Container Port Efficiency and Productivity in 2019 and 2020: A Directional Distance Function Incorporating Vessel Waiting Time

Abstract

This study examines change in operational efficiency and productivity across a balanced panel of 15 container ports for the years 2019 and 2020. Berth length, gantry cranes, and other cranes are inputs; high container throughput is desirable, and extended anchorage waiting time is undesirable. Waiting time is calculated as the unweighted mean of weekly port estimates published by the Asian Development Bank. A pooled convex variable-returns-to-scale directional distance function with weak disposability provides a common reference technology, and the VRS global Malmquist–Luenberger (GML) index compares the two years. The mean transformed efficiency score was 0.855 across 30 port-year observations, declining from 0.878 in 2019 to 0.833 in 2020. The arithmetic mean GML score was 0.951: one port improved, ten declined, and four remained unchanged. A throughput-only model and leave-one-port-out re-estimation show that waiting time treatment and influential reference ports affect individual comparisons. In particular, the omission of Shanghai or Tanjung Pelepas substantially changed some rankings and scores.

1. Introduction

Ports handle the bulk of international trade by volume, and their operational performance affects the cost and reliability of global supply chains. Port efficiency has become increasingly important as vessel sizes have grown, shipping alliances have consolidated, and trade patterns have changed. Efficient ports can attract carrier calls and support regional logistics and industrial activity, whereas inefficient ports increase congestion and transport costs. Because investments in berths, cranes, channels, and yards are capital-intensive and long-lived, reliable efficiency estimates are important to terminal operators and public agencies.

Port efficiency is difficult to evaluate because ports operate under different physical, economic, and institutional conditions. Data envelopment analysis (DEA) is widely used for this purpose because it can evaluate comparable decision-making units (DMUs) with multiple inputs and outputs without imposing a functional form. Previous studies have applied DEA to compare port productivity, competitiveness, and environmental performance under a range of model specifications.

International port comparisons are affected by differences in scale, terminal coverage, cargo mix, and local conditions. DEA measures performance relative to an observed comparison set; thus, the resulting scores depend on the included ports and on consistent definitions of production variables.

Directional distance functions (DDFs) permit simultaneous expansion of desirable output and contraction of an undesirable outcome [1]. Applying the approach to airlines, Xu et al. [2] included flight delay alongside greenhouse gas emissions as undesirable outputs and showed that accounting for delay can alter efficiency assessments. We adapt the treatment of service delay to vessel waiting at anchorage, while recognizing that the airline and port settings have different production processes and data definitions.

Ports produce container throughput while vessel queues impose delays. Waiting at anchorage is a relevant undesirable operational indicator, although it is influenced by carriers, weather, and demand, as well as terminal operations. It must not be interpreted as a direct measure of emissions or entirely controllable port performance.

The study contributes a transparent 2019–2020 comparison for the 15 ports observed in both supplied infrastructure files and the AIS-based waiting-time series. It combines a common global frontier, a directional measure of undesirable waiting, port-level productivity change, a throughput-only sensitivity check, and exhaustive leave-one-port-out re-estimation. The small matched sample and unsettled source boundaries limit claims about absolute performance.

2. Literature Review

2.1. DEA for Port Efficiency Measurement

DEA has been used to measure port and container-terminal efficiency since the 1990s because it accommodates multiple inputs and outputs without requiring a specified production function. Roll and Hayuth [3] presented an early application to port benchmarking, and Tongzon [4] evaluated selected Australian and international ports. Park and De [5] proposed an alternative framework for seaport efficiency, while Cullinane et al. [6] used window analysis to examine changes in container port efficiency over time. Studies of European and Nordic ports further showed that estimated efficiency depends on the sample, returns-to-scale assumption, and input–output specification [7,8,9]. A recent study of 53 container ports in lower–middle-income countries also found that scale and hub status interact with measured efficiency [10].

Subsequent research extended DEA models to different port processes and operating conditions. Wanke [11] used a two-stage network DEA model to distinguish infrastructure from shipment consolidation in Brazilian ports. Yuen et al. [12] examined the relationships among foreign participation, competition, and container port efficiency in China. Woo et al. [13] reviewed the expansion of methods in seaport research and emphasized the importance of matching the model to the operating process. These studies establish DEA as a flexible benchmarking method, but they also caution against interpreting a single-stage score as a measure of managerial efficiency when operating environments differ. Krmac and Mansouri Kaleibar [14] reviewed 116 port DEA studies and identified gaps regarding how inefficiency is interpreted and how benchmarking can be translated into improvement. Caldas et al. [15] used an order-α frontier to examine contextual variables, including water depth and regional economic conditions. Their analysis reinforces the need to distinguish infrastructure utilization from differences in operating context.

Recent productivity studies also distinguish efficiency levels from changes over time. Danladi et al. [16] applied DEA–Malmquist analysis to 39 container ports over the 2001–2012 period and attributed average productivity growth mainly to efficiency change. Chen and Tsai [17] examined global container ports over the 2018–2022 period using physical infrastructure inputs and throughput, finding that productivity gains were primarily associated with technological change. These contrasting findings motivate reporting index components separately; their conventional Malmquist decompositions are distinct from the EC–BPC decomposition used here.

2.2. Directional Distance Functions and Undesirable Outputs

A DDF evaluates feasible improvements along an explicitly chosen direction, allowing desirable output to increase as undesirable output decreases [1]. Chung et al. [1] established this framework for joint production of good and bad outputs. Xu et al. [2] used DDF DEA to evaluate U.S. airlines, and selected flight delay and greenhouse gas emissions as undesirable outputs; comparing a model that includes delay with one that excludes it provides a useful precedent for testing the role of port waiting time. Oh et al. [18] combined a global reference technology with directional distances to measure productivity change over time. Our pooled technology follows this common-reference rationale, while its estimates remain conditional on the selected ports and the direction vector.

An undesirable output is an unwanted outcome associated with a production process. DDF DEA represents a feasible increase in a desirable output jointly with a decrease in the undesirable outcome [1,2]. In the port setting, anchorage waiting time is an operational delay indicator, not a direct measure of emissions. The selected direction and waiting time equality assumptions are modeling choices, and alternative waiting time directions are examined through sensitivity analysis.

Recent port research has provided a direct precedent for combining DDF and GML. Liu et al. [19] used a DDF-based super-efficiency DEA–GML model to assess the growth of green productivity at Chinese coastal ports by incorporating an environmental undesirable-output indicator. This supports the relevance of directional productivity analysis to ports, although environmental burdens and anchorage delay represent different outcomes and require different interpretations.

Port performance research increasingly accounts for time and congestion. Martínez-Moya et al. [20] use berth time and a metafrontier to compare Mediterranean container ports; however, their berth-time construct differs from the waiting-time field in our data. Krmac and Mansouri Kaleibar [21] assess input congestion at Adriatic container terminals. These studies motivate sensitivity to the physical meaning of delay and to the allocation of port inputs. Waiting time here is an operational delay indicator and is not a direct measure of emissions.

Zhang et al. [22] compared the top 80 container ports from the perspectives of operators and shipping companies using AIS information and metafrontier DEA. They found that operator efficiency need not imply efficiency that is relevant to shipping companies, highlighting the importance of service time and stakeholder objectives. Together with berth-time and input-congestion studies [20,21], this evidence motivates the incorporation of waiting time alongside throughput while retaining explicit limitations on port heterogeneity and operational control.

2.3. Research Gap and Contribution

The reviewed literature addresses infrastructure productivity [16,17], environmental productivity [19], and time-sensitive or stakeholder-specific efficiency [20,21,22]. Our study combines annual infrastructure and throughput data with a separately sourced anchorage waiting-time series [23] in a balanced 2019–2020 panel. It applies a directional distance model [1,2] and global reference technology [18] to compare throughput expansion and waiting time reduction jointly, and uses specification changes and port exclusions to assess sensitivity. This is an application of a distinct operational measure of delay rather than a new DDF or GML method. Anchorage waiting time reflects vessel arrivals, weather, and port access, as well as terminal operations, so the estimates remain descriptive and conditional on source coverage and benchmark composition.

3. Data and Methods

3.1. Matched Port-Year Sample and Sources

The analytical sample comprises the following 15 container ports observed in both 2019 and 2020 (30 port-years): Antwerp, Busan, Guangzhou, Hamburg, Hong Kong, Kaohsiung, Ningbo, Port Klang, Qingdao, Rotterdam, Shanghai, Singapore, Tanjung Pelepas, Tianjin, and Xiamen. Ports were included when observations on the three inputs, container throughput, and annual anchorage waiting time were available for both years and could be matched across data sources. Applying these inclusion criteria yields a balanced panel for annual efficiency and productivity comparisons. The analysis uses 2019–2020 port data obtained from S&P Global Market Intelligence (formerly IHS Markit) [24].

We use berth length (m), gantry cranes (count), and other cranes (count) as inputs, with annual data obtained from S&P Global Market Intelligence (formerly IHS Markit) [24]. Average depth is retained in the source dataset but excluded from the primary specification. The selected inputs characterize cargo-handling infrastructure, whereas depth primarily characterizes nautical accessibility and vessel accommodation. Its exclusion keeps the primary model focused and limits dimensionality in the small sample. Because depth may nevertheless affect performance, we assess a four-input specification including depth and acknowledge residual heterogeneity in nautical accessibility. The “other cranes” variable is measured as a count. The 2019 source identifies this category as yard cranes comprising rubber-tyred gantry cranes (RTGs) and rail-mounted gantry cranes (RMGs). The corresponding 2020 field is labeled “crane,” separately from “gantry crane,” but does not specify the equipment types included. We retain the reported counts and assess sensitivity to this classification uncertainty through an additional specification excluding this variable.

The Asian Development Bank (ADB) Port Traffic Database derives its congestion indicators from AIS records of container ships [23]. This study uses the weekly anchorage waiting-time observations for 2019 and 2020. For each port and calendar year, we take the simple arithmetic mean of all available weekly average waiting time entries (Table S3). This gives each reported week equal weight, rather than weighting by weekly vessel calls. The resulting annual waiting time, measured in hours, is included in the DEA model as an undesirable output, alongside container throughput as a desirable output. This specification reflects the objective of increasing cargo throughput while reducing vessel waiting time. The ADB measure captures waiting time before berthing rather than service time at berth. Container throughput, measured in units of 10,000 TEU, is included as a desirable output, with data for 2019 and 2020 obtained from S&P Global Market Intelligence [24].

Table 1 summarizes the 30 port-year observations for 2019–2020. Mean berth length was 10,732.73 m, with averages of 107.93 gantry cranes and 259.10 other cranes. Container throughput averaged 1900.88 units of 10,000 TEU, ranging from 873 to 4330. Average vessel waiting time was 10.56 h (SD = 5.54), with a range of 2.69–24.87 h. Average depth is defined as the midpoint of the minimum and maximum depths, measured in meters. We obtained the 2019 and 2020 values from S&P Global Market Intelligence [24]. Across the 30 port-year observations, average depth ranges from 9.10 to 16.10 m, with a mean of 13.14 m and a standard deviation of 2.25 m. This variable is included only in the four-input sensitivity specification. These variations indicate substantial heterogeneity in infrastructure scale, cargo throughput, and vessel waiting time across the sampled observations.

Table 1. Descriptive statistics for the balanced 2019–2020 panel (N = 30 ports).

Variable	Maximum	Minimum	SD	Mean
Berth length (m)	21,490.00	5040.00	4029.41	10,732.73
Gantry cranes	242.00	54.00	41.14	107.93
Other cranes	662.00	20.00	131.95	259.10
Average depth (m)	16.10	9.10	2.25	13.14
Throughput (10,000 TEU)	4330.00	873.00	991.17	1900.88
Waiting time (h)	24.87	2.69	5.54	10.56

3.2. Directional Distance Function and Global Productivity

The DDF is suited to the study objective because it evaluates potential throughput expansion and waiting time reduction jointly, conditional on existing port infrastructure [1,2]. The DDF analyses were conducted using MaxDEA version 12.5 (MaxDEA Software Ltd., Tsawwassen, BC, Canada). Holding inputs fixed reflects the limited short-term adjustability of berth length and crane stocks. Proportional output directions express both outcomes within one performance measure, while a pooled frontier supplies a common benchmark for annual comparisons [18]. Waiting time also reflects external conditions, so the resulting scores measure relative operational performance rather than exclusively managerial efficiency.

Let R denote an annual reference set or the pooled 2019–2020 reference set G. For port i in year t, x(i,t) is the vector of three inputs, y(i,t) is throughput, and b(i,t) is annual anchorage waiting time. We use the convex VRS weak-disposability technology proposed by Kuosmanen [25]. Let u and v be nonnegative productive and inactive intensity vectors. The directional distance is obtained from the following optimization problem:

$${\beta }_R(i,t) = {max}_{\beta ,u,v} \beta$$

(1)

subject to

$$X_R(u+v) \le x(i,t),$$

(2)

$$Y_{R}u \ge y(i,t)(1+\beta ),$$

(3)

$$B_{R}u=b(i,t)(1-\beta ),$$

(4)

$$\Sigma (u+v)=1,$$

(5)

$$u, v, \beta \ge 0.$$

(6)

Productive intensities enter both outputs, while total intensities enter inputs and the VRS convexity constraint. Joint output contraction by any factor θ ∈ [0, 1] is feasible by replacing u with θu and v with v + (1 − θ)u, preserving input use and convexity. Thus, weak disposability is imposed on the technology rather than inferred from the waiting-time equality alone. The signed output direction is (y(i,t), −b(i,t)). Because waiting time is positive, the baseline program implies β ≤ 1. We report the transformed score:

$$E_R(i,t) = {\displaystyle \frac{1}{1 + {\beta }_R(i,t)}}$$

(7)

The score ranges from 0.5 to 1; unity denotes no improvement along the selected direction. This is a transformed DDF score rather than a conventional radial efficiency score.

Weak disposability is adopted as a maintained assumption of the benchmarking technology rather than an empirically established property of port congestion. It assumes that a feasible throughput–waiting time combination remains feasible when both outcomes are proportionally contracted at fixed inputs [25]. This does not imply that reducing waiting necessarily requires lower throughput; operational improvements may allow for throughput to increase while waiting time decreases. Because the waiting time indicator is an average duration rather than an aggregate burden, the proportional contraction assumption may not fully represent the relationship between traffic volume and congestion.

In line with Oh [18], the VRS global Malmquist–Luenberger (GML) index is GML(i) = [1 + β_G(i,2019)]/[1 + β_G(i,2020)] = E_G(i,2020)/E_G(i,2019). Efficiency change is EC(i) = [1 + β₂₀₁₉(i,2019)]/[1 + β₂₀₂₀(i,2020)]. Define Q(i,t) = E_G(i,t)/E_t(i,t), the contemporaneous-to-global best-practice gap. Best-practice gap change is BPC(i) = Q(i,2020)/Q(i,2019) = GML(i)/EC(i), so GML(i) = EC(i) × BPC(i). A GML score above one indicates measured productivity improvement, below one a decline, and a score of one indicates no change. EC describes change in proximity to the annual frontier; BPC describes change in the gap between annual and global benchmarks. Neither identifies causal technological progress. We retain the GML ratio and decomposition while extending Oh’s CRS implementation to a convex weakly disposable VRS technology [18,25]; a CRS specification is also examined.

Given the limited sample size, the primary specification uses three inputs and two outputs to limit model dimensionality. The global frontier is constructed from 30 port-year observations, whereas each contemporaneous frontier used in the EC decomposition contains 15 ports. The repeated observations represent the same ports in two years, rather than 30 independent ports. Pooling expands the global reference set but does not eliminate the small-sample limitation of the annual frontiers. Specification sensitivity and benchmark influence are assessed through alternative models and leave-one-port-out re-estimation; the estimates are interpreted as relative performance measures for the sampled ports. In this study, productivity change refers specifically to changes in the joint performance of container throughput and anchorage waiting time relative to the pooled reference technology, conditional on the observed infrastructure inputs. The VRS GML index is therefore interpreted as a model-specific measure of relative operational productivity change, rather than an unrestricted measure of total factor productivity. Its EC and BPC components describe changes in annual-frontier efficiency and annual-to-global benchmark gaps, respectively; they do not separately identify technological innovation or its causes.

3.3. Sensitivity and Influence Checks

To assess sensitivity to the inclusion of waiting time, we estimate a throughput-only VRS directional distance model using the same three inputs and the pooled 2019–2020 reference set of 30 port-year observations. For port i in year t, the model is formulated as

$$\begin{array}{c}{{\beta }_G}^{TO}(i,t)={max}_{\beta ,\lambda } \beta \\ \mathrm{subject} \mathrm{to}\\ X_G\lambda \le x(i,t),\\ Y_G\lambda \ge y(i,t)(1+\beta ),\\ 1^T\lambda =1,\\ \lambda \ge 0, \beta \ge 0.\end{array}$$

(8)

Here, $X_G \mathrm{a}\mathrm{n}\mathrm{d} Y_G$ contain the three infrastructure inputs and container throughput, respectively, for the pooled reference observations. The directional vector is g = (0₃, y(i,t)): inputs remain fixed, while throughput is expanded proportionally to its observed value. Waiting time is omitted from both the direction and the technology constraints. The VRS assumption is imposed through the constraint that the reference intensities sum to one.

The reported efficiency score is obtained using the following transformation:

$${E_G}^{TO}(i,t) = {\displaystyle \frac{1}{1 + {{\beta }_G}^{TO}(i,t)}}.$$

(9)

The transformed score lies in (0, 1], with a score of one indicating no feasible throughput expansion along the specified direction. Within each year, ports are ranked in descending order of these scores, with rank 1 assigned to the highest score. Scores are rounded to nine decimal places before ranking, and tied scores receive average ranks. Both years are evaluated against the same pooled reference set. A two-input VRS weak-disposability specification excludes other cranes and retains berth length and gantry cranes. The outputs, directional vector, score transformation, and reference sets remain unchanged.

4. Results

4.1. Efficiency and Annual Comparison

The VRS global Malmquist–Luenberger (GML) index summarizes productivity change from 2019 to 2020 with throughput as a desirable output and waiting time as an undesirable output. Its decomposition, GML = EC × BPC, distinguishes efficiency change relative to annual frontiers from best-practice gap change relative to the pooled benchmark. Table 2 records declines in 10 of the 15 ports, no change in four, and improvement in one. Port Klang is the only port to record productivity growth (GML = 1.031, equivalent to a 3.1% increase), as its efficiency gain (EC = 1.133) offsets a BPC value of 0.910. Antwerp, Hamburg, Shanghai, and Tanjung Pelepas have unity values for all three indicators, indicating no measured change along the selected direction.

Table 2. Global-frontier efficiency scores and productivity decomposition, 2020 relative to 2019.

Port	E 2019	E 2020	BPC	EC	GML
Antwerp	1.000	1.000	1.000	1.000	1.000
Busan	1.000	0.984	0.984	1.000	0.984
Guangzhou	0.896	0.793	0.926	0.955	0.885
Hamburg	1.000	1.000	1.000	1.000	1.000
Hong Kong	0.916	0.806	0.926	0.951	0.881
Kaohsiung	0.791	0.753	1.001	0.950	0.951
Ningbo	0.732	0.684	0.906	1.033	0.935
Port Klang	0.656	0.677	0.910	1.133	1.031
Qingdao	1.000	0.809	0.953	0.849	0.809
Rotterdam	0.673	0.643	0.973	0.982	0.956
Shanghai	1.000	1.000	1.000	1.000	1.000
Singapore	1.000	0.951	0.951	1.000	0.951
Tanjung Pelepas	1.000	1.000	1.000	1.000	1.000
Tianjin	0.796	0.699	0.956	0.919	0.879
Xiamen	0.703	0.700	0.947	1.051	0.995

Note: E 2019 and E 2020 are transformed DDF scores against the global frontier, E_G(i,t) = 1/[1 + β_G(i,t)]. GML = E_G(i,2020)/E_G(i,2019); EC uses separate annual frontiers; BPC = GML/EC reflects best-practice gap change. All primary estimates use the convex VRS weak-disposability technology. Values are rounded to three decimals; calculations and classifications use unrounded values.

Qingdao records the largest decline (GML = 0.809), followed by Tianjin (0.879), Hong Kong (0.881), and Guangzhou (0.885). All four ports have both EC and BPC below one. Busan and Singapore saw unchanged annual-frontier efficiency (EC = 1.000), with declines reflected in BPC. Ningbo and Xiamen exhibit efficiency gains (EC = 1.033 and 1.051), but their BPC values of 0.906 and 0.947 offset these gains, yielding GML values of 0.935 and 0.995. Kaohsiung differs: its EC decline (0.950) outweighs a small BPC increase (1.001), producing GML = 0.951. Overall, BPC is below one in 10 ports, above one in one, and unchanged in four; EC declines in six, improves in three, and is unchanged in six. These patterns describe changes in relative performance and benchmark gaps, without identifying their underlying causes.

Table 3 reports seven frontier observations in 2019 (46.7%) and six in 2020 (40.0%); the pooled global frontier comprises 11 (36.7%). Frontier status is defined by β ≤ 10⁻⁶ and refers to efficiency along the selected direction, rather than strong Pareto efficiency. The substantial frontier shares indicate that discrimination remains limited despite the parsimonious specification. Against the common global frontier, mean transformed efficiency declines from 0.878 in 2019 to 0.833 in 2020; the overall mean is 0.855 (Table 2). The arithmetic mean port-level GML score is 0.951, corresponding to an average decline of 4.9% in the specified relative operational productivity index. This change concerns the joint throughput–waiting time performance measured by the model and should not be interpreted as a 4.9% decline in cargo throughput or economy-wide total factor productivity.

Table 3. Frontier observations under the primary directional specification.

Reference Frontier	Observations	Frontier Observations	Share (%)
2019	15	7	46.7
2020	15	6	40.0
Global	30	11	36.7

4.2. Sensitivity to Model Specification

Previous port studies have emphasized specification sensitivity and the choice of input and output measures [26,27]. Table 4 summarizes sensitivity to output specification, input selection, direction, and returns to scale. The mean GML score remains below unity in every specification for which productivity results are reported, ranging from 0.939 to 0.966. Adding depth or halving the waiting time contraction preserves the primary classification of one improving port, ten declining ports, and four unchanged ports. Doubling the waiting time contraction produces two improvements, nine declines, and four unchanged ports, whereas the CRS specification produces one improvement, twelve declines, and two unchanged ports. Thus, the direction of mean productivity change is consistent across these specifications, while its magnitude and some individual classifications vary. The throughput-only and waiting-time-inclusive efficiency scores use distinct technologies; their comparison assesses specification sensitivity and does not identify a causal effect of waiting time. Excluding the other cranes variable yields a mean transformed efficiency of 0.807 and a mean GML of 0.970, with two improving, eleven declining, and two unchanged ports. Mean GML remains below unity, although Antwerp changes from unchanged to improving and Hamburg from unchanged to declining.

Table 4. Sensitivity of efficiency and productivity estimates to model specification.

Model Specification	Mean Transformed Efficiency	Mean GML	Improving Ports	Declining Ports	Unchanged Ports
Primary: Three-input VRS DDF with waiting time	0.855	0.951	1	10	4
Throughput-only VRS	0.676	—	—	—	—
Four-input VRS DDF including depth	0.864	0.948	1	10	4
VRS DDF with waiting time direction 0.5b	—	0.939	1	10	4
VRS DDF with waiting time direction 2b	—	0.966	2	9	4
Three-input CRS DDF with waiting time	0.785	0.944	1	12	2
Two-input VRS DDF excluding other cranes	0.807	0.970	2	11	2

Note: Mean transformed efficiency is calculated across 30 port-year observations, and mean GML score is the arithmetic mean across 15 ports. The primary output direction is (y, −b); alternative waiting directions are (y, −0.5b) and (y, −2b), where y denotes container throughput and b denotes average anchorage waiting time. Ports are classified as improving, declining, or unchanged using a tolerance of 10⁻⁶ around GML = 1. Efficiency scores depend on the reference technology and direction and are not directly comparable across specifications. — indicates a value not reported.

Supplementary Tables S1 and S2 report efficiency scores and within-year ranks with and without waiting time. Spearman rank correlations are 0.718 in 2019 and 0.731 in 2020. Busan changes from rank 12 in the throughput-only model to an average tied rank of 4 in the waiting-time-inclusive model in 2019 and from rank 12 to rank 5 in 2020. Hong Kong changes from rank 13 to rank 8 in both years, whereas Ningbo changes from rank 8 to rank 12 in 2019 and from rank 7 to rank 13 in 2020. These differences demonstrate the sensitivity of the individual ordering to the waiting time specification. They do not identify a causal effect for waiting time, because the two specifications employ distinct reference technologies.

4.3. Leave-One-Port-Out Influence

We removed both observations of each port and re-estimated the frontier to assess benchmark influence, as shown in Table 5. This follows the general logic of observation-exclusion checks in seaport frontier research [28], whose CNLS implementation differs from the present DEA–GML analysis. Across all 15 exclusions, the mean GML score of the retained ports remains below one (range 0.942–0.990). Omitting Shanghai raises the mean from 0.947 to 0.983 for the same 14 ports; the improvement/decline/tie status of three ports changes; and the Spearman correlation is 0.558. Omitting Tanjung Pelepas raises the matched mean from 0.947 to 0.990; one port changes status, with the correlation being 0.670; and Port Klang has the largest absolute GML score shift (0.491). Omitting Antwerp changes one port’s status. Thus, the sample-average direction is stable across these exclusions, but individual scores, classifications, and ordering remain sensitive to benchmark ports.

Table 5. Leave-one-port-out GML index summary (both years for excluded port removed).

Omitted Port	Re-Estimated Mean GML Index	Baseline Mean GML Index	Spearman Rank Correlation	Status Changes
Antwerp	0.950	0.947	0.956	1
Busan	0.942	0.948	0.946	0
Guangzhou	0.955	0.955	1.000	0
Hamburg	0.947	0.947	1.000	0
Hong Kong	0.956	0.956	1.000	0
Kaohsiung	0.950	0.950	1.000	0
Ningbo	0.952	0.952	1.000	0
Port Klang	0.945	0.945	1.000	0
Qingdao	0.960	0.961	0.996	0
Rotterdam	0.950	0.950	1.000	0
Shanghai	0.983	0.947	0.558	3
Singapore	0.950	0.950	1.000	0
Tanjung Pelepas	0.990	0.947	0.670	1
Tianjin	0.956	0.956	1.000	0
Xiamen	0.947	0.947	1.000	0

Note: Re-estimated mean GML score uses the frontier refitted after excluding both observations of the specified port. Baseline mean GML score uses the original frontier for the same 14 retained ports. Spearman rank correlation compares their GML rankings before and after exclusion. Status changes count ports switching between improvement, decline, and no change, using a tolerance of 10⁻⁶ around GML = 1.

5. Discussion

The mean GML score of 0.951 indicates a decline in the model-specific index of relative operational productivity between 2019 and 2020, with throughput and anchorage waiting time evaluated jointly against the pooled VRS reference technology. The mean GML index remains below unity across specifications with reported productivity results and all leave-one-port-out re-estimations, although the magnitude of change and individual port comparisons depend on the reference set and modeling assumptions.

However, the index does not identify the causes of deterioration or isolate pandemic effects. Recent infrastructure-based DEA–Malmquist research likewise evaluates port performance across the pandemic period [17], while stakeholder-based analysis shows that efficient resource utilization need not imply efficient service for shipping companies [22]. The policy relevance of the present results therefore lies in identifying areas for operational diagnosis, rather than assigning responsibility to port managers.

For port authorities, the findings support a performance framework that monitors throughput together with anchorage waiting time, berth service time, and schedule reliability. The distinction between waiting before berthing and time at berth matters because these delays require different interventions. Where operational diagnosis identifies coordination problems, authorities and terminals could prioritize shared forecasts of berth availability, coordinated pilot and tug scheduling, and the timely exchange of arrival and departure information. Just-in-time arrival offers a practical framework for aligning vessel arrival with berth and nautical-service readiness [29]. These measures should be developed jointly with carriers and service providers, since anchorage waiting time is not controlled by terminals alone.

Waiting time reductions also have potential environmental benefits. IMO guidance identifies lower greenhouse gas and air-pollutant emissions through shorter waiting times and reduced maneuvering near ports, together with voyage-speed optimization [29]. Consequently, coordination that avoids unnecessary early arrival can support both service efficiency and greener shipping. This interpretation complements the environmental-productivity perspective adopted by Liu et al. [19], although waiting time in our study serves as an operational indicator rather than a direct measure of emissions. Our results do not quantify fuel savings, carbon reductions, or local air-quality improvements; those outcomes require vessel-specific activity, fuel, and emissions data.

Public investment and green-port programs should therefore combine operational coordination with evidence on the actual sources of congestion. The throughput-only and depth specifications show that assessed performance depends on the production objective and infrastructure coverage; they do not establish that adding cranes, extending berths, or deepening channels will reduce waiting times. Before committing to capacity expansion, policymakers could assess berth utilization, vessel arrival concentration, yard and hinterland bottlenecks, and nautical-access constraints. IMO guidance also supports advance clearance and improved ship–berth compatibility as measures that contribute towards optimized port stays [30]. A phased coordination pilot, evaluated against throughput, waiting time, and measured emissions, would provide more decision-relevant evidence than an efficiency rank alone.

The influence analysis further argues for caution in using DEA rankings to allocate subsidies, set port charges, or impose performance targets. Omitting Shanghai or Tanjung Pelepas substantially changes some individual estimates, despite preserving the direction of mean change. Regulators could use the scores to initiate peer-learning and operational reviews, while checking whether reference ports have comparable traffic patterns, terminal scope, and operating conditions. Incentives for verified improvements in port-call coordination should account for weather and other external disruptions and monitor the full port call, so that apparent waiting reductions are not achieved by shifting delay outside the reported waiting zone.

This study has several limitations. The balanced panel contains only 15 ports over two years, limiting frontier discrimination and preventing assessment of longer-term productivity trends. The exclusion analysis shows that individual rankings remain sensitive to influential reference ports. Anchorage waiting time also reflects vessel arrival patterns, weather, and access conditions that are not separately controlled for in the model. Annual waiting time is calculated as an unweighted mean of reported weekly estimates and may differ from vessel-call-weighted experience. Finally, we maintain weak disposability and the proportional direction as modeling assumptions. Joint proportional contraction of throughput and average waiting time may not fully represent actual congestion dynamics, and the waiting time indicator does not directly measure fuel consumption or emissions. Differences in the equipment coverage of the crane variable across ports and years could not be fully verified. The exclusion analysis indicates that mean GML remains below unity, although its magnitude and some individual port classifications are sensitive to this variable.

Future research should expand the port sample and observation period to assess longer-term trends and performance across different operating conditions. Vessel-call-level AIS data could support weighted waiting measures and analysis of vessel size, arrival concentration, and seasonal disruptions. Linking these observations to fuel consumption and emissions inventories would allow for direct evaluation of environmental benefits. Larger samples could also support comparisons among more homogeneous port groups and alternative directional specifications. Finally, prospective evaluations of just-in-time arrival or port-call coordination pilots could test whether the proposed policies improve service performance and reduce emissions.

6. Conclusions

A convex VRS weak-disposability DDF incorporating anchorage waiting time yields a mean transformed efficiency of 0.855 and an arithmetic mean GML score of 0.951 for 15 matched ports in 2019 and 2020. Ten ports recorded declines, one improved, and four remained unchanged. The mean GML score remained below one under the examined specification changes and every port exclusion, although influential benchmarks materially affect individual estimates. The findings describe relative operational performance conditional on the data, direction, and technology assumptions. Future research may extend the period and port coverage, examine vessel-call-weighted waiting measures, and assess environmental heterogeneity and alternative technologies.