operations and development (Marti Puig et al., 2015). Therefore, this paper will be useful for policy makers and stakeholders when making decisions about the port environmental performance and maritime transport in general. In addition, the maritime community can use the two-stage model to identify best practices by comparing numerous and diverse ports. Depending on data availability, this approach can also be used to assess individual parts of the port. In addition, the two-stage non-radial DEA model can be used to identify the impact of various measures to improve the environmental performance of individual parts of the port.

This paper is organized as follows: The next section presents the literature review, followed by section dedicated to the methodology using the DEA models. Section 34 presents the results of the ports evaluated. Section 45 discusses the evaluation of ports using distance metrics and presents the possible improvements for inefficient DMUs. The last section concludes the paper.

2 Theoretical background

A two-step methodology was developed to introduce a two-stage DEA model suitable for port EE assessment (see Fig. 1). As a first step, a literature review was conducted to search for two-stage models for the port EE. Two-stage DEA models for EE assessment can be found in the literature for various domains (see Sects. 2.1.2 and 2.1.3). Since only two articles used two-stage models that consider port efficiency but do not include environmental factors, the second step was to adapt the non-radial DEA model used by Djordjevic et al. (2018) to evaluate the port EE with a two-stage model.

Fig. 1
figure 1

Process of literature review and development of methodology

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There are numerous articles in scientific databases (Web of Science, Scopus) that use DEA to evaluate the efficiency of ports. Since the objective of the study is related to the EE of ports, the focus was only on such studies. The literature search focused on English language articles that were freely available in full text. Based on the number of articles on port EE reviewed in (Clarice Neffa Gobbi et al., 2019), it can be seen that numerous studies have used different DEA models.

2.1 One-stage DEA Models for the EE of Ports

Studies that address port EE using a one-stage DEA model can be found in Table 1. The one-stage DEA models are used because of their ability to combine multiple inputs and outputs in an optimization framework (Clarice Neffa Gobbi et al., 2019). However, the hidden nature of one-stage DEA is related to the fact that DMUs are treated as black boxes, where the sources of inefficiency and the interconnectedness of factors are not explicitly investigated (Chen et al., 2021; Liu et al., 2015).

Table 1 DEA for the EE of ports
Full size table

Therefore, in addition to the studies listed in Table 1 that demonstrate the successful application and verification of one-stage DEA models for port EE measurement, there are also studies that recognize the weaknesses of one stage DEA. According to (Wanke, 2013), some intermediate outputs between production and service processes are produced and consumed in the port. Consequently, the study of the internal relationships between the factors related to the performance of DEA is necessary. Therefore, one-stage model DEA is extended to a two-stage model DEA to treat DMUs separately by different components producing outputs by using intermediate outputs derived from their previous components (Wanke, 2013).

2.2 Two-stage DEA Models in Transportation

The application of two-stage DEA models has been used in various areas of transportation, such as airport and airline efficiency evaluation (Yan-chang et al., 2010), (Carlos Pestana Barros & Peypoch, 2009), (Rico Merkert & Williams, 2013), (Rico Merkert & Mangia, 2014), (Merkert & Assaf, 2015), (Zhongfei Chen et al., 2017), (Chen et al., 2021) and national civil aviation strategies (Itani et al., 2015). Two-stage DEA models have also been applied to analyze the efficiency of rail freight (Dalmo Marchetti & Wanke, 2017), passenger transport (Link, 2019), urban transport terminals (Sun, 2007), 113 Arterial Bus Routes (Hahn et al., 2011) and six public bus operators (Zehmed Karim & Fouad, 2018). However, the application of two-stage DEA models to evaluate the EE of transport modes was not found.

The measurement of port efficiency using the two-stage network model DEA was presented by (Wanke, 2013).Using Brazilian ports as a case study, the efficiency assessment was considered for physical infrastructure and for transport consolidation. The number of berths, storage areas, and yard areas were presented as inputs, while the frequency of bulk cargo and the frequency of containers were used as intermediate variables. The outputs of the process were defined as solid bulk and container throughput. (Pham et al., 2020) measured the operational efficiency of 40 container ports in the world using the two-stage uncertainty DEA combined with FCM (Fuzzy Clustering Method). Wang et al. (2022) used two-stage DEA for measuring the performance efficiency of Vietnam’s top 18 seaports. However, there is a lack of evaluation of ports and other modes using the two-stage model DEA in terms of EE.

2.3 Two-stage DEA Models for EE assessment

Two-stage DEA models have been used in the literature to evaluate EE in various fields. Two-stage network DEA model to evaluate the influence of generation forms of power systems on EE performance was used in (Bai-Chen 2012). Then, the network model DEA was introduced by (Lozano, 2017) for the evaluation of EE. The network model was illustrated on coal-fired power plants as a case study. The application of two-stage DEA models in environmental and energy efficiency assessment can be found in (Song et al., 2014), (Jie et al., 2016) and (Lei Chen et al., 2018) where new two-stage DEA approaches were introduced. The application of these models was illustrated by water use in industry, industrial production systems, and water efficiency of Chinese industry, respectively.

(Zhang et al., 2019) have used a two-stage DEA model to evaluate the efficiency of resource allocation to combat the pollution problem in China. A novel two-stage DEA model was developed by (Mavi et al., 2019) to evaluate the eco-efficiency and eco-innovation of OECD countries in the context of Big Data. To evaluate the efficiency of recycling treatment and reuse of industrial waste, including wastewater, waste gas and solid waste, (Li et al., 2020) also used the two-stage model DEA.

2.4 Two-stage DEA models considering undesirable factors

In real-world processes, the application of DEA models can result in undesirable factors—i.e., inputs and outputs—in addition to desirable factors. Most of discussions only involve undesirable final outputs, while in two-stage DEA models, other variables such as inputs and intermediate measures, can be either desirable and undesirable (Liu et al., 2015). According to (Liu et al., 2015), desirability of outputs is often determined by the decision maker in real applications. If the goal in a system is to produce as much as possible are desirable outputs and otherwise, they are undesirable outputs. Literature review was conducted to identify transport studies that modelled variables as desirable and undesirable in two-stage models. Desirable and undesirable outputs were considered in evaluating the efficiency of 113 arterial bus routes by (Hahn et al., 2011). (Maghbouli et al., 2014) introduced a two-stage DEA approach to analyze the performance of these processes with intermediate undesirable measures. Also, (Wu et al., 2015) proposed an additive DEA model to evaluate the efficiency of a two-stage network process with intermediate undesirable measures. In the evaluation of airline efficiency (Chen et al., 2017), flight delays and CO2 emissions were considered as undesirable outputs. Undesirable outputs were also considered in the study of (Lozano, 2017). In addition, intermediate elements were included in the two-stage EE assessment model in (Chen et al., 2018). Both desirable and undesirable elements were considered in (Zhang et al., 2019) to assess pollution control measures in 30 provinces. Finally, undesirable inputs, intermediates, and outputs were modelled in (Liu & Deng, 2015) and (Mavi et al., 2019). In addition, undesirable inputs were used in (Li et al., 2020) to evaluate the efficiency of recycling treatment and reuse of industrial waste.

3 Method

The overall process of determining the EE levels of ports, in our case the ports of Koper and Dublin, using one- and two-stage models is shown in Fig. 2. The two-stage model is an extension of the one-stage model presented by (Djordjević et al., 2018) and follows the methods described in (Cook et al., 2010). Since a port terminal can be divided into two parts, seaward and landside (Carlo et al., 2014a, b), the overall efficiency of a port depends on both the seaward and landside parts and is mainly affected by the equipment and processes (Lee et al., 2014). Therefore, for such processes that may consist of two separate and distinct phases, such as processes in ports (Mahdiloo et al., 2016), a two-stage model DEA is chosen.

Fig. 2
figure 2

Process of ports EE evaluation

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According to (Mahdiloo et al., 2016), two-stage models did not consider the lack of discriminatory power and weighting of decision makers for inputs, intermediate measures, and outputs. To overcome these two problems, they applied the multiple criteria DEA (MCDEA) approach. This is why in our study models with decision maker weights and strong discriminatory power were introduced.

3.1 Selected DEA models

DEA method was chosen in this study because it has attracted considerable attention in the evaluation of environmental efficiency due to its ability to incorporate pollutants into the traditional DEA framework. Previous studies have often used the radial model to evaluate the environmental efficiency. For the purpose of this study, a non-radial model was selected due to advantages such as higher discriminatory power and prioritization of factors by decision makers (Zhou et al., 2007). The one-stage radial DEA presented in (Djordjević, et al., 2018) was extended to a two-stage model to overcome the disadvantage of one-stage models of considering DMUs as black boxes. There are a number of papers in the literature that deal with centralised DEA approaches (Liu et al., 2015). In this study, the two-stage model was formulated as a centralized two-stage approach because, unlike the traditional DEA models that assume DMUs are independent units, the centralized model assumes that all DMUs are under the control of a high-level authority (Abedian et al., 2022; Liang et al., 2008).

3.2 One-stage Non-radial DEA Model

The one-stage NRDEA (non-radial DEA) model introduced by(Djordjević et al., 2018) is following:

$$\theta_{k = } {\text{min}} W_{n} \frac{1}{N}\mathop \sum \limits_{n = 1}^{N} \theta_{n} + W_{l} \frac{1}{L}\mathop \sum \limits_{l = 1}^{L} \theta_{l} + W_{j} \frac{1}{J}\mathop \sum \limits_{j = 1}^{J} \theta_{j}$$
(1)

subject to:

$$\sum \limits_{k = 1}^{K} \lambda_{k} x_{nk}^{1} \le \theta_{n}^{1} x_{n1}^{1} \;\quad n = 1,.. ,N.$$
(2)
$$\sum \limits_{k = 1}^{K} \lambda_{k} e_{lk}^{1} \le \theta_{l}^{1} e_{l1}^{1} \;\quad l = 1,.. ,L.$$
(3)
$$\sum \limits_{k = 1}^{K} \lambda_{k} y_{mk}^{1} \ge y_{m1}^{1} \;\quad m = 1,.. ,M.$$
(4)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} u_{jk}^{1} = \theta_{j}^{1} u_{j1}^{1} \;\quad j = 1,.. ,J.$$
(5)
$$\lambda_{k} \ge 0\;\quad k = 1,..,K.$$
(6)
$$\theta_{k}^{1} \le 1$$
(7)
$$\sum W_{n} + W_{l} + W_{j} = 1,$$
(8)

where undesirable and desirable inputs, and undesirable outputs are represented as \(\theta_{n}\), \(\theta_{l}\), and \(\theta_{j}\) respectively, while λ is a vector of variables and decision maker weights are denoted as \(W_{n}\),\(W_{l}\),\(W_{j}\). The variables \(x = \left( {x_{1} , \ldots ,x_{NK} } \right)\),\(e = \left( {e_{1} , \ldots ,e_{LK} } \right)\), \(y = \left( {y_{1} , \ldots ,y_{MK} } \right)\) and \(u = \left( {u_{1} , \ldots ,u_{JK} } \right)\) denotes N desirable and L undesirable inputs, and M desirable and J undesirable outputs respectively for each DMU. This model is able to calculate the total efficiency with simultaneous reduction of desirable and undesirable inputs and undesirable outputs for a given level of desirable outputs. The optimal values of total efficiency \({\theta }_{k}\) are in the interval between 0 and 1. In addition, the total efficiency of DMUs can be calculated using the weights assigned to all three efficiency scores as determined by the decision maker.

3.3 Centralized two-stage non-radial DEA model

In this study, centralized two-stage model represents the extension of the one-stage NRDEA model presented in (Djordjević et al., 2018). The extension is based on the introduction of intermediate measures. In addition, the evaluation is conducted as a two-stage process, with the two stages considered separately. Individual efficiency measures \(\theta_{k}^{1}\) and \(\theta_{k}^{2}\) are defined for each stage. The efficiencies of DMUk, without distinguishing between desirable and undesirable variables, in the first and second stages are defined as traditional CCR models (9) and (10), as follows:subject to:

$$\begin{gathered} \theta _{k}^{1} = {\text{max}}\sum\limits_{{m = 1}}^{M} {u_{m}^{1} } y_{{mk}}^{1} /\sum\limits_{{n = 1}}^{N} {v_{k}^{1} } x_{{nk}}^{1} \hfill \\ {\text{subject to:}}\sum\limits_{{m = 1}}^{M} {u_{m}^{1} } y_{{mk}}^{1} /\sum\limits_{{n = 1}}^{N} {v_{k}^{1} } x_{{nk}}^{1} \le 1 \hfill \\ u,v \ge 0,\;{\text{m}} = 1, \ldots ,{\text{M}},{\text{ n}} = 1, \ldots .,{\text{N}} \hfill \\ \end{gathered}$$
(9)

and

$$\begin{gathered} \theta _{k}^{2} = \text{max}\sum\limits_{{i = 1}}^{{\text{I}}} {w_{k}^{2} } z_{{ik}}^{2} /\sum\limits_{{m = 1}}^{M} {u_{m}^{2} } y_{{mk}}^{2} \hfill \\ {\text{subject to}}:\sum\limits_{{i = 1}}^{{\text{I}}} {w_{k}^{2} } z_{{ik}}^{2} /\sum\limits_{{m = 1}}^{M} {u_{m}^{2} } y_{{mk}}^{2} \le 1 \hfill \\ w,u \ge 0,{\text{i}} = 1, \ldots ,{\text{I}},{\text{ m}} = 1, \ldots .,{\text{M}} \hfill \\ \end{gathered}$$
(10)

In model (9), \(v_{n}^{1}\) and \(u_{m}^{1}\) are the input and output weights in the first stage, and \(u_{m}^{2}\) and \(z_{i}^{2}\) in model (10) are the input and output weights in the second stage. Since the nonlinear output-oriented models (10) and (11–13) do not consider undesirable inputs and outputs, (9) and (10) were modified and extended to the following nonlinear programming problems (11–13) and (14–16) (Song et al., 2014).

$$\theta_{k}^{1} = {\text{max}}\frac{{\mathop \sum \nolimits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} }}{{\mathop \sum \nolimits_{n = 1}^{N} v_{k}^{1} x_{nk}^{1} + \mathop \sum \nolimits_{l = 1}^{L} \delta_{l}^{1} e_{lk}^{1} - \mathop \sum \nolimits_{j = 1}^{J} \mu_{j}^{1} u_{jk}^{1} }}$$
(11)

subject to

$$\mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} /\mathop \sum \limits_{n = 1}^{N} v_{k}^{1} x_{nk}^{1} + \mathop \sum \limits_{l = 1}^{L} \delta_{l}^{1} e_{lk}^{1} - \mathop \sum \limits_{j = 1}^{J} \mu_{j}^{1} u_{jk}^{1} \le 1$$
(12)
$$u,v,\delta ,\mu \ge 0, {\text{m}} = 1, \ldots ,{\text{M}},{\text{ n}} = 1, \ldots .,{\text{N}},{\text{ l}} = 1, \ldots ,{\text{L}},{\text{ j}} = 1, \ldots .,{\text{J}},$$
(13)

where \(v_{n}^{1}\) and \(u_{m}^{1}\) are the first stage desirable input and output weights or intermediate weights of the second stage while \(\delta_{l}^{1}\) and \(\mu_{j}^{1}\) represent undesirable input and undesirable output,and

$$\theta_{k}^{2} = {\text{max}}\frac{{\mathop \sum \nolimits_{i = 1}^{{\text{I}}} w_{k}^{2} z_{ik}^{2} }}{{\mathop \sum \nolimits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} + \mathop \sum \nolimits_{l = 1}^{L} \mu_{l}^{1} u_{lk}^{1} - \mathop \sum \nolimits_{t = 1}^{T} \partial_{t}^{2} v_{tk}^{2} }}$$
(14)

subject to

$$\mathop \sum \limits_{i = 1}^{{\text{I}}} w_{k}^{2} z_{ik}^{2} /\mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} + \mathop \sum \limits_{l = 1}^{L} \mu_{l}^{1} u_{lk}^{1} - \mathop \sum \limits_{t = 1}^{T} \partial_{t}^{2} v_{tk}^{2} \le 1$$
(15)
$$w,u,\mu ,\partial \ge 0, = 1, \ldots ,{\text{I}},{\text{ m}} = 1, \ldots .,{\text{M}},{\text{ l}} = 1, \ldots ,{\text{L}},{\text{ t}} = 1, \ldots .,{\text{T}},$$
(16)

where \(w_{k}^{2}\) and \(u_{m}^{1}\) are the desirable output and input weights of the second stage while \(\mu_{l}^{1}\) and \(\partial_{t}^{2}\) stands for undesirable input and undesirable output.

To ensure that in models (11–13) and (14–16) desirable inputs and the undesirable inputs and outputs remain unchanged and that the desirable output is maximized, the linear programming models (17–20) and (21–24) were constructed as follows:

$$\theta_{k}^{1} = {\text{max}}\mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1}$$
(17)

subject to:

$$\mathop \sum \limits_{n = 1}^{N} v_{k}^{1} x_{nk}^{1} + \mathop \sum \limits_{l = 1}^{L} \delta_{l}^{1} e_{lk}^{1} - \mathop \sum \limits_{j = 1}^{J} \mu_{j}^{1} u_{jk}^{1} = 1$$
(18)
$$\mathop \sum \limits_{n = 1}^{N} v_{k}^{1} x_{nk}^{1} + \mathop \sum \limits_{l = 1}^{L} \delta_{l}^{1} e_{lk}^{1} - \mathop \sum \limits_{j = 1}^{J} \mu_{j}^{1} u_{jk}^{1} \ge \mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1}$$
(19)
$$u,v,\delta ,\mu \ge 0, {\text{m}} = 1, \ldots ,{\text{M}},{\text{ n}} = 1, \ldots .,{\text{N}},{\text{ l}} = 1, \ldots ,{\text{L}},{\text{ j}} = 1, \ldots .,{\text{J}}$$
(20)

and

$$\theta_{k}^{2} = {\text{max}}\mathop \sum \limits_{i = 1}^{{\text{I}}} w_{k}^{2} z_{ik}^{2}$$
(21)

subject to:

$$\mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} + \mathop \sum \limits_{l = 1}^{L} \mu_{l}^{1} u_{lk}^{1} - \mathop \sum \limits_{t = 1}^{T} \partial_{t}^{2} v_{tk}^{2} = 1$$
(22)
$$\mathop \sum \limits_{m = 1}^{M} u_{m}^{1} y_{mk}^{1} + \mathop \sum \limits_{l = 1}^{L} \mu_{l}^{1} u_{lk}^{1} - \mathop \sum \limits_{t = 1}^{T} \partial_{t}^{2} v_{tk}^{2} \ge \mathop \sum \limits_{i = 1}^{{\text{I}}} w_{k}^{2} z_{ik}^{2}$$
(23)
$$w,u,\mu ,\partial \ge 0, m = 1,..,M, i = 1, \ldots ,I, j = 1, \ldots .,J.$$
(24)

3.3.1 Total efficiency

Under the centralized two-stage NRDEA model, the dual problem of the previous model is obtained by adding the real variables and the non-negative vector \(\lambda = \left( {\lambda_{1} ,\lambda_{2} , \ldots .,\lambda_{k} } \right)\) (Song et al., 2013). Considering the production technology and the model presented by (Wu, 2015), the dual programming of models (17–20) and (21–24) become models (36–43) and (44–51).

$$\theta_{k}^{{{\text{centralized}}}} = {\text{min}} W_{n} \frac{1}{N}\mathop \sum \limits_{n = 1}^{N} \theta_{n}^{1} + W_{l} \frac{1}{L}\mathop \sum \limits_{l = 1}^{L} \theta_{l}^{1} + W_{j} \frac{1}{J}\mathop \sum \limits_{j = 1}^{J} \theta_{j}^{1} + W_{n} \frac{1}{N}\mathop \sum \limits_{n = 1}^{N} \theta_{n}^{2} + W_{j} \frac{1}{J}\mathop \sum \limits_{j = 1}^{J} \theta_{j}^{2} + W_{t} \frac{1}{T}\mathop \sum \limits_{t = 1}^{T} \theta_{t}^{2}$$
(25)

subject to:

$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} x_{nk}^{1} \le \theta_{n}^{1} x_{n1}^{1} \;\quad n = 1,.. ,N.$$
(26)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} e_{lk}^{1} \le \theta_{l}^{1} e_{l1}^{1} \;\quad l = 1,.. ,L.$$
(27)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} y_{mk}^{1} \ge y_{m1}^{1} \;\quad m = 1,.. ,M.$$
(28)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} u_{jk}^{1} = \theta_{j}^{1} u_{j1}^{1} \;\quad j = 1,.. ,J.$$
(29)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} y_{mk}^{1} \le \theta_{n}^{2} y_{m1}^{1} \;\quad m = 1,.. ,M.$$
(30)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} u_{jk}^{1} \le \theta_{j}^{2} u_{j1}^{1} \;\quad j = 1,.. ,J.$$
(31)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} z_{ik}^{2} \ge z_{i1}^{2} \;\quad k = 1,.. ,K.$$
(32)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} v_{tk}^{2} = \theta_{t}^{2} v_{t1}^{2}$$
(33)
$$\lambda_{k} \ge 0$$
(34)
$$\sum W_{n} + W_{l} + W_{j} + W_{t} = 1$$
(35)

Within the models, undesirable inputs, first stage intermediate measures \(\theta_{l}^{1}\) and \(\theta_{j}^{1}\), and second stage undesirable inputs and outputs \(\theta_{j}^{2}\) and \(\theta_{t}^{2}\) were defined for the undesirable inputs \(\theta_{n}^{1}\) and \(\theta_{n}^{2}\) along with the weights of the decision makers \(W_{n}\), \(W_{l}\), \(W_{j} { }\), \(W_{t}\) to improve the discriminatory power of the model.

3.3.2 Stage 1

In the first stage for K DMUs include N desirable inputs (here: total number of cranes and total number of terminals) and L undesirable inputs (here: vessels arrived) and M desirable outputs (here: goods received and goods forwarded) and J undesirable outputs (here: total energy consumed per ton of volume throughput) denoted as \(x = \left( {x_{1} , \ldots ,x_{NK} } \right)\), \(e = \left( {e_{1} , \ldots ,e_{LK} } \right)\), \(y = \left( {y_{1} , \ldots ,y_{MK} } \right)\) and \(u = \left( {u_{1} , \ldots ,u_{JK} } \right)\). The variable \(x_{1}\) denotes the desirable inputs of the first DMU, while \(x_{nK}\) denotes the nth desirable inputs of the kth DMU.

$$\theta_{k}^{{{\text{centralized\_1}}}} = min W_{n} \frac{1}{N}\mathop \sum \limits_{n = 1}^{N} \theta_{n}^{1} + W_{l} \frac{1}{L}\mathop \sum \limits_{l = 1}^{L} \theta_{l}^{1} + W_{j} \frac{1}{J}\mathop \sum \limits_{j = 1}^{J} \theta_{j}^{1}$$
(36)

subject to:

$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} x_{nk}^{1} \le \theta_{n}^{1} x_{n1}^{1} \;\quad n = 1,.. ,N.$$
(37)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} e_{lk}^{1} \le \theta_{l}^{1} e_{l1}^{1} \;\quad l = 1,.. ,L.$$
(38)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} y_{mk}^{1} \ge y_{m1}^{1} \;\quad m = 1,.. ,M.$$
(39)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} u_{jk}^{1} = \theta_{j}^{1} u_{j1}^{1} \;\quad j = 1,.. ,J.$$
(40)
$$\lambda_{k} \ge 0\;\quad k = 1,.. ,K.$$
(41)
$$\theta_{k}^{1} \le 1$$
(42)
$$\sum W_{n} + W_{l} + W_{j} = 1$$
(43)

3.3.3 Stage 2

In the second stage, the NRDEA model includes M desirable outputs (here: goods received and goods forwarded) \(y = \left( {y_{1} , \ldots ,y_{MK} } \right)\) and J undesirable outputs (here: total energy consumed per ton of volume throughput)\(u = \left( {u_{1} , \ldots ,u_{JK} } \right)\) of the first stage, representing desirable and undesirable inputs of the second stage (i.e., intermediate measures), and I desirable outputs (here: total number of vehicles/trucks) \(z = \left( {z_{1} , \ldots ,z_{IK} } \right)\) and T undesirable outputs (here: total emissions produced per year) \(v = \left( {v_{1} , \ldots ,v_{TK} } \right)\) of the second stage.

$$\theta_{k}^{{{\text{centralized\_2}}}} = min W_{m} \frac{1}{M}\mathop \sum \limits_{m = 1}^{M} \theta_{n}^{2} + W_{j} \frac{1}{J}\mathop \sum \limits_{j = 1}^{J} \theta_{j}^{2} + W_{t} \frac{1}{T}\mathop \sum \limits_{t = 1}^{T} \theta_{t}^{2}$$
(44)

subject to:

$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} y_{mk}^{1} \le \theta_{n}^{2} y_{m1}^{1} \;\quad m = 1,..,M.$$
(45)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} u_{jk}^{1} \le \theta_{j}^{2} u_{j1}^{1} \;\quad j = 1,..,J.$$
(46)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} z_{ik}^{2} \ge z_{i1}^{2} \;\quad k = 1,..,K.$$
(47)
$$\mathop \sum \limits_{k = 1}^{K} \lambda_{k} v_{tk}^{2} = \theta_{t}^{2} v_{t1}^{2} \;\quad t = 1,..,T.$$
(48)
$$\lambda_{k} \ge 0\;\quad k = 1,..,K.$$
(49)
$$\theta_{k}^{2} \le 1$$
(50)
$$\sum W_{m} + W_{t} + W_{j} = 1.$$
(51)

The proposed two-stage NRDEA model allows the inefficiency of individual DMUs in each of the two stages to be determined, but it’s also possible to evaluate the entire process. The two-stage NRDEA model proportionally and simultaneously reduces the number of desirable and undesirable inputs to the first stage, which in turn are desirable and undesirable inputs to the second stage (i.e., intermediate measures), and the undesirable outputs to the second stage as much as possible for the given level of desirable outputs. The efficiency score of each stage (i.e., EE of sea-side and EE of port-side), i.e., \(\theta_{k}^{{{\text{centralized\_1}}}}\) and \(\theta_{k}^{{{\text{centralized\_2}}}}\), and the total efficiency score, denoted as \(\theta_{k}^{centralized}\), can be in the interval between 0 and 1. A DMU with efficiency score equal to 1 is an efficient DMU. A DMU with an efficiency score closer to 1 has better efficiency and can reduce more desirable inputs, intermediate measures, and undesirable outputs. Moreover, the efficiency score can be determined and regulated by applying certain weights (\(W_{n}\), \(W_{l}\), \(W_{j} , W_{m}\), \(W_{t}\)) associated with each of the efficiency scores (\(\theta_{n}\), \(\theta_{l}\), \(\theta_{j} , \theta_{m}\), \(\theta_{t}\)). In the two-stage NRDEA model, the sum of the weights should be 1 (i.e., \(\sum W = 1)\).

The main advantage of the two-stage NRDEA model is its stronger discriminatory power, which is achieved by the weights of the decision makers and the efficiency scores assigned to the desirable and undesirable inputs, intermediate actions, and outputs. The decision maker weights can be used to determine the priority and degree of desirability of adjustments to the desired and undesired inputs, intermediate actions, and outputs. Because of these advantages, the ranking of DMUs is better recognized, so we don’t need additional ranking methods.

3.4 Case study selection

The ports of Dublin and Koper were selected as case studies. The EE was conducted for these ports for several reasons. The first reason for these ports is that homogeneous data available for all inputs and outputs. Another reason is the argument made in (Chang, 2013) about the characteristics that compared ports should have, and these two ports are quite heterogeneous in terms of handling similar types of cargo. Other reasons for selecting these ports are related to their environmental status, strategies, and concerns.

In recent years, the Port Authority of Koper has been renowned for its environmental awareness and received the environmental award in the category of International environmental partnership in the Environmental Meeting (Koper Port, 2021a). In addition to air and energy, the Port of Koper has addressed the port’s impact in the following areas: noise, waste and light. The port of Koper has adopted a number of measures and strategies to minimize and limit the environmental impact of port activities (Jittrapirom, 2021; Koper Port, 2021b) and has developed a system for marine protection, waste management and energy efficiency (Jittrapirom, 2021; Koper Port, 2021a). In addition, the port of Koper has completed a protocol on port sustainability and energy efficiency, which is key to reducing the environmental impact of ports and improving the quality of life on both sides of the national border. As part of this project, the Port of Koper installed a radar system to monitor and detect pollutant emissions at sea and also purchased wallbox sockets for electric cars (Interreg, 2022; Koper Port, 2022). The port of Koper has an advantage over other ports, such as Hamburg and Rotterdam, due to its strategic location (Jittrapirom, 2021). In addition, the port of Koper is the first by annual TEU capacity, has the largest number of handled TEUs and the most cranes in the Adriatic (Barić et al., 2021). Considering the port capacity and throughput, as well as environmental activities, the port is a suitable case study to monitor and compare EE and with another port.

Dublin port is also committed to the environment and wildlife surrounding the port. Since 2006, Dublin port has implemented an Environmental Management System (EMS) as part of numerous projects to ensure that operations are conducted in an environmentally responsible manner (Dublin, 2022). Demand for freight and passenger traffic at the port is forecast to increase in the coming years (Dublin, 2018). However, projections indicate that emissions and energy consumption will continue to exceed targets in the coming years, requiring mitigation measures (Dublin, 2022). To enable the safe and efficient movement of goods and passengers and to meet the needs of customers and the community, Dublin port company has developed a master plan. Strategic environmental objectives were included and outlined in the Master Plan as a part of the environmental impact assessment and reports required by the European Directive (2001/42/EC) (Dublin, 2018). Based on environmental steps and measures, Dublin port is also a good example of measuring and benchmarking of EE.

3.5 Selected variables and data

For the EE assessment of Dublin and Koper ports, inputs, intermediate measures, and outputs were selected based on the selection of variables in the reviewed articles (see Table 1) and the availability of data for ports. These measures were classified as desirable and undesirable based on the studies evaluated and port operation (see Table 2).

Table 2 Measures used for the evaluation of ports
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Data for total number of cranes and total number of terminals for 2017 and 2018 for Dublin port were taken from (DPC, 2019). The same value for these inputs was assumed for the other years. For the port of Koper, the data was taken from the Port Authority. Both inputs were classified as desirable inputs, as their number and efficiency contribute positively to the overall efficiency of the port operation. The total number of cranes was selected because cranes are the main energy consumer in ports and cause CO2 emissions (Na et al., 2017), while the total number of terminals indicates the expansion of the port, which is a negative contribution to society and the environment.

The number of vessels arrived, the amount of goods received and goods forwarded, and the total number of vehicles/trucks for the port of Koper were obtained from the Slovenian Statistical Office (SiStat, 2021) while the data for the port of Dublin were obtained from the Central Statistics Office (CSO) of Ireland (Ireland, 2019). Since vessels are the main source of emissions on the seaward side of ports, they were selected and categorized as undesirable inputs (Na et al., 2017).

Since the transportation of goods on the land and sea sides of the port causes energy consumption and emissions, the goods received and forwarded were selected as desirable outputs because the amount of goods handled indicates the activity of the port.

Total energy consumption per ton of volume handled was selected as an undesirable output of the port’s operational processes. The data for this indicator came from (Koper Port, 2017, 2018) for the port of Koper, while it was taken from the sustainability reports of the port of Dublin (DPC, 2019). The results of the first stage of the NRDEA model represent intermediate variables that feed into the second stage (see Table 2). Aside from the fact that trucks generate emissions on the land side of the port, this indicator was identified as a desirable output because their operation is closely related to cargo handling. The port’s total emissions per year were classified as a second-tier undesirable output. Data for this was collected from Dublin Port Company (DPC, 2019), and for the Port of Koper from (Koper Port, 2017, 2018).

4 Results

The one-stage NRDEA results for the ports of Koper and Dublin are shown in Table 3 and Table 4. From these results, the port of Koper was efficient in 2014, 2016, 2017, and 2018, while all DMUs of the port of Dublin were inefficient. The port of Koper was the least inefficient in 2013, while the port of Dublin was the least inefficient in 2010.

Table 3 Koper (one-stage)
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Table 4 Dublin (one-stage)
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The results of each stage and the overall efficiency for the port of Koper are shown in Table 5. Based on the results of the two-stage model, both ports were inefficient. The lowest level inefficiency of the first stage for the port of Koper was 0.7220 in 2010 and 2011, and that of the second stage was 0.5770 in 2011. The lowest level of overall efficiency for the port of Koper was 0.4166 in 2011.

Table 5 Koper (two-stage)
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The results of the first and second stage efficiency and overall efficiency for Dublin port can be found in Table 6. The two-stage model also showed that Dublin port was inefficient in both stages, so the overall efficiency was also low/. The lowest inefficiency for the first stage was 0.5980 in 2010 and for the second stage was 0.4870 in 2010. Consequently, the lowest overall efficiency in 2010 was 0.5920.

Table 6 Dublin (two-stage)
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5 Discussion

Using the results of the one-stage model, both ports can identify efficient and inefficient years of operation. Nevertheless, the results and determinants/facilitators of the ports’ efficiency or inefficiency cannot be determined. However, the calculation of efficiency by individual port processes can provide further implications for the ports. Therefore, the evaluation of EE for ports should be conducted using a two-stage model. From the results in Table 5 and 6, it can be seen that the operation of the ports is not efficient. However, the improvement in the efficiency of both ports in the last year is due to the increased throughput of the ports and the reduction of undesirable factors by incorporating environmental measures. Nevertheless, the energy consumption of the port of Koper has increased in recent years, which is due to the increased transport volume. Energy consumption in ports can be reduced by incorporating renewable or alternative energy sources, as well as by introducing measures such as environmentally friendly driving and ecological routing within the port area. An additional and promising strategy to improve EE on the port side is to shift to rail as a more environmentally friendly mode of transport.

Looking at the real data for both stages and the overall efficiency results in Tables 5 and 6, some implications for the ports can be seen. The implications are elaborated as two potential scenarios for ports by identifying the best benchmarks and comparing them to other DMUs. The first potential scenario that ports can perform is to increase port throughput for a given level of undesirable factors. In Table 5 of the one-stage results, the DMUs with the highest efficiency had the highest value for one of DO. Although the 2018 had the highest value for UDO and 2009 had a higher value than other DMUs for the two-stage results, their efficiency level was the highest due to the level of DO. A similar situation can be seen in Table 6.

However, a different scenario is possible for the ports. In the first stage, the port of Koper can see that the inefficiency of the port DO was lower in 2010 and 2011 than in 2009 and 2011. Although the year 2010 has the highest level of UDI, the lower level of UDI in 2011 did not make the port more efficient compared to 2015 and 2016. The same is true for the port of Dublin. The lowest efficiency of 2010 in the one-stage and two-stage model is due to the high value of UDO and the lower value of DI and DO compared to other DMUs. Therefore, ports can recognize that the level of energy consumption and emissions plays an important role in EE. Based on this, ports need to focus their attention on the part that is under their control. This means that ports need to plan measures to reduce energy consumption and emissions on the port side.

Based on the input data used of incoming goods and outgoing goods, it can be seen that both have increased in recent years. This increase in transportation volume may require expansion of ports. As a result, additional terminals and handling equipment will be needed, resulting in more noise, energy consumption, and emissions. However, better resource planning can improve efficiency and further offset the impacts of capacity expansion. In addition, environmental impacts can be further limited through the implementation of environmental measures and strategies and the use of new equipment.

To identify potential improvements for inefficient DMUs of the ports of Koper and Dublin, the distance metric is used. The improvement potential of the ports EE is analyzed using the Minkowski distance metric (Metcalf & Casey, 2016). The analysis was performed based on the distance of DMUs from the DMU with the highest efficiency level with respect to two (desirable and undesirable) factors. The distance is calculated using formula (52), where \(x_{i}\) denotes the inefficient DMUs and \(y_{j}^{*}\) denotes the highly efficient DMUs.

$$d_{i} = \left( {\mathop \sum \limits_{i = 1}^{n} \mathop \sum \limits_{j = 1}^{m} \left| {x_{i} - y_{j}^{*} } \right|^{p} } \right)^{1/p}$$
(52)

In the case of the port of Koper, the highest efficiency was achieved with the proposed two-stage model in 2009. The distance of the other DMUs to 2009 as the reference DMU was calculated. The red numbers denote the raw data of energy consumption and goods received (see Fig. 3 and 4), while the blue references denote the increase in goods received and the decrease in energy consumption to reach the 2009 efficiency level. For example, Fig. 3 shows that in 2010, goods received must increase by 1439 tons and energy consumption must be reduced by 5.5 kWh/ton to reach the 2009 level.

Fig. 3
figure 3

Distance to the best DMU in case of port of Koper

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Fig. 4
figure 4

Distance to the best DMU in the case of port of Dublin

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Port of Dublin had the highest efficiency of 0.8333 in 2018. Similar to the previous case, the distance between the other DMUs and 2018 was determined. The DMU closest to 2018 in terms of efficiency is 2017 (see Table 6). However, in order to reach the 2018 efficiency level, the goods received would need to increase by 1033 tons and energy consumption would need to decrease by 5 kWh/ton in 2017.

The results in both figures confirm the two scenarios above. From the figures, it can be concluded that the DMUs of the port of Koper require a larger increase in goods received and a reduction in energy consumption than the port of Dublin. Nevertheless, ports can use this distance measure to check the condition of DMUs for other pairs of two variables.

The overall results of this study are useful not only for the port, but also for the maritime sector. The results show the influence and importance of energy consumption and emissions on EE. In addition, the results of the study indicate the need to create alternative new policies for the development of future energy and environmental measures and strategies. Based on the results, awareness of environmental issues in the maritime sector should be further raised.

6 Conclusion

In this study, the EE evaluation of two ports—the Port of Dublin and the Port of Koper—was conducted using a one-stage and a two-stage NRDEA models. The aim of the study was to verify the adequacy of the newly defined two-stage NRDEA model for the assessment of the port EE. Therefore, the results obtained with these models were analyzed.

Section 4 shows that the results obtained with the two models are different. The main reason for the different results is the fact that the one-stage model behaves like a "black box". The one-stage model considers all variables together, while the two-stage model distinguishes them according to the first and second stage variables. In addition, the differences in the results of the two models are related to the number of input and output variables included in each model.

6.1 One-stage EE assessment

The results of the one-stage model show that the port of Koper was efficient in 2014, 2015, 2016, 2017, and 2018. In the case of the port of Dublin, none of the DMUs were efficient. The inefficiency of the port of Koper was observed in the remaining DMUs. However, Dublin Port was inefficient in all years considered.

6.2 Two-stage EE assessment

From the two-stage model, it can be seen that in the first stage, the efficiency of port of Koper was higher than that of the port of Dublin in almost all years, while the efficiency of the port of Dublin improved only in 2017. In the second stage, the port of Koper dominated again until 2015, while the efficiency of the port of Dublin started to increase until 2018.

If we look at the results of the efficiency of the two models, we can see completely different results. The main reason for this is the structure of the models. The two-stage model provides the opportunity to divide the complex process into stages and reveal the inefficiency in each stage that is hidden in the one-stage model.

Looking at the variables, the efficiency of the first stage of the port of Koper has gradually improved and decreased in 2017. This could be due to the fact that the value of transported goods has decreased, while the value of energy consumption has increased. In the second phase, the efficiency of Koper port has decreased in 2018 due to the increase in energy consumption and emissions. The efficiency of Dublin Port has improved in recent years as the values of desired output have increased while the undesired output has decreased.

To examine the potential improvements, a distance metric is introduced in Sect. 5. Using the Minkowski distance equation, the improvements of the inefficient DMUs were calculated based on the distance to the best DMU. For the ports of Koper and Dublin, the improvements were considered in terms of the undesirable factor energy consumption and the desirable factor goods received. From Figs. 3 and 4, it can be seen that the desirable factor increases and the undesirable factor decreases. In addition, different combinations of desirable and undesirable factors can indicate the necessary changes for inefficient units. This approach can be particularly useful for policymakers to learn from best practices. They can use the results of this approach to decide which strategies should be implemented to achieve the highest level of efficiency.

From the case studies evaluated, it is evident that EE varies depending on the valuation approach. Evaluating EE with a model that is not appropriately chosen can lead to inaccurate results. Evaluating EE using the individual parts may provide a more realistic picture of efficiency. In addition, the findings from the results of such an assessment are readily apparent. For the ports evaluated, it is obvious that energy and emissions cause the lower efficiency level. Nevertheless, the efficiency level for some DMUs improves due to higher port throughput, while the percentage of undesirable outputs is high. The results of the two-stage model can help policy makers find the best improvement scenario by comparing one company with others. In addition, policy makers can use the weights of the variables to prioritize the problems that are most important to them. Using the comparative analysis, policymakers can then look at the comparison years with the higher rankings in each port year. Years in which a port operation ranks poorly with respect to EE should help policymakers move the operation to a higher level of EE. Otherwise, knowing a port operation’s position in a given year with respect to EE can help in developing alternative strategies to improve EE. However, alternative strategies should not be unique to a single port or pair of ports. Instead, the identification of adaptation strategies should be consistent with EU policy objectives related on mitigation deployment and monitoring EE and can be an effective approach to decarbonizing maritime transport.

Appropriate strategies need to be implemented to ensure a better EE for port of Koper and to achieve a balance between desirable and undesirable factors for port of Dublin. Energy efficiency measures should be implemented to reduce fuel consumption, while a reduction in GHG emissions can be achieved by replacing fossil fuels with renewable fuels. Reductions in GHG emissions can be achieved by switching to alternative fuels such as liquefied natural gas, LPG, methanol, and electricity. Another way to reduce emissions is through design measures such as the proportion of modern ships and design improvements that go beyond EEDI 3 (Energy Efficiency Design Index 3). A greater reduction in GHG emissions than the above measures are possible if operational measures such as reducing ship speed, berthing and anchoring times, environmentally friendly maneuvering and faster connection to shore power are applied. Reducing overall turnaround time also depends on the efficiency of loading and unloading facilities. Therefore, investments in new “zero-emission” technologies are necessary to maintain the EE of ports.

A limitation of this study is the availability of data for a limited number of years. Port equipment is one of the largest energy consumers and emission sources in the port area. However, the updating of data in the same sources such as reports or statistical databases related to equipment changes in ports is still pending. Therefore, the collection of such data from different sources is necessary. In addition, the energy consumption and emissions data were not attributed to specific sources such as port equipment, port infrastructure, or trucks, etc. Future work on the proposed models could therefore include the inclusion of energy consumption in different parts of the port and emissions on both the sea and port sides. In addition, the development of a new two-stage or multi-stage DEA model to evaluate the port EE could be part of future research. This research focuses on only two ports, so it might be useful for future research to increase the number of ports, at least at the European level. Results from numerous ports will provide a more comprehensive picture and trend from EE and provide the opportunity to identify further best practices.