Toward Integrated Marine Renewables: Prioritizing Taiwan’s Offshore Wind Projects for Wave Energy Compatibility Through a Cross-Efficiency Data Envelopment Analysis Approach

Abstract

Offshore wind energy has become a critical component of global efforts to transition toward low-carbon and sustainable energy systems, and although Taiwan’s advantageous geographical position has accelerated its progress in this domain, many of Taiwan’s upcoming offshore wind projects remain in a pre-construction phase, raising questions about their viability for complementary wave energy integration. To address this challenge, this study proposes a hybrid Cross-Efficiency Slacks-Based Measure (CE-SBM) Data Envelopment Analysis (DEA) model. Thirteen announced offshore wind projects were evaluated using spatial and resource-related input variables and energy-centric output variables. The self-efficiency results from the SBM stage highlighted several projects—most notably Zhu Ting, Wo Neng, and Chu Tin—as highly effective in resource utilization under their own weighting schemes. However, the subsequent cross-efficiency analysis added a consensus-based perspective, revealing a clear performance hierarchy and identifying inefficiencies in projects such as Greater Changhua Northeast and Winds of September. These findings underscore the value of combining DEA-based models with slacks-based and cross-efficiency features to guide multifaceted energy development. By prioritizing projects with robust efficiency profiles, policymakers and stakeholders can expedite Taiwan’s broader adoption of integrated wind–wave energy systems, ultimately fostering a more reliable and sustainable marine energy portfolio.

1. Introduction

Offshore wind energy has been rapidly recognized as a vital pillar in the global shift toward low-carbon and environmentally sustainable energy systems [1]. This growing prominence can be attributed to the widespread recognition that reducing dependence on fossil fuels and curbing greenhouse gas emissions is imperative. Taiwan, due to its advantageous geographical position along strategic maritime corridors and its plentiful offshore wind resources, has been propelled to the forefront of offshore wind energy development [2,3]. In recent years, multiple large-scale offshore wind farm projects have been planned, approved, or commenced along Taiwan’s coastline, thereby underscoring the nation’s commitment to achieving ambitious renewable energy targets, diversifying its energy mix, and bolstering energy security [4,5]. Meanwhile, wave energy—another branch of marine renewable energy—has increasingly been viewed as a promising complementary resource [6]. The synergy between wind and wave resources may offer enhanced system stability, reliability, and economic feasibility [7]. Nevertheless, selecting and prioritizing offshore wind projects for integration with wave energy constitutes a complex challenge, necessitating a thorough evaluation of the technical feasibility, economic costs, environmental impacts, and projected outcomes [8,9].

Taiwan presents a particularly promising setting for researching offshore wind–wave energy integration. The island’s coastal waters benefit from steady, high-speed winds throughout much of the year, resulting in favorable conditions for large-scale offshore wind projects. Simultaneously, Taiwan’s location in the western Pacific subjects it to complex wave dynamics, opening the door to supplementary power generation from wave energy converters [10]. In recent years, Taiwan’s government has actively promoted the expansion of renewable energy infrastructure through supportive policies and incentives, further fueling interest in combined wind–wave systems [11]. Nonetheless, the region’s frequent typhoons, seismic activity, and deeply variable marine environments pose engineering and logistical challenges that require careful planning and robust technological solutions [12]. By focusing on Taiwan, this study not only leverages a setting with high integration potential but also addresses real-world complications—from extreme weather events to navigational constraints—that highlight the practical considerations of merging offshore wind and wave energy.

The strategic fusion of offshore wind and wave energy is believed to be transformative in strengthening the resilience and sustainability of the energy sector. By harnessing two distinct yet interrelated marine resources, integrated wind–wave systems could help mitigate intermittency challenges and reduce the need for significant energy storage or standby generation. However, various obstacles must be navigated by stakeholders—including government agencies, energy developers, financial institutions, and local communities—to determine projects that optimally balance environmental stewardship, economic viability, and engineering feasibility. In Taiwan, where the government has been aggressively expanding the offshore wind capacity and where wave energy interest is increasing, a transparent, objective, and robust decision-making framework is urgently required. This study was therefore motivated by the need to establish a systematic, evidence-based approach for assessing and ranking offshore wind projects in terms of their readiness for wave energy integration. The insights gained from this research are intended to inform Taiwan’s renewable energy trajectory and support future policies aimed at guiding the nation toward a more sustainable and self-reliant energy landscape.

In pursuit of these objectives, a Data Envelopment Analysis (DEA) framework was employed as the principal methodological instrument. DEA has frequently been endorsed for benchmarking and comparative evaluation across multiple decision-making units (DMUs), owing to its capacity to accommodate diverse inputs and outputs without the need for predefined weighting schemes. Since its introduction by Charnes, Cooper, and Rhodes, DEA has found wide-ranging applications, including in healthcare, education, manufacturing, and, more recently, energy systems [13]. Its flexibility has been further enriched by specialized extensions—such as the Slacks-Based Measure (SBM) and cross-efficiency—that address non-radial inefficiencies and enable rankings informed by both self- and peer assessments [14,15,16]. These advanced DEA-based methods have also been integrated with behavioral and multi-criteria decision-making (MCDM) frameworks in various energy and sustainability studies, highlighting their adaptability and robustness. For the specific purposes of this study, the Cross-Efficiency SBM Model was adopted. This approach has been shown to merge the strengths of the SBM—specifically its responsiveness to slack variables that reveal over- or underused resources—with the capacity of cross-efficiency analysis to incorporate peer evaluations [14,17,18,19,20]. In practice, each offshore wind project assessed was rated according to its own efficiency metrics and subsequently evaluated relative to other projects, generating a more balanced, consensus-based ranking. Recent studies have demonstrated that combining DEA with advanced modeling components, including Prospect Theory, Regret Theory, or hybrid MCDM approaches, enables complex decision-making scenarios—particularly in renewable energy site selection—to be captured more effectively [21,22,23]. Consequently, the adoption of this Cross-Efficiency SBM Model is expected to yield a robust methodology, offering not only an identification of the top-performing projects but also insights into the underlying reasons for efficiency differentials across multiple criteria such as costs, energy yields, and environmental impacts. In the context of offshore wind–wave energy integration, the ability of DEA to address several often-conflicting criteria in a single analytic framework has been recognized as particularly advantageous. Indeed, project developers and policymakers must concurrently evaluate capital and operational expenditures for offshore wind turbines and wave energy converters, estimate energy production and resource variability, account for potential environmental consequences for marine life and coastal populations, and assess the technical reliability over the lifecycle of each project. By leveraging both self-evaluation and peer comparison, the Cross-Efficiency SBM Model can highlight the most efficient offshore wind projects and offer pathways for improving underperforming (inefficient) ones. This capacity to reconcile divergent stakeholder priorities is especially valued in multi-stakeholder environments [24,25,26]. The broader literature has thus consistently underscored the relevance of DEA-based models for guiding sustainable development in energy systems, further validating their suitability for selecting and prioritizing offshore wind–wave projects.

Ultimately, this study aimed to propose a rigorous, data-driven, and transparent framework for identifying and ranking offshore wind projects in Taiwan that display the greatest potential for wave energy integration. Three specific objectives were formulated to fulfill this aim: (1) the Cross-Efficiency SBM Model will be applied to evaluate the relative efficiency of the chosen offshore wind projects by considering technical, economic, and environmental indicators; (2) the most promising candidates for successful wind–wave energy integration will be pinpointed, thereby directing policymakers and industry stakeholders toward optimal resource allocation; and (3) actionable strategies will be proposed for refining project planning and public policy. By achieving these objectives, Taiwan’s progress in renewable energy was expected to be reinforced, while broader international discussions on integrated marine energy systems would be enriched. It was thus hoped that this study would endow stakeholders, researchers, and decision-makers with greater clarity in promoting renewable energy endeavors that are both economically beneficial and environmentally sustainable, advancing Taiwan and other nations toward a cleaner energy future.

This article is organized into five sections to present the study comprehensively. Following this introduction, Section 2, Methodology, outlines the Cross-Efficiency SBM Model and its application to the prioritization of offshore wind energy projects. Section 3, Numerical Results, presents the efficiency scores and rankings of the evaluated projects, offering a detailed comparison of their relative performance. Section 4 and Section 5, Discussion, interpret the findings, exploring their implications for energy policy and integration strategies in Taiwan. Finally, Section 6, Conclusion, summarizes the key contributions of the study, discusses its limitations, and provides recommendations for future research. This structured presentation ensures clarity and accessibility for readers, facilitating the application of the study’s findings to real-world challenges.

2. Methodology

In this study, a comprehensive methodological framework is proposed to identify and prioritize offshore wind energy projects in Taiwan for wave energy integration. This framework builds on the foundational principles of Data Envelopment Analysis and extends them through the Slacks-Based Measure and the cross-efficiency approach. By combining the advantages of both the SBM and cross-efficiency, this methodology aims to generate nuanced efficiency scores and robust, consensus-based rankings that can guide policymakers, industry stakeholders, and researchers in making informed decisions.

Data Envelopment Analysis is a straightforward yet powerful technique for comparing multiple “units” (such as companies, departments, or—in our case—offshore wind projects) based on the resources they consume (inputs) and the results they produce (outputs). By looking at how well different units transform inputs into outputs, DEA creates a benchmark of the top performers and pinpoints exactly where the others might be underutilizing resources or failing to reach their full potential. Unlike many statistical or econometric methods, DEA does not assume a preset formula linking inputs to outputs. This makes it especially useful for complex scenarios—like offshore wind development—where projects have diverse characteristics and require multiple forms of resources. In our study, DEA provided a flexible, data-driven way to rank the announced offshore wind farms and identify those that appear most promising for wave energy integration, all while revealing specific opportunities for efficiency improvement.

2.1. Slacks-Based Measure Model

The Slacks-Based Measure (SBM), introduced by Tone (2001), addresses a key limitation of traditional models such as the CCR (Charnes, Cooper, and Rhodes) and BCC (Banker, Charnes, Cooper) models by explicitly incorporating input and output slack into the efficiency score [27,28,29]. Rather than focusing exclusively on proportional changes, the SBM measures the total relative reduction in inputs (or expansion of outputs) required to place a DMU on the efficiency frontier. In doing so, it offers a more direct representation of inefficiency, as each unused input (input slack) or under-realized output (output slack) is highlighted. A standard input-oriented SBM model can be written as

$$\begin{gathered} Maximum \rho ={\displaystyle \frac{1-\frac{1}{m}\sum _{i=1}^m\frac{s_i^{-}}{x_{io}}}{1+\frac{1}{s}\sum _{r=1}^{s }\frac{s_r^{+}}{y_{ro}}}} \\ \mathrm{subject} \mathrm{to} \\ {x}_{io}=\sum _{j=1}^n{\lambda }_j{x}_{ij}+{ s}_i^{-}, \forall i=1,\dots ,m \\ {y}_{ro}=\sum _{j=1}^n{\lambda }_j{y}_{rj}-{ s}_r^{+}, \forall r=1,\dots ,s \\ \sum _{j=1}^n{\lambda }_j=1 \\ {\lambda }_j \ge 0, \forall j=1,\dots ,n \\ {s}_i^{-} \ge 0, \forall i=1,\dots ,m \\ {s}_r^{+} \ge 0, \forall r=1,\dots ,s \end{gathered}$$

(1)

where

• $x_{io}$: The amount of input $i$ used by DMU $o$, $i=\mathrm{1,2},\dots ,m.$
• $y_{ro}$: The amount of output $r$ used by DMU $o$, $r=\mathrm{1,2},\dots ,s.$
• $s_i^{-}$ is the slack in input $i$ (the amount by which input $i$ can be reduced without affecting the outputs).
• $s_r^{+}$ is the slack in output $r$ (the amount by which output $r$ could be increased using the same inputs).
• $\rho$ is the SBM efficiency score ranging between 0 and 1.

A value of $\rho$ = 1 indicates that there is no slack in any input or output dimension; hence, the DMU is fully efficient. If any slack exists, the SBM score decreases, pinpointing exactly where inefficiencies arise. This comprehensive view of inefficiency is advantageous for complex systems, such as energy projects, where certain resources might be underutilized and certain outputs might be underachieved.

2.2. Cross-Efficiency in DEA

While classical DEA (including the SBM) provides valuable insights into inefficiencies, it often yields multiple efficient units with no further distinction among them. In addition, traditional DEA can exhibit self-evaluation bias, whereby each DMU picks weights (multipliers) that maximize its own efficiency score. The cross-efficiency technique was introduced to address these issues through a two-stage approach that includes both self-evaluation and peer-evaluation [30].

First, each DMU $o$ solves a DEA model (e.g., the SBM) to obtain its optimal weights, typically denoted as $u_{ro}^{*}$ for each output, $r,$ and $v_{io}^{*}$ for each input, $i$. In an output-oriented DEA formulation, these weights maximize the ratio of the weighted outputs to the weighted inputs for DMU $o$. Next, each DMU $o$ employs the weight set derived from every other DMU, $k$ $\left(k \ne o\right),$ to recalculate its efficiency. This process produces a cross-efficiency score for DMU $o$ evaluated under DMU $k’s$ optimal weights. Mathematically, the cross-efficiency of DMU $j$ under DMU $k’s$ weight set ($u_{rk}^{*},{ v}_{ik}^{*}$) can be expressed as follows (in an output-oriented context):

$${CE}_{jk}={\displaystyle \frac{\sum _{r=1}^{s }{u}_{rk}^{*}{y}_{rj}}{\sum _{i=1}^m{v}_{ik}^{*}{x}_{ij}}}$$

(2)

where

• $x_{ij}$ and $y_{rj}$ are, respectively, the inputs and outputs for DMU $j$.
• $u_{rk}^{*}$ is the optimal multiplier for output $r$ obtained by DMU $k$.
• $v_{ik}^{*}$ is the optimal multiplier for input $i$ obtained by DMU $k$.
• ${CE}_{jk}$ is the cross-efficiency of DMU $j$ under DMU $k’s$ weighting scheme.

After computing these pairwise cross-efficiency scores, an overall score for each DMU is typically derived by averaging its cross-efficiency values across all other DMUs (or by using an alternative aggregation method, such as geometric means). As a result, a single cross-efficiency measure is assigned to every DMU, enabling a complete ranking of all DMUs. This consensus-oriented efficiency score is less prone to overestimation because it incorporates the viewpoints (optimal weights) of all DMUs in the dataset.

2.3. Proposed Cross-Efficiency SBM Model and Implementation for Offshore Wind–Wave Energy Projects

In this study, a Cross-Efficiency SBM Model is proposed to evaluate and rank the announced offshore wind energy projects in Taiwan for prospective wave energy integration. By combining the Slacks-Based Measure with the cross-efficiency, the model incorporates a detailed analysis of non-radial inefficiencies (slack in the inputs and outputs) while also ensuring that each project’s performance is appraised under a consensus-based lens that considers all other projects’ best weighting schemes. The result is a two-tier mechanism:

• SBM-based efficiency calculation: Each project (DMU) is first evaluated using the SBM approach, which highlights the input slacks (e.g., excessive capital expenditures, unused man-hours) and output slacks (e.g., unrealized energy production or insufficient environmental benefits). This stage yields the initial SBM scores and the optimal weight sets for each DMU.
• Cross-evaluation and aggregation: Each DMU’s weight set is then used to compute the efficiency of every other DMU. The resulting cross-efficiency matrix captures how each project fares when judged by the weight schemes that rival DMUs found optimal. Finally, aggregated cross-efficiency scores are derived, providing a definitive project ranking.

As shown in Figure 1, the implementation procedure includes the following.

Step 1: Indicator Selection and Data Collection.

A thorough literature review, coupled with stakeholder consultations, is carried out to identify relevant inputs (e.g., capital cost, operating expenses, environmental compliance cost) and outputs (e.g., energy yield, carbon reduction, local job creation). Data for each announced offshore wind farm project are gathered from government reports, developer announcements, and national/international databases.

Step 2: Data Preprocessing.

Because DEA models are sensitive to scale and data irregularities, the normalization or standardization of certain variables may be performed. Missing or outlier data points could be managed through interpolation or exclusion, as appropriate.

Step 3: SBM Computation.

The Slacks-Based Measure model is executed to obtain a baseline efficiency score for each project, along with the optimal weight vector. Each DMU’s slack values for both inputs and outputs are recorded, illuminating specific inefficiency areas.

Step 4: Cross-Efficiency Evaluation.

Using each project’s optimal weights, derived in step 3, every other project’s efficiency score is recalculated. This process results in a comprehensive cross-efficiency matrix, ${CE}_{jk}$, indicating how well DMU $j$ performs under DMU $k’s$ weights.

Step 5: Score Aggregation and Project Ranking.

For each DMU $j$, an overall cross-efficiency score is computed by taking the average of all cross-efficiency values, ${CE}_{jk} (k \ne j)$. The DMUs are then ranked from the highest to lowest mean cross-efficiency score, creating a clear hierarchy of offshore wind projects.

Step 6: Results Interpretation and Policy Recommendations.

By combining the SBM-derived slack information and the final cross-efficiency ranking, actionable insights can be furnished to policymakers and energy developers. Projects that consistently rank highly across multiple weight schemes and exhibit minimal slack in critical resources are likely to offer the strongest potential for wind–wave integration. Conversely, projects with low cross-efficiency scores or high slack values may benefit from technological upgrades, policy support, or redesign before integration with wave energy is considered.

3. Numerical Results

The following section presents the empirical findings derived from implementing the Cross-Efficiency SBM Model on the selected offshore wind energy projects in Taiwan. First, the key inputs and outputs are briefly revisited to underscore how they capture the multidimensional nature of each project’s performance. Then, the computed efficiency scores from the initial Slacks-Based Measure (SBM) calculations are reported, highlighting the presence (or absence) of non-radial inefficiencies. Subsequently, the cross-efficiency evaluations are performed, yielding a consensus-based hierarchy of the projects in terms of the overall efficiency.

3.1. Decision-Making Unit Selection

In this study, a total of thirteen offshore wind energy projects within Taiwan’s maritime jurisdiction were identified as DMUs, as shown in

Table 1. The considered offshore wind projects [31].

No.	Project Name	Location (Approx. Lat, Long)
1	Zhu Ting	24.9734, 120.7393
2	Chu Tin	24.8753869, 120.7190737
3	Winds of September	24.8039, 120.8826
4	Formosa 5	24.603823, 120.577307
5	Wo Neng	24.5965, 120.2214
6	Greater Changhua Northeast	24.24462, 120.133437
7	Xu Feng No. 1	24.1815, 119.923
8	Feng You	24.053971, 120.153521
9	Zhong Neng	23.8978, 120.217
10	Formosa 3	23.9654028, 120.0344971
11	Xu Feng No. 2	24.0589, 119.923
12	Xu Feng No. 3	24.067, 119.8362
13	Guo Feng	23.95554, 119.737534

and Figure 2. Although Taiwan has numerous offshore wind initiatives—ranging from the early planning stages to fully operational farms—the scope of this research specifically targeted projects that had been formally announced but had not yet proceeded to construction. The rationale for this focus lay in the practical needs of policymakers and stakeholders who seek to prioritize or reassess these projects prior to large-scale capital deployment, allowing them to incorporate complementary wave energy systems more effectively.

By restricting the analysis to confirmed but pre-construction DMUs, the framework could better illuminate opportunities for early-stage design modifications, resource reallocation, and strategic planning. This selection criterion also ensured a sufficiently homogeneous set of projects in terms of their developmental status, thereby enhancing the comparability of the efficiency scores and eventual rankings. While it is acknowledged that certain offshore wind farms under construction or already operational may have yielded additional insights, concentrating on announced projects that awaited construction maximized the policy relevance of this study’s recommendations for Taiwan’s evolving offshore wind and wave energy landscape.

3.2. Inputs, Outputs, and Data

According to references and experts’ recommendation, a total of five inputs and four outputs were selected for this analysis, each chosen to capture a distinct facet of the offshore wind project feasibility and potential synergy with wave energy integration [6,7,21,32,33]. In identifying these variables, particular attention was paid to ensuring comprehensive coverage of the economic, logistical, and environmental dimensions that together define the viability and effectiveness of pre-construction projects in Taiwan’s coastal regions. The interplay among these variables formed the basis for a robust, multidimensional efficiency evaluation, one that aligned with the strategic objective of exploring how wind and wave resources can be optimally harnessed in tandem.

The first input, the distance to the grid in km (Input 1), denoted the physical separation between the proposed offshore wind farm location and the nearest onshore power transmission network. A greater distance generally translates into higher infrastructure investment costs, given the substantial length of undersea cables required, and can also elevate the operational complexity. This parameter is especially pivotal for multi-technology developments (wind plus wave) because it indicates how challenging and expensive it will be to transfer the aggregated energy back to the mainland grid. A second closely related variable, the distance to the substation in km (Input 2), served as a more localized indicator of connectivity. While the distance to the grid primarily reflects the broader transmission context, the distance to the substation zeroes in on the specific point of interconnection where voltage step-ups and grid stabilization occur. Additional substation components—such as switchgear, transformers, and control equipment—may need to be installed or upgraded to handle the combined capacity from wind turbines and potential wave energy converters. Longer distances to suitable substations can intensify engineering hurdles, raise costs, and demand more rigorous project planning, especially if new substation infrastructure must be developed. By comparison, the distance to the shore in km (Input 3) shed light on a range of logistical concerns, including the vessel travel time for installation and maintenance, the exposure to harsh marine conditions, and even the intricacies of environmental permissions. Project sites further offshore may benefit from stronger, more consistent winds—thus boosting their generation capacity—but also face a steeper cost curve in terms of daily operations, safety requirements, and specialized equipment (e.g., jack-up vessels or dynamically positioned ships). Accordingly, the distance to the shore underscores the classic trade-off between resource abundance and installation expenditure that underpins large-scale offshore energy ventures. Additionally, the distance to the closest population center in km (Input 4) addressed socio-economic and environmental considerations. Offshore developments situated near densely populated coastal areas must navigate tighter regulations related to noise, visual impacts, and ecological disturbance. Proximity to large populations can carry certain advantages—such as improved local support if job creation or community investment are highlighted—but can also generate heightened public scrutiny and necessitate more comprehensive stakeholder engagement. In short, this variable provides a lens into how the human dimension intersects with marine renewable energy installations. Finally, the bathymetry in m (Input 5) reflected the depth of the seabed at each proposed project site. The bathymetry heavily influences the foundation design (e.g., monopiles vs. jacket structures) and dictates installation methods, vessel selection, and potential future modifications for wave energy converters. Shallow waters generally reduce the foundation complexity but may limit the types of turbines that can be installed, whereas deeper waters can unlock higher wind speeds at the cost of advanced foundation technologies and higher construction expenses. Hence, the bathymetry represents a direct measure of geological feasibility and serves as a critical input for both technical planning and cost modeling in offshore energy systems.

On the output side, the tidal current velocity in m/s (Output 1) was selected to capture the strength of local tidal currents, which may support the co-location of tidal or wave energy converters in the region. Even when the primary focus is wind energy, strong tidal flows can enhance the overall efficiency of a hybrid marine system by adding more consistent or supplemental power generation. Higher tidal velocities also introduce dynamic loading factors for offshore structures, making them especially relevant when exploring complex wind–wave–tidal synergies. A related metric, the tidal current elevation in m (Output 2), encapsulated water-level fluctuations over the tidal cycle. While the tidal velocity reflects lateral water movement, the tidal elevation underscores the vertical displacement of water, which can affect the wave height, frequency, and nearshore hydrodynamics. Projects located in areas with pronounced tidal ranges might experience more significant interactions between wind-driven waves and tidal patterns, leading to a potentially higher cumulative energy yield but also introducing greater system complexity. Thus, including the tidal elevation as an output ensured that any project offering robust combined-generation prospects was duly recognized. The maximum velocity in m/s (Output 3) considered the peak flow rates within the marine environment. This variable supplies insights into the operational stress limits that energy converters—wind turbines, wave devices, or hybrid technologies—would encounter under extreme conditions. By capturing these maximum velocities, the model evaluates the resilience and potential reliability of each project over its lifecycle, especially given the unpredictable nature of marine environments. A site capable of enduring higher flow velocities may ultimately prove more suitable for multi-technology integration, assuming engineering designs can accommodate these conditions. Lastly, the power density in W/m² (Output 4) served as an overarching measure of energy resource availability. In addition to depicting the intensity of wind and wave actions within a given area, the power density synthesizes the various oceanographic factors to signal how much energy can be harvested. Offshore wind developers often look to the power density when prioritizing among multiple locations, but for joint wind–wave installations, this measure provides a quantifiable reference for comparing combined resource potentials across prospective sites. In essence, a project with high power density in both wind and wave domains naturally lends itself to more rewarding returns on investment.

As shown in

Table 2. The input data.

Project Name	Distance to Grid (km)	Distance to Substation (km)	Distance to Shore (km)	Distance to the Closest Population Center (km)	Bathymetry (m)
Zhu Ting	26.16	222.43	23.08	24.97	76
Chu Tin	23.4	231.99	19.93	22.7	73
Winds of September	5.34	245.14	3.09	8.4	13
Formosa 5	14.55	256.92	12.38	13.73	55
Wo Neng	47.05	251.66	42.9	44.35	60
Greater Changhua Northeast	33.11	289.83	32.89	33.02	37
Xu Feng No. 1	49.21	269.39	47.29	28.86	46
Feng You	23.52	311.03	20.24	21.52	36
Zhong Neng	8.68	328.72	6.64	10.54	36
Formosa 3	23.36	320.26	25.87	26.25	31
Xu Feng No. 2	38.7	309.97	41.22	41.6	31
Xu Feng No. 3	45.94	309.33	41.65	48.8	28
Guo Feng	48.98	322.23	41.65	42.46	28

and

Table 3. The output data.

Project Name	Tidal Velocity (m/s)	Tidal Elevation (m)	Maximum Velocity (m/s)	Power Density (W/m2)
Zhu Ting	0.33	1.2	0.64	0.01
Chu Tin	0.3	1.22	0.56	0.01
Winds of September	0.29	1.19	0.52	0.01
Formosa 5	0.19	1.31	0.4	0
Wo Neng	0.14	1.38	0.3	0
Greater Changhua Northeast	0.16	1.34	0.36	0
Xu Feng No. 1	0.66	1.28	1.01	0.07
Feng You	0.63	1.19	1.08	0.08
Zhong Neng	0.51	1.11	0.87	0.05
Formosa 3	0.63	1.08	1.01	0.07
Xu Feng No. 2	0.59	1.12	1.03	0.08
Xu Feng No. 3	0.51	1.12	0.86	0.04
Guo Feng	0.44	1.1	0.64	0.02

, all relevant data pertaining to the selected inputs and outputs were drawn from publicly accessible and widely recognized databases maintained by reputable international organizations [34,35,36]. These data repositories, which include detailed records on the offshore wind potential, maritime characteristics, bathymetry, and oceanographic conditions, were deemed both reliable and methodologically sound. By using well-documented and open-source data, this study ensured a transparent and reproducible approach, allowing policymakers, industry stakeholders, and researchers to confidently interpret and validate the findings.

3.3. Self-Efficiency and Optimal Weight Set Determination

In this step, the Slacks-Based Measure approach was employed to compute the self-efficiency scores of each DMU using Lingo Solver. The process involves minimizing slack in both the inputs and outputs, thereby offering a more nuanced view of project inefficiencies than conventional radial DEA models. By focusing on the slack values directly, the SBM helps pinpoint whether any excessive resource usage or underperformance in outputs is driving inefficiency. Throughout this stage, each DMU’s efficiency is considered from its own perspective, setting the groundwork for the subsequent cross-efficiency analysis.

As illustrated in Figure 3, the majority of DMUs attained a perfect self-efficiency score of 1, suggesting that they exhibited minimal slack when evaluated according to their own best weight structures. However, four DMUs displayed varying degrees of inefficiency: Chu Tin, Xu Feng No. 3, Guo Feng, and Greater Changhua Northeast. Among these, Greater Changhua Northeast recorded the lowest self-efficiency score of 0.38438, indicating that it stands to benefit from considerable resource optimization or output enhancement. Chu Tin’s score (0.93297) placed it closer to the efficiency frontier than the other underperforming DMUs, yet it still signals a need to address certain slack issues, possibly in its spatial constraints or projected outputs. Xu Feng No. 3 and Guo Feng demonstrated moderate inefficiency levels (0.59229 and 0.49380, respectively), which could be mitigated through targeted improvements in, for instance, connection distances or wave energy-related output expansions.

In addition to providing efficiency scores, the SBM solution process generates optimal weight sets for the inputs and outputs, which are tailored for each DMU so it can achieve its maximal self-efficiency. These weight vectors are crucial as they represent the relative prioritization of various factors by a DMU in its quest to minimize the input slack and maximize the output performance. For instance, in the context of offshore wind and wave energy projects, a DMU might assign higher weights to critical factors if these elements significantly influence its performance. Conversely, other DMUs may place greater emphasis on parameters depending on their specific operational contexts or resource availability. These optimal weight sets, detailed in

Table 4. The obtained optimal weights of the inputs.

Project	Input 1	Input 2	Input 3	Input 4	Input 5
Zhu Ting	0.01	0.01	0.01	0.01	0.00
Chu Tin	0.01	0.03	0.01	0.01	0.00
Winds of September	0.04	0.00	188.76	0.02	0.02
Formosa 5	0.01	0.04	0.02	0.01	0.00
Wo Neng	0.00	0.02	0.00	0.00	0.00
Greater Changhua Northeast	0.01	0.00	0.01	0.01	0.01
Xu Feng No. 1	0.50	0.38	0.00	0.01	0.00
Feng You	0.01	0.36	3.23	0.01	0.01
Zhong Neng	0.02	0.00	0.03	0.02	0.01
Formosa 3	0.27	0.00	0.01	0.01	4.36
Xu Feng No. 2	0.01	0.35	0.00	0.00	1.03
Xu Feng No. 3	0.00	0.00	0.00	0.00	0.01
Guo Feng	0.00	0.00	0.00	0.00	0.01

and

Table 5. The obtained optimal weights of the outputs.

Project	Output 1	Output 2	Output 3	Output 4
Zhu Ting	0.00	2.15	2.31	0.00
Chu Tin	0.00	5.91	0.00	4.40
Winds of September	463.76	221.80	283.41	3826.05
Formosa 5	0.00	7.85	0.00	0.00
Wo Neng	0.00	4.67	0.00	0.00
Greater Changhua Northeast	0.00	0.29	0.00	0.00
Xu Feng No. 1	51.24	24.51	31.31	422.73
Feng You	70.80	33.86	43.27	584.12
Zhong Neng	0.00	0.00	0.00	20.00
Formosa 3	74.29	5.93	45.40	612.90
Xu Feng No. 2	74.29	0.00	45.40	612.90
Xu Feng No. 3	1.33	0.00	0.00	0.00
Guo Feng	1.22	0.00	0.00	0.00

, provide a comprehensive view of how each DMU internally values and allocates importance to different input and output dimensions. Each weight reflects the relative significance of a particular criterion in achieving the DMU’s efficiency, shedding light on its internal decision-making strategy. For high-performing DMUs, these weights often reveal a balanced and strategic allocation that aligns well with the characteristics of an efficient system. On the other hand, for less efficient DMUs, the weights can highlight potential areas of misallocation, such as an overemphasis on less critical inputs or the underutilization of impactful outputs.

3.4. Cross-Efficiency Determination and Prioritization

In this section, a detailed examination of the cross-efficiency results is provided, offering a more comprehensive view of how each offshore wind project (DMU) performed under alternative weight sets determined by other DMUs. Whereas the self-efficiency scores from the SBM model highlight how efficiently a project can allocate inputs and outputs under its own optimal weighting, the cross-efficiency expands the lens by integrating peer evaluations. This methodology mitigates the potential bias of self-selected weighting schemes and facilitates a more discriminating ranking of DMUs. Ultimately, it enables stakeholders to identify projects that exhibit consistent efficiency under a variety of operational and strategic priorities—a critical consideration when planning multi-technology integrations and complex marine energy systems.

Table 6. The obtained cross-efficiency.

Project	Zhu Ting	Chu Tin	Winds of September	Formosa 5	Wo Neng	Greater Changhua Northeast	Xu Feng No. 1
Zhu Ting	1.000	0.950	1.000	0.883	0.742	0.722	1.000
Chu Tin	1.000	0.991	1.000	1.000	0.964	0.865	0.890
Winds of September	0.147	0.161	1.000	0.210	0.056	0.076	0.128
Formosa 5	0.983	0.977	1.000	1.000	0.943	0.855	0.839
Wo Neng	1.000	0.988	1.000	1.000	1.000	0.891	0.888
Greater Changhua Northeast	0.340	0.367	1.000	0.521	0.302	0.384	0.307
Xu Feng No. 1	0.726	0.674	0.679	0.521	0.424	0.415	1.000
Feng You	0.626	0.622	0.903	0.563	0.302	0.341	0.696
Zhong Neng	0.086	0.094	0.335	0.000	0.000	0.000	0.397
Formosa 3	0.197	0.188	1.000	0.164	0.117	0.212	0.678
Xu Feng No. 2	0.384	0.346	0.522	0.222	0.161	0.203	0.977
Xu Feng No. 3	0.394	0.376	1.000	0.304	0.146	0.218	0.762
Guo Feng	0.384	0.367	1.000	0.301	0.139	0.209	0.734
Project	Feng You	Zhong Neng	Formosa 3	Xu Feng No. 2	Xu Feng No. 3	Guo Feng
Zhu Ting	0.976	0.859	0.864	0.853	0.770	0.655
Chu Tin	0.783	0.708	0.684	0.703	0.679	0.637
Winds of September	0.306	0.734	0.222	0.144	0.112	0.090
Formosa 5	0.743	0.689	0.649	0.658	0.650	0.619
Wo Neng	0.757	0.686	0.667	0.693	0.690	0.654
Greater Changhua Northeast	0.424	0.551	0.366	0.287	0.270	0.267
Xu Feng No. 1	1.000	0.793	0.905	0.907	0.697	0.534
Feng You	1.000	1.000	0.829	0.695	0.544	0.428
Zhong Neng	0.821	1.000	0.641	0.487	0.223	0.113
Formosa 3	0.928	0.718	1.000	1.000	0.800	0.592
Xu Feng No. 2	1.000	0.716	0.948	1.000	0.744	0.525
Xu Feng No. 3	1.000	1.000	0.983	0.750	0.625	0.540
Guo Feng	0.977	1.000	0.953	0.714	0.591	0.514

below shows how each DMU (row) was evaluated using every other DMU’s optimal weight sets (columns). The resulting matrix underscores project’s performance when faced with a wide array of perspectives on the relative importance of the inputs and outputs. A key insight emerging from this matrix is the divergence between projects that remained consistently high-performing under multiple weighting schemes and those that excelled primarily under their own self-selected weights. For instance, Zhu Ting, Chu Tin, and Wo Neng notably achieved scores above 0.70 or 0.80 in many columns, indicating that the manner in which they balanced inputs (e.g., engineering complexity, proximity to shore) and outputs (e.g., tidal velocities, power density) was recognized as effective across different DMUs’ perspectives. By contrast, Winds of September demonstrated high scores only in a handful of columns—most strikingly its own, but also occasionally under other DMUs that may have shared similar weighting emphases. This discrepancy points to the project’s dependence on a more narrowly tailored set of assumptions, possibly tied to unique wave characteristics or localized resource potential that peers do not consider as valuable. Similarly, Zhong Neng often yielded very low cross-efficiency values (e.g., 0.000 or 0.086), suggesting a stark misalignment between its resource usage or site conditions and those of other DMUs with different priorities. Another observable pattern was that certain DMUs, such as Formosa 5 and Xu Feng No. 1, exhibited moderate to high cross-efficiency across a majority of columns, but varied in some cells. This fluctuation can hint at the presence of specialized inputs (e.g., deep-water foundations, advanced substation requirements) that raise the cost profiles and lead to suboptimal scores when scrutinized by DMUs focusing on minimizing those same inputs.

To yield a more streamlined prioritization framework, each DMU’s cross-efficiency scores were averaged across all other DMUs’ weighting schemes, generating a single composite indicator of how favorably each project was viewed in a consensus context. Figure 4 presents the final average cross-efficiency scores and corresponding rankings.

Zhu Ting took the top spot, boasting an average cross-efficiency of 0.8672, followed closely by Wo Neng (0.8396), Chu Tin (0.8388), and Formosa 5 (0.8157). The consistency of these projects’ high scores across various columns reveals a balance in how they manage distance-to-shore constraints, bathymetry challenges, and energy outputs. From a practical standpoint, these high-performing DMUs are natural front-runners for an immediate policy and investment focus, particularly concerning the integration of additional marine energy technologies like wave or tidal converters. Their robust cross-efficiency profiles suggest that even if national priorities shift toward environmental or socio-economic objectives, these DMUs would remain solid candidates. Xu Feng No. 1, Feng You, Xu Feng No. 3, Guo Feng, and Xu Feng No. 2 formed the “middle of the pack”, with average cross-efficiency scores ranging from roughly 0.60 to 0.71. Although these DMUs did not reach the highest consensus-based efficiency levels, they still demonstrated moderate adaptability. In practice, mid-tier projects may benefit from targeted interventions—such as optimizing substation connections or mitigating certain geographic disadvantages—enabling them to move closer to the efficiency frontier. For stakeholders with constrained budgets, these DMUs can represent viable alternatives if improvements are made in areas highlighted as weaknesses during the cross-efficiency assessment. Formosa 3, Greater Changhua Northeast, Zhong Neng, and Winds of September rounded out the lowest ranks, exhibiting average cross-efficiency values below 0.60. Their relatively weaker peer evaluations point to potential cost inefficiencies, resource underutilization, or location-specific constraints that were not well aligned with the optimization targets valued by other DMUs. Although they may still have merits under certain specialized scenarios—such as leveraging unique tidal patterns or focusing on local manufacturing benefits—they require more substantial project redesign or policy incentives if they aim to be strong contenders for wave energy integration. For instance, Greater Changhua Northeast might focus on reconfiguring its input usage and reexamining its site feasibility, while Winds of September should investigate why its perceived performance lags so notably behind under other DMUs’ weight schemes, potentially revisiting installation strategies or output expectations.

4. Discussion

The cross-efficiency analysis conducted in this study serves as a multifaceted lens through which Taiwan’s announced offshore wind projects can be comprehensively evaluated. In contrast to conventional self-efficiency assessments, the cross-efficiency introduces a consensus-oriented framework that incorporates the perspectives of multiple DMUs, thereby mitigating self-serving weight selections. By examining each project not only under its own optimal weight set but also through the optimal weight sets of its peers, this study offers a richer, more equitable understanding of which offshore wind projects are truly capable of excelling under diverse strategic priorities and resource constraints. Such an approach is especially pivotal in multi-technology integration scenarios, where offshore wind farms are increasingly expected to operate in tandem with wave, tidal, or other marine energy systems. In these contexts, the cost structures, resource availability, environmental constraints, and socio-economic impacts must be viewed holistically to ensure that projects align with national goals for sustainability and energy security.

Comparisons between the self-efficiency and cross-efficiency scores illuminated important insights into how different DMUs structure their inputs and outputs. Projects like Zhu Ting, Wo Neng, and Chu Tin exhibited consistently high ratings even when subjected to various weight priorities, suggesting that they maintain well-balanced configurations that resonate with the broader consensus on what constitutes effective resource utilization and energy outputs. These high performers are likely characterized by favorable distances to the grid or substations, manageable bathymetry, and potentially strong tidal characteristics that contribute to robust power densities. They also appear to avoid overreliance on unique or niche conditions that might cause them to falter when evaluated through alternative frameworks.

By contrast, certain DMUs—such as Greater Changhua Northeast and Winds of September—demonstrated an evident gap between their self-efficiency and cross-efficiency results. While self-efficiency scores can be inflated through individually tailored weight sets that exploit local advantages (e.g., shallow water or particularly strong wave resources), their performance under peers’ weight sets points to inefficiencies. These inefficiencies may stem from excessive distances to infrastructure, deeper bathymetry leading to higher installation costs, or insufficient synergy between wind and wave conditions. In real-world terms, such discrepancies mean that unless these DMUs significantly adapt their project designs—perhaps through technology upgrades, improved logistics, or refined cost structures—they may struggle to remain competitive if wave energy is introduced or if policy priorities shift toward integrated marine solutions.

An equally crucial observation is that the middle-tier projects demonstrated moderate consensus-based performance, often indicating that they had a balanced but not outstanding resource configuration. For instance, moderate cross-efficiency scores suggest some alignment with common weight priorities (e.g., moderate distances, decent power densities), yet there may be specific areas—like substation connections, foundation technologies, or environmental permissions—that remain suboptimal. These projects can often ascend to the top echelon if they address targeted bottlenecks. Policymakers and investors thus face decisions about whether incremental investments—such as improved maintenance vessels, better cabling routes, or minor reconfigurations of turbine layouts—could meaningfully elevate these DMUs’ standings. Even modest efficiency gains can, in some cases, propel a mid-tier project into a higher rank that warrants greater policy support or commercial enthusiasm.

A final but essential aspect of the cross-efficiency findings lies in their relevance to wave energy integration. The impetus to co-develop wind and wave resources hinges on the possibility that diversified marine energy systems can offset one another’s intermittency and lower the overall cost of energy. Projects that rank highly in cross-efficiency are likely to manage this diversification more seamlessly, as they are already efficient in resource use and have outputs that appear robust under multiple evaluative scenarios. Conversely, projects with low cross-efficiency may find wave integration more challenging, especially if they exhibit stark inefficiencies regarding site logistics or environmental impacts. However, this does not entirely discount their future potential: a low cross-efficiency score can also serve as an impetus for redesign, compelling project developers to rectify critical inefficiencies if they aim to join forthcoming wave energy initiatives.

5. Implications

These cross-efficiency results hold vital implications for a wide array of stakeholders, encompassing policymakers, investors, local communities, and industry participants tasked with shaping Taiwan’s offshore renewable energy landscape. Projects that consistently excel—most notably Zhu Ting, Wo Neng, and Chu Tin—emerge as immediate candidates for priority funding, streamlined permission processes, and demonstration programs involving wave energy converters. Their multi-perspective efficiency signals that even if economic conditions or policy objectives change—such as a shift toward a greater emphasis on environmental impacts or social acceptability—these DMUs are still likely to remain strong contenders for continued support.

For mid-tier projects, the cross-efficiency framework highlights specific dimensions where marginal improvements could yield significant gains in their overall standing. By diagnosing inefficiencies—perhaps through slack analyses and incremental scenario testing—developers and local governments can identify realistic action plans, such as optimizing cable routes to shorten distances, investing in advanced turbine foundations, or forging cooperative ventures with specialized wave energy technology providers. These targeted interventions, while potentially modest in cost compared to a full-scale overhaul, may be enough to elevate mid-tier DMUs closer to or even into the top ranks.

At the lower end of the ranking, certain projects may require more profound strategic realignments if they intend to remain viable in a future marked by integrated wind–wave developments. Major redesign efforts could involve relocating the project sites to areas with shallower waters or better wind–wave synergies, securing advanced engineering solutions to handle deeper bathymetry, or forging partnerships with financial institutions to reduce capital expenditure risks. Policymakers could, for example, introduce tailored incentives to spur innovation or risk-sharing arrangements for these projects, especially if regional economic growth or job creation is a high priority in the proximate area. Still, the path to improvement may be steeper for these DMUs, and in some cases, it might be more prudent for policymakers to concentrate public resources on higher performing alternatives.

6. Conclusions

Taiwan’s rapid push toward renewable energy, driven by ambitious government targets and a globally recognized imperative to reduce carbon emissions, has ignited substantial interest in offshore wind power. At the same time, wave energy is gaining traction as a complementary marine resource that can help stabilize the overall energy production and lower system costs. Within this context, a robust decision-making framework is needed to evaluate which announced pre-construction offshore wind projects hold the greatest potential for wave energy integration. Identifying where to optimally deploy finite resources is particularly urgent, given the considerable capital expenditures and technical complexities involved in large-scale marine energy systems.

To address this need, a hybrid Cross-Efficiency SBM Model was proposed and applied to thirteen announced offshore wind projects in Taiwan. After defining a set of carefully selected inputs (e.g., distances to the shore, grid, and substations, plus bathymetry) and outputs (e.g., tidal velocity, tidal elevation, maximum velocity, and power density), an SBM analysis was conducted to gauge each project’s self-efficiency. Subsequently, a cross-efficiency evaluation was performed, allowing each project to be assessed not only under its own optimal weighting schemes but also under those determined by its peers. This dual-stage process provided a consensus-based ranking that mitigated self-serving weight allocations and yielded deeper insights into which projects exhibit robust efficiency across varied stakeholder priorities.

The results revealed a marked distinction between the top-performing DMUs—most notably Zhu Ting, Wo Neng, and Chu Tin—and those that rely more heavily on niche or project-specific weight sets. High-ranking projects displayed strong performance across multiple scenarios, suggesting that they stand to benefit from any future move toward wave energy integration, as they already optimize inputs and produce outputs that align well with diverse operational viewpoints. In contrast, certain projects, such as Greater Changhua Northeast and Winds of September, demonstrated low cross-efficiency scores, indicating underlying inefficiencies that would need to be resolved before they could fully exploit synergy with wave resources. Overall, the findings highlight a clear stratification within Taiwan’s offshore wind pipeline, pointing to tangible strategies for policymakers and developers aiming to foster integrated wind–wave systems.

This study contributes to the emerging discourse on multi-technology marine energy systems by offering a transparent, data-driven framework to prioritize offshore wind initiatives. Methodologically, the integration of the Slacks-Based Measure (SBM) with the cross-efficiency in a marine energy context strengthens the analytical capacity to detect non-radial inefficiencies and reconcile differing stakeholder perspectives. Practically, the results provide actionable information for policymakers, developers, and investors about which projects are more likely to succeed under various strategic assumptions, thereby guiding future resource allocations, environmental impact assessments, and technology partnerships. The analysis also enriches the international literature by demonstrating how consensus-based DEA techniques can be employed to optimize energy planning in coastal regions with abundant yet underutilized marine resources.

Several limitations should be acknowledged. First, while this study leveraged governmental and reputable open-source databases, greater reliance on reanalysis-based datasets and external GIS resources would help capture real-time changes in marine conditions, project financing, and regulatory shifts. Second, behavioral and policy dimensions—such as community acceptance or targeted government incentives—were not explicitly modeled, despite their significant impact on project viability. Third, the selected input–output variables, though designed for comprehensive coverage, may omit critical qualitative or ancillary factors (e.g., local biodiversity effects, logistics resilience). Future research could address these gaps by employing dynamic DEA models that account for temporal policy and technology shifts, incorporating behavioral economics to reflect stakeholder preferences, and integrating MCDM frameworks that consider expert judgments. These enhancements would further refine the model’s precision and bolster its applicability in guiding integrated offshore wind–wave energy initiatives.