Sustainable Port Horizontal Transportation: Environmental and Economic Optimization of Mobile Charging Stations Through Carbon-Efficient Recharging

Abstract

Electrifying port horizontal transportation is constrained by downtime and deadheading from fixed charging/swapping systems, large battery sizes, and the lack of integrated decision tools for life-cycle emissions. This study develops a carbon-efficiency-centered bi-objective optimization framework benchmarking Mobile Charging Stations (MCSs) against Fixed Charging Stations (FCSs) and Battery Swapping Stations (BSWSs). The framework integrates operational parameters such as charging power, range, dispatch, and non-operational mileage, along with grid carbon intensity, battery embodied emissions, and carbon-market factors. It generates Pareto fronts using the NSGA-II algorithm with real port data. Port horizontal transportation refers to the movement of goods within the port area, typically involving the use of specialized vehicles to transport containers short distances across the terminal. Results show that MCSs can reuse idle windows to reduce deadheading and infrastructure demand, yielding significant economic improvements. The trade-off between emissions and profitability is context-dependent: at low-to-moderate reuse levels, low-carbon and profitable solutions coexist; beyond a threshold of approximately 0.5–0.75, the Pareto fronts shift to high emissions and high profits, highlighting the context-specific advantages of MCSs for port-infrastructure planning. MCSs thus provide context-dependent advantages over FCSs and BSWSs, offering practical guidance for port infrastructure planning and carbon-informed policy design.

1. Introduction

As port electrification expands, horizontal transportation systems encounter significant challenges, including high infrastructure and battery costs [1], limited energy density [2], and persistent inefficiencies in fleet utilization [3]. Although advances in fast-charging technology have been made, charging remains slower than conventional refueling, affecting productivity and energy management [4]. In this study, port horizontal transportation involves electric vehicles (EVs), including Intelligent Guided Vehicles (IGVs) and yard tractors (known as container trucks), which move containers between quay cranes and yard blocks. These systemic barriers highlight the need for holistic, carbon-efficient strategies that reconcile economic viability, environmental sustainability, and operational efficiency in the transition toward fully electrified ports. Specifically, the transformation from fossil-fuel-based to electric horizontal transportation faces several interconnected core challenges: (1) Grid capacity issues from simultaneous high-power charging; (2) Operational inefficiency due to charging-related detours and downtime, reducing vehicle utilization; (3) High capital cost and land scarcity for deploying sufficient fixed charging/swapping infrastructure; (4) Range anxiety that limits operational flexibility; (5) Balancing lifecycle carbon emissions with economic profitability. These challenges, particularly (1) to (3), are well-documented in studies of existing FCS and BSWS deployments, as discussed below. Addressing such challenges further requires multi-stakeholder collaboration and institutional innovation, in line with broader perspectives on sustainability transitions and the triple helix framework [5].

Fixed Charging Stations (FCSs) and Battery Swapping Stations (BSWSs), though widely deployed, continue to face major operational and economic barriers. Charging-based EVs suffer from utilization loss due to detours and prolonged charging times, a problem exacerbated by battery-preserving policies that limit deep discharging [6]. Similarly, battery-swapping EVs require detours to geographically sparse stations, which also reduces service time and utilization [7]. At a macro scale, such detours can increase travel time by up to 40% [8]. In port operations, these issues manifest as frequent micro-detours for charging, significantly curtailing effective service time [9]. Sadati et al. [10] point out that the charging process for electric vehicles itself takes a long time, and although fast charging can shorten the time, it still cannot wholly avoid interruptions. BSWSs provide sub-5 min replenishment [11]. Capital expenditure is 30–50% higher than for fast-charging stations [12], driven by 20–40% additional spare-battery inventory [13] and elevated maintenance/balancing costs from multi-cycle operation [14]. Consequently, FCS downtime (about 1 h) versus BSWS downtime (about 4 min) disrupts efficiency [15], with cases such as at Shenzhen Mawan Port requiring 2 km detours that further increase non-productive travel [16]. High-capacity batteries (>200 kWh) drive up acquisition costs, while poor FCSs allocation risks over-investment or congestion [17]. Land and grid constraints ultimately restrict large-scale electrification, making both models technically and economically challenging [18].

In contrast, Mobile Charging Stations (MCSs), typically trucks or vans equipped with energy storage systems, provide a flexible, on-site alternative [19]. As illustrated in Figure 1, conventional systems, i.e., Option 1 (BSWSs) and Option 2 (FCSs), require EVs to stop for battery swapping or charging, whereas Option 3 (MCSs) enables on-site charging, reducing both idle time and dependence on fixed infrastructure. By charging IGVs directly at operation sites, MCSs reduce unproductive travel, enhance utilization, and mitigate both infrastructure and battery costs. Leijon et al. [20] highlight their benefits for congestion relief, infrastructure savings, and grid efficiency during peak demand. Optimized scheduling strategies, such as mixed-integer linear programming, can further enhance efficiency and reduce costs [21]. Integration of FCSs with MCSs through facility layout optimization increases service flexibility and coverage while reducing construction costs [22]. Optimized allocation of mobile and fixed stations has been shown to lower investment while improving service performance [23]. Collaborative charging strategies combining FCSs and MCSs reduce overall costs by 12.6% compared to FCSs alone and 14.9% compared to MCSs alone [24]. Moreover, MCSs can significantly decrease EV waiting times and enhance charging efficiency, particularly when optimized charging and discharging strategies are applied [25].

Nevertheless, most MCS research has focused on urban EV systems rather than ports. Port electrification still emphasizes shore power, FCSs, and BSWSs deployment, with MCSs treated mainly as backup or emergency support [24]. Although valued for mobility and demand responsiveness, ports follow predictable charging patterns that favor fixed infrastructure: truck-mounted mobile chargers are dispatched to fixed windows of morning and evening peaks [26], while optimal scheduling still allocates the bulk of charging power to permanent 11 kW AC posts rather than to vehicle-to-grid or mobile units [27]. Land scarcity further constrains the expansion of fixed charging, making MCSs advantageous for flexible siting [28]. Moreover, repetitive charging cycles suggest greater cost-effectiveness for MCSs in ports [23]. Charging interruptions can delay ships, increase reliance on fuel-based equipment, and intensify localized emissions, whereas MCSs provide responsive, low-emission solutions that support port-wide electrification.

In light of these challenges, an optimal port horizontal electrification system should aim to fulfill several integrated requirements: (1) seamless operational continuity with minimal charging-induced downtime; (2) grid-friendly integration to avoid peak load stress; (3) spatial and infrastructure efficiency to conserve scarce port land; (4) lifecycle economic viability competitive with conventional systems; and (5) flexibility to adapt to operational fluctuations. Achieving all these goals simultaneously is inherently challenging, as they often involve trade-offs.

To address these gaps and navigate the aforementioned trade-offs, this study develops a bi-objective optimization model that evaluates economic, land-use, and carbon-efficiency dimensions to maximize fleet utilization, reduce grid load, and align operations with sustainability goals.

The main contributions of this work are summarized as follows:

i.

A unified carbon-efficiency framework: We develop a novel bi-objective framework for directly comparing Mobile Charging Stations (MCSs), Fixed Charging Stations (FCSs), and Battery Swapping Stations (BSWSs). Unlike studies that evaluate these technologies in isolation, our model integrates both operational electricity use and embedded battery carbon emissions under a carbon-efficiency paradigm.

ii.

Operational realism with real-world validation: The model incorporates critical operational factors often overlooked in strategic planning, such as vehicle detours, non-operational mileage, and the reuse of crane idle time for charging. It is calibrated and validated using real-world data from Shenzhen Mawan Port, including vehicle routes, energy consumption, and task schedules.

iii.

Identification of a critical operational threshold: Our analysis reveals a key nonlinear threshold (0.5–0.75) in the reuse ratio, defining a shift from carbon-conserving to profit-maximizing regimes. This finding provides actionable insights for port operators to balance environmental and economic objectives.

iv.

Practical decision support for infrastructure planning: The framework generates deployable configurations and offers clear guidance for port planners to select among MCSs, FCSs, and BSWSs based on specific priorities, including carbon-profit trade-offs, land constraints, and achievable reuse levels.

The remainder of this paper is organized as follows. Section 2 (Materials and Methods) formulates the carbon-efficiency-centered bi-objective optimization model and details the key assumptions, parameters, and data sources. Section 3 (Results) presents the simulation outcomes, including the derived Pareto fronts and the comparative analysis of MCSs, FCSs, and BSWSs. Section 4 (Discussion) interprets the broader implications of the results, focusing on the critical reuse ratio threshold and its significance for operational strategy. Finally, Section 5 (Conclusions) summarizes the main findings and proposes directions for future research.

2. Materials and Methods

This section outlines the hybrid modeling framework, data sources, and simulation protocols employed to evaluate the carbon-efficient-driven performance of MCSs in port horizontal transportation systems. The methodology integrates operational efficiency, cost-effectiveness, and carbon-efficient metrics, building on empirical insights from prior research on MCSs [14].

2.1. MCSs Solution

To maintain continuous operations with minimal investment, the MCSs model is introduced as a more flexible alternative to FCSs and BSWSs. A MCS, typically a truck or van equipped with an energy storage system, offers a mobile, efficient solution for rapid charging of EVs, such as Intelligent Guided Vehicles (IGVs). MCSs can deliver charging services directly to EVs while they are in use. During idle times, such as when vehicles are queuing or waiting under cranes for container handling, the MCSs efficiently recharge the operating vehicles. Once a MCS’s battery is depleted, it autonomously returns to a fast-charging station to recharge itself.

To define the operational boundaries for uninterrupted horizontal transportation vehicle workflows, this study adopts the following simplifications: (1) Exogenous disturbances, including ad hoc tasks, equipment failures, and traffic congestion, are excluded to isolate charging system performance. (2) Vehicle energy consumption is modeled as a constant rate, independent of cargo weight variations. (3) Technical complexities in MCS–vehicle charging interfaces are abstracted to a fixed preparation time. (4) Additional assumptions include a stable grid power supply (i.e., port-wide power failures and backup systems are not modeled), instantaneous MCSs dispatch availability, negligible battery degradation, and uniform environmental conditions. (5) A charging efficiency of 95% is assumed for both $\phi$_fcs and $\phi$_mcs (see

Table 1. Variables and parameters with descriptions.

Symbol	Description	Unit	Data Source/Value
α	Weighting coefficient for carbon emissions	/	Equal-weight aggregation, α = 1 for simplicity (no separate weighting of direct/embedded emissions)
β	Weighting coefficient for maintenance costs differentiated across charging modalities (FCSs, BSWSs, MCSs)	/	Assumed values based on operational complexity: 5% for FCSs, 8% for BSWSs, 6% for MCSs
Bev	Battery capacity for the operating EV fleet	kWh	280 for FCSs and 210 for BSWSs [16]
Bmcs	The battery capacity of one MCS	kWh	Decision Variable (0–300)
Cbattery	The cost of battery acquisition per kWh	CNY/kWh	1000 [16]
Ccap	Initial acquisition cost (including MCSs, batteries, and charging equipment)	CNY	Calculated, Equation (14), using Nev, Cev, Nmcs, Cmcs, Bev, Bmcs, Cbattery, Ccharger
Ccharger	The cost of the charging infrastructure for EVs	CNY	150,000 [16]
Cev	The cost of one EV without battery	CNY	550,000 (Based on typical market values for EVs in port operations)
Cmcs	The cost of one MCS without battery	CNY	500,000 [16]
Cop	The operational costs (including energy costs, maintenance fees, etc.)	CNY	Calculated, Equation (15), using β, Ccap
Ctotal_bsws	The total life-cycle carbon emissions of BSWSs solution	kg CO2	Calculated, Equation (1), using T, E1, α, E2
Ctotal_fcs	The total life-cycle carbon emissions of FCSs solution	kg CO2	Calculated, Equation (1), using T, E1, α, E2
Ctotal_mcs	The total life-cycle carbon emissions of MCSs solution	kg CO2	Calculated, Equation (1), using T, E1, α, E2
ΔEmissions	Difference in total carbon emissions between MCS and BSWS/FCS	kg CO2	Calculated from Ctotal_bsws, Ctotal_fcs, Ctotal_mcs
ΔNPV	Relative Net Present Value	CNY	Calculated from NPVbsws, NPVfcs, NPVmcs
dday	The total distance traveled by one EV during one operational day	km	Calculated, Equation (12), using Top, Tev_op, Tev_empty, Tev_charging, Nev, Bev, SOCev, Vport, Pcons_ev_op
dempty	Round-trip distance to charging station	km	2 [16]
dloop	Average distance for EVs to load/unload one TEU	km	2 [16]
DoD	Depth of Discharge (percentage of battery discharge)	/	Calculated, Equation (18), using SOCmcs, SOCev
E1	Direct carbon emissions	kg CO2	Calculated, Equation (2), using Top, Nev, Pcons_ev_op, ɛev_op, Pcons_ev_empty, εev_empty, Nmcs, Pcons_mcs_op, εmcs_op, Pcons_mcs_empty, εmcs_empty, λcarbon
E2	Embedded carbon emissions	kg CO2	Calculated, Equation (3), using Nev, Bev, Nmcs, Bmcs, λwhole_carbon
$\eta$mcs	Proportion of MCSs’ output covering charging demand	/	Calculated, Equation (17), using Tmcs_op, Tmcs_empty, Tmcs_charging
$\phi$fcs	Charging conversion efficiency of FCSs to EVs or MCSs	/	0.95 [29]
$\phi$mcs	Charging conversion efficiency of MCSs to EVs	/	0.95 [29]
λ1	Comparative ratio for MCS energy consumption (see Equation (19))	/	0.9 (Assumed to reflect a ~10% reduction due to lighter vehicle mass)
λcarbon	Grid carbon emission factor	kg CO2/kWh	0.57 kg CO2/kWh (Chinese regional grid benchmark)
λwhole_carbon	Life-cycle carbon intensity of the battery	kg CO2/kWh	65 (based on industry reports and lifecycle assessments [29])
Ncharger_bsws_battery	The quantity of BSWSs’ charging batteries	/	Calculated, Equation (30), using Nev, Ncharger_per_day_bsws, Bev, SOCev, Pbsws
Ncharger_fcs_pile	The quantity of FCSs’ charging piles	/	Calculated, Equations (26) and (27), using Nev, Ncharger_per_day_fcs, Bev, SOCev, Pfcs, Tev_charging, Tev_op, Top
Ncharger_mcs_pile	The quantity of MCSs’ charging piles	/	Calculated, Equations (22) and (23), using Nmcs, Ncharger_per_day_mcs, Bmcs, SOCmcs, Pfcs, Tmcs_charging, Tmcs_op, Top
Ncharger_per_day_bsws	The daily charging frequency of BSWSs	/	Calculated, Equation (29), using Top, Tcycle_bsws
Ncharger_per_day_fcs	The daily charging frequency of FCSs	/	Calculated, Equation (25), using Top, Tcycle_fcs
Ncharger_per_day_mcs	The daily charging frequency of MCSs	/	Calculated, Equation (21), using Top, Tcycle_mcs
Nev	The quantity of operating EVs	/	Decision Variable (Nev ∈ R+)
Nmcs	The quantity of MCSs deployed	/	Decision Variable (Nmcs ∈ R+)
NPVbsws	Net Present Value of BSWSs solution	CNY	Calculated, Equation (10), using T, Rop, Cop, r, Ccap
NPVfcs	Net Present Value of FCSs solution	CNY	Calculated, Equation (10), using T, Rop, Cop, r, Ccap
NPVmcs	Net Present Value of MCSs solution	CNY	Calculated, Equation (10), using T, Rop, Cop, r, Ccap
Pbsws	Charging power from BSWSs to EVs	kW	200 (Estimated industry benchmark)
Pcons_ev_empty	Driving energy consumption coefficient of EVs under non-operation	kW	15 (Estimated industry benchmark)
Pcons_ev_op	Driving energy consumption coefficient of EVs under operation	kW	30 (Estimated industry benchmark)
Pcons_ev_op_mcs	Operative driving energy consumption coefficient of EVs (MCSs solution)	kW	Calculated, Equation (19), using Pcons_ev_op, λ1
Pfcs	Charging power supplied by FCSs to EVs or MCSs	kW	200 (Estimated industry benchmark)
Pmcs	Charging power of the MCSs	kW	Decision Variable (100–600)
r	Discount rate for NPV calculations	/	5% (Assumed for financial assessments)
ratio	MCS deployment ratio (proportion of charging time during EVs’ waiting for quay and yard cranes)	/	Parameter for sensitivity analysis, tested in the range 0–1
Rcarbon	The carbon emission benefit from carbon trading for port enterprises	CNY	Calculated, Equation (13), using Ctotal_fcs, Ctotal_mcs, Rcarbon_trading
Rcarbon_trading	The carbon emission price	CNY/ton	100 (baseline carbon price assumed for the model; the official closing price on 31 December 2024 was 97.49 CNY/ton [30])
Rop	The operational revenue	CNY	Calculated, Equation (12), using Rteu, Nteu, Rcarbon
Rteu	The revenue per twenty-foot equivalent unit	CNY/TEU	20 (Estimated industry benchmark)
SOCev	State of charge of EVs	/	Parameter for constraints in Equation (18)
SOCmcs	State of charge of MCSs	/	Parameter for constraints in Equation (18)
T	Lifecycle duration (consistent with EVs’ service life and battery lifespan)	year	8 (Typical EV/battery service life)
Tcycle_bsws	The interval between single charges of BSWSs	hour	Calculated, Equation (28), using Bev, SOCev, Pcons_ev_op
Tcycle_fcs	The interval between single charges of FCSs	hour	Calculated, Equation (24), using Bev, SOCev, Pcons_ev_op
Tcycle_mcs	The interval between single charges of MCSs	hour	Calculated, Equation (20), using Bev, SOCev, Pcons_ev_op_mcs
Tev_charging	Charging interval between successive EVs charging sessions	hour	$\mathrm{Calculated}, \mathrm{Equation} \left(6\right), \mathrm{using} \phi$mcs, Bev, SOCev, Pfcs, Pmcs
Tev_empty	Non-operational interval between successive EVs charging sessions	hour	Calculated, Equation (5), using dempty, Vport
Tev_op	Operational interval between successive EVs charging sessions	hour	Calculated, Equation (4), using Bev, SOCev, Pcons_ev_op
Tmcs_charging	Charging interval between successive MCSs charging sessions	hour	$\mathrm{Calculated}, \mathrm{Equation} \left(9\right), \mathrm{using} \phi$fcs, Bmcs, SOCmcs, Pfcs
Tmcs_empty	Non-operational interval between successive MCSs charging sessions	hour	Calculated, Equation (8), using dempty, Vport
Tmcs_op	Operational interval between successive MCSs charging sessions	hour	$\mathrm{Calculated}, \mathrm{Equation} \left(7\right), \mathrm{using} \phi$mcs, Bmcs, SOCmcs, Pmcs
Top	Port operation duration per day	hour	12 (Estimated industry benchmark)
Vport	Average vehicle speed in port	km/h	15 [16]

), based on typical industry standards for mobile charging systems, such as those described in Jahnes et al. [29], which reports a peak efficiency of 99.5% for a transformerless EV charger. This value is adjusted to account for operational conditions and energy losses during power conversion and transmission.

2.2. Data Sources

The data utilized in this study are derived from multiple sources, encompassing operational, technical, and carbon-efficient-related parameters. Operational data was obtained from real-world logistics operations at Shenzhen Mawan Port, including vehicle routes (with an average cycle range of 2.6 km), hourly energy consumption (ranging from 10 to 15 kWh per vehicle), and task schedules, which account for 24 h operations. Although the port operates 24 h per day, the model uses an average of 12 effective operational hours per day to account for variations in vehicle utilization, idle time, and lower nighttime activity. This averaged value ensures the model reflects typical daily energy consumption and charging demands. Empirical trials informed the technical parameters, including charging efficiencies (4 kWh/min for FCSs and 4 min for BSWSs), battery capacities (280 kWh for vehicles with FCSs and 210 kWh for BSWSs), and downtime intervals (e.g., 5 min for recharging preparation).

Finally, carbon-efficient metrics were sourced from industry reports and lifecycle assessments, covering the carbon intensity of battery production (55–77.4 CO₂ eq/kWh) [31], safety risk indices (such as traffic accident rates near fixed stations), and governance costs (including infrastructure permits and grid upgrade expenses). The carbon emission price in this study is calculated using a baseline price of 100 CNY per ton, which is set with reference to the closing price of the Chinese national carbon market at the end of 2024 (97.49 CNY/ton) [30]. The port, as a nationwide carbon-emission control enterprise, adopts the electricity grid carbon emission factor of 0.57 kg CO₂/kWh from the Chinese regional grid benchmark.

It is important to note that while the simulation model is based on real operational data from Shenzhen Mawan Port, including vehicle energy consumption, charging power, battery size, vehicle speed, and other operational parameters, cross-validation with actual MCS performance data was not conducted. This is because MCSs are not yet deployed in the port, and thus, real-world performance data for MCSs is unavailable. Future validation of the model will be possible once MCSs are operational at the port.

A number of technical and operational parameters in this model (e.g., charging power, energy consumption coefficients, as listed in Table 1) are based on commercially sensitive data that is not publicly disclosed by individual ports or equipment manufacturers. Therefore, all such values are set as estimated industry benchmarks, derived from a synthesis of typical technical specifications and operational patterns reported in the sector literature and industry analyses. These representative values are utilized to ensure the general applicability and reproducibility of the model’s scenario analysis.

2.3. Carbon-Efficient-Driven Multi-Objective Optimization Model

The Environment, Social, and Governance (ESG) performance evaluation of the port-level transportation system requires integrating these dimensions. However, the focus of this study is on quantifying the impact of MCSs on port operational efficiency and total life-cycle costs. The innovative mechanisms of MCSs, such as dynamic energy replenishment and flexible battery capacity configuration, directly influence environmental benefits (E) and economic feasibility. In contrast, social (S) and governance (G) indicators, such as health impacts and stakeholder engagement, rely on long-term operational data or policy frameworks, which fall beyond the scope of this empirical analysis. Accordingly, the Carbon-Efficient index system proposed in this study is based on a “dual-core” framework that integrates environmental and economic factors, as outlined below. The Carbon-MCS optimization model developed in this study includes two types of decision variables, two objective functions, and two types of constraints.

2.3.1. Carbon-Efficient Metrics

This study aims to minimize the carbon emissions (including non-operational transportation energy consumption and battery production-related pollution) and energy consumption:

i.

E₁: Direct carbon emissions refer to physical emissions within a defined boundary, such as tailpipe emissions during vehicle operation or grid-based emissions during charging. For electric vehicles, this primarily involves emissions from electricity production during charging. Activity-Based Accounting is used to quantify CO₂-equivalent emissions throughout the entire horizontal transportation process.

ii.

E₂: Embedded carbon emissions include greenhouse gas emissions from battery production and recycling, covering indirect emissions from raw material extraction, manufacturing, transportation, and recycling processes.

2.3.2. Definition of Decision Variables

There are three continuous variables:

i.

B_ev ∈ (0, 300]: Battery capacity for the operating EV fleet (e.g., 210 kWh for battery-swapped EVs, 280 kWh for charging EVs [16]). The battery capacity must meet the EV range requirements to ensure they can complete tasks between charging sessions. Increasing the battery capacity significantly raises vehicle acquisition costs, necessitating a balance between range requirements and cost considerations.

ii.

P_mcs ∈ [100, 600]: Charging power of the MCSs, in kilowatts (kW). Higher charging power can reduce charging time, improving equipment utilization and lowering operational costs. However, the purchase and operational expenses of high-power charging equipment are also higher.

iii.

B_mcs ∈ (0, 1500]: The battery capacity of one MCS (in kWh). The battery capacity must be sufficient to meet the operational range requirements of MCSs, ensuring they can charge EVs during their operation without needing to return to the FCSs for recharging.

Two discrete variables are defined:

i.

N_mcs ∈ R+: The quantity of MCSs deployed, which must be determined based on the port’s operational and charging demands. The quantity of MCSs should strike a balance among acquisition, operating, and land opportunity costs, while ensuring sufficient scheduling flexibility to adapt to dynamic changes in port operations.

ii.

N_ev ∈ R+: The quantity of operating EVs. This refers to the total quantity of electric vehicles actively operating at the port. The quantity of EVs influences charging service demand and should be optimized to ensure sufficient charging capacity while minimizing idle time and improving operational efficiency across both EVs and MCSs.

To better illustrate the logical relationships between these variables, the objectives, and the corresponding constraints, an integrated optimization framework is presented in Figure 2.

2.3.3. Objective Function Framework

i.

Environmental Objective Function (Minimizing Total Life-Cycle Carbon Emissions)

$$Min C_{total}={\sum }_{i=1}^T\left(E_1\right(i)+\alpha ·E_2(i\left)\right)$$

(1)

$$\begin{array}{c}{E}_1=(N_{ev}·B_{ev}·{SOC}_{ev}·{\displaystyle \frac{T_{op}}{T_{{ev}_{op}}+T_{{ev}_{empty}}+T_{{ev}_{charging}}}}+N_{mcs}·B_{mcs}·{SOC}_{mcs}·\\ {\displaystyle \frac{T_{op}}{T_{{mcs}_{op}+T_{{mcs}_{empty}}+T_{{mcs}_{charging}}}}})·{\lambda }_{carbon}\end{array}$$

(2)

$$E_2=\left(N_{ev}·B_{ev}+N_{mcs}·B_{mcs}\right)·{\lambda }_{{whole}_{carbon}}$$

(3)

$$T_{{ev}_{op}}={\displaystyle \frac{B_{ev}·{SOC}_{ev}}{P_{{cons}_{{ev}_{op}}}}}$$

(4)

MCSs move to charge IGVs on-site, so we have

$$T_{{ev}_{empty}}=\left\{\begin{array}{c}{\displaystyle \frac{d_{empty}}{V_{port}}},\hspace{1em}\hspace{1em}for FCSs/BSWSs model\\ 0,\hspace{1em}\hspace{1em}for MCSs model\end{array}\right.$$

(5)

BSWSs have fixed swapping times, so we have

$$T_{{ev}_{charging}}=\left\{\begin{array}{c}4 \min , for BSWSs model\\ {\displaystyle \frac{{\phi }_{mcs}·B_{ev}·{SOC}_{ev}}{P_{fcs}}}, for FCSs model\\ {\displaystyle \frac{{\phi }_{mcs}·B_{ev}·{SOC}_{ev}}{P_{mcs}}}, for MCSs model\end{array}\right.$$

(6)

For the MCSs model, the operation time, empty moving time, and charging time are as follows:

$$T_{{mcs}_{op}}={\displaystyle \frac{{\phi }_{mcs}·B_{mcs}·{SOC}_{mcs}}{P_{mcs}}}$$

(7)

$$T_{{mcs}_{empty}}={\displaystyle \frac{d_{empty}}{V_{port}}}$$

(8)

$$T_{{mcs}_{charging}}={\displaystyle \frac{{\phi }_{fcs}·B_{mcs}·{SOC}_{mcs}}{P_{fcs}}}$$

(9)

This framework aims to minimize the total carbon emissions by considering both direct emissions during vehicle operation (E₁) and embedded emissions associated with battery production and lifecycle (E₂).

ii.

Economic Objective Function to maximize Net Present Value (NPV)

To assess the economic sustainability of the MCSs solution, this study develops a dynamic programming model that integrates three key components: operational revenue (Rop), initial capital expenditure (CAPEX, which is the Ccap), and operational expenditure (OPEX, which is the Cop). The objective is to maximize the NPV over the system’s entire life cycle:

$$Max NPV={\sum }_{t=1}^T{\displaystyle \frac{R_{op}-C_{op}}{{\left(1+r\right)}^t}}-C_{cap}$$

(10)

where r is the discount rate (5%), it is used to calculate the present value of future cash flows, accounting for the time value of money in financial assessments and cost–benefit analyses.

The interplay of decision variables in the economic model is as follows:

i.

As the quantity of MCSs (N_mcs) increases, the acquisition cost (C_cap) rises linearly due to the higher quantity of units, while operational costs (C_op) may decrease. This is because more MCSs improve scheduling efficiency, reducing the frequency of individual MCS usage and maintenance costs.

ii.

As battery capacity (B_ev) decreases, C_cap decreases due to lower battery capacity and thus lower initial costs. However, C_op may increase due to more frequent charging, leading to higher energy and maintenance costs.

iii.

As charging power (P_mcs) increases, C_cap may rise due to the higher expense of high-power charging equipment. However, C_op may decrease because the reduced charging time enhances equipment utilization.

Calculated based on port operations and transportation contracts. Assuming the revenue per twenty-foot equivalent unit (TEU) is Rteu, and the annual quantity of TEUs handled by the operating EV fleet is Nteu, transportation revenue is given by:

$$R_{op}=R_{teu}·N_{teu}+R_{carbon}$$

(11)

$$N_{teu}=365·{\displaystyle \frac{d_{day}}{d_{loop}}}=365·{\displaystyle \frac{\frac{T_{op}}{T_{{ev}_{op}}+T_{{ev}_{empty}}+T_{{ev}_{charging}}}·N_{ev}·B_{ev}·{SOC}_{ev}·\frac{V_{port}}{P_{{cons}_{{ev}_{op}}}}}{d_{loop}}}$$

(12)

The reduced carbon emissions can be monetized through carbon trading. The calculation formula is as follows:

$$R_{carbon}=\left(C_{{total}_{fcs}}-C_{{total}_{mcs}}\right)·R_{{carbon}_{trading}}$$

(13)

In this study, the carbon emission quota is calculated using the FCSs scheme’s carbon emissions as the baseline (C_{total_fcs}). The deployment of MCSs can increase the utilization of electric vehicles, thereby improving port transport efficiency and growing revenue. Therefore, the quantity of MCSs (N_mcs) and charging power (P_mcs) influence the transportation revenue.

$$C_{cap}=N_{ev}·C_{ev}+N_{mcs}·C_{mcs}+\left(N_{ev}·B_{ev}+N_{mcs}·B_{mcs}\right)·C_{battery}+C_{charger}$$

(14)

Maintenance cost assessments for different charging solutions reveal significant variations. FCSs incur maintenance costs primarily from the wear and tear of charging equipment, stability checks of grid interfaces, and anti-corrosion treatments for fixed infrastructure. These stations have a low maintenance frequency but higher unit costs, especially for high-voltage equipment. BSWSs involve higher costs due to the wear and tear on robotic arms and conveyors, health management of spare batteries (including capacity balancing and thermal runaway protection), and maintenance of specialized storage environments. The technological complexity of these systems results in maintenance costs that are considerably higher than those of FCSs, particularly for updates to battery management systems. MCSs, on the other hand, face maintenance costs for vehicle components, such as tires and power systems; optimizing onboard energy storage systems for seismic resilience; and frequent wear on charging interfaces. While maintenance occurs more frequently, the cost per maintenance session tends to be lower, focusing primarily on routine vehicle upkeep.

$$C_{op}=\beta ·C_{cap}$$

(15)

where β is the weighting coefficient, reflecting the maintenance costs differentiated across charging modalities, with FCSs, BSWSs, and MCSs assigned annual coefficients of 5%, 8%, and 6% of infrastructure investment, respectively. These values are assumed based on expected differences in maintenance complexity and operational requirements for each system.

2.3.4. Normalization of Output Metrics

In order to facilitate fair and transparent comparison between different configurations (MCSs, FCSs, BSWSs), the output metrics—specifically Net Present Value (NPV) and carbon emissions—are normalized based on the total TEU handling capacity. This ensures that the performance of each configuration is assessed on a per-unit basis (per TEU), allowing for more meaningful comparisons in large-scale port operations.

i.

Normalized NPV: This is computed by dividing the NPV by the total TEU throughput, yielding a normalized value that reflects the economic efficiency per unit of cargo handled.

ii.

Normalized Carbon Emissions: Similarly, carbon emissions are normalized by dividing total emissions by the total TEU throughput, enabling a fair comparison of carbon efficiency across different system configurations.

By normalizing these metrics, the study can objectively compare the trade-offs between environmental and economic performance in a consistent manner.

2.3.5. Constraints Decomposition

The model includes three types of physical and operational constraints to ensure the feasibility of the solution.

i.

Satisfying Charging Demand

$${\sum }_{i=1}^{N_{mcs}}{P}_{mcs}·{\eta }_{mcs}\ge N_{ev}·P_{{cons}_{{ev}_{op}}}$$

(16)

where η_mcs represents the proportion of the total output power of MCSs that can cover the real-time charging power demand, i.e., the proportion of the MCSs’ own operational time.

$${\eta }_{mcs}={\displaystyle \frac{T_{{mcs}_{op}}}{T_{{mcs}_{op}}+T_{{mcs}_{empty}}+T_{{mcs}_{charging}}}}$$

(17)

ii.

Satisfying Energy Storage Safety Limits

$${SOC}_{mcs}, {SOC}_{ev}\in \left[20\%, 80\%\right]$$

(18)

SOC_mcs and SOC_ev are the state of charge (SOC) of MCSs/EVs batteries, constrained to 20–80% to prevent deep discharge or overcharging. According to [32], adjusting the charging strategy, such as avoiding overcharging (limiting SOC below 80%) and preventing overdischarge (keeping SOC above 20%), can significantly reduce battery degradation.

iii.

Satisfying Charging Pile and Battery Capacity Limits

To achieve the rational allocation of charging infrastructure, the model introduces dual charging pile capacity constraints (Charging turnover rate constraint and Concurrent charging constraint) for the three types of solutions to ensure that the technical solution meets the physical limitations of actual operation: (1) Charging pile/battery turnover rate constraint (Strong constraint, severe penalty): The charging capacity must meet the daily maximum charging demand, with consideration given to redundancy design (redundancy coefficient 10%). (2) Concurrent charging constraint (Weak constraint, low penalty): To avoid charging queue congestion, the quantity of simultaneous charging devices during peak periods must not exceed the available charging pile capacity.

i.

For the MCSs solution

The operational energy consumption of EVs, P_{cons_ev_op_mcs}, is scaled from the baseline consumption P_{cons_ev_op} by a comparative ratio λ₁ (Equation (19)).

$$P_{{cons}_{{ev}_{{op}_{mcs}}}}=P_{{cons}_{{ev}_{op}}}·{\lambda }_1$$

(19)

In Equation (19), λ₁ is assumed to be 0.9, reflecting the operational energy consumption reduction due to the lighter vehicle mass in the MCSs configuration. This value is a simplifying assumption based on the relationship between vehicle weight and energy consumption, and it approximates a 10% reduction in energy consumption compared to FCSs and BSWSs. In Equation (20), the ‘np.ceil’ function rounds up to the nearest integer, ensuring the calculated quantity of daily charges is sufficient for operations.

$$T_{{cycle}_{mcs}}={\displaystyle \frac{B_{ev}·{SOC}_{ev}}{P_{{cons}_{{ev}_{{op}_{mcs}}}}}}$$

(20)

$$N_{{charge}_{{per}_{{day}_{mcs}}}}=np.ceil\left({\displaystyle \frac{T_{op}}{T_{{cycle}_{mcs}}}}\right)$$

(21)

$$N_{{charger}_{{mcs}_{pile}}}\ge \left(1+10\%\right)·{\displaystyle \frac{N_{mcs}·N_{{charge}_{{per}_{{day}_{mcs}}}}}{\frac{24}{B_{mcs}·\frac{{SOC}_{mcs}}{P_{fcs}}}}}$$

(22)

$$N_{{charger}_{{mcs}_{pile}}}\ge max \left(N_{mcs}·{\displaystyle \frac{T_{{mcs}_{charging}}}{T_{{mcs}_{op}}}},N_{{charge}_{{per}_{{day}_{mcs}}}}·{\displaystyle \frac{T_{{mcs}_{charging}}}{T_{op}}}\right)$$

(23)

ii.

For the FCSs charging pile:

$$T_{{cycle}_{fcs}}={\displaystyle \frac{B_{{ev}_{fcs}}·{SOC}_{ev}}{P_{{cons}_{{ev}_{op}}}}}$$

(24)

$$N_{{charge}_{{per}_{{day}_{fcs}}}}=np.ceil\left({\displaystyle \frac{T_{op}}{T_{{cycle}_{fcs}}}}\right)$$

(25)

$$N_{{charger}_{{fcs}_{pile}}}\ge \left(1+10\%\right)·{\displaystyle \frac{N_{ev}·N_{{charge}_{{per}_{{day}_{fcs}}}}}{\frac{24}{B_{{ev}_{fcs}}·\frac{{SOC}_{ev}}{P_{fcs}}}}}$$

(26)

$$N_{{charger}_{{fcs}_{pile}}}\ge max \left(N_{ev}·{\displaystyle \frac{T_{{ev}_{charging}}}{T_{{ev}_{op}}}},N_{{charge}_{{per}_{{day}_{fcs}}}}·{\displaystyle \frac{T_{{ev}_{charging}}}{T_{op}}}\right)$$

(27)

iii.

For the BSWSs Charging Battery:

$$T_{{cycle}_{bsws}}={\displaystyle \frac{B_{{ev}_{bsws}}·{SOC}_{ev}}{P_{{cons}_{{ev}_{op}}}}}$$

(28)

$$N_{{charge}_{{per}_{{day}_{bsws}}}}=np.ceil\left({\displaystyle \frac{T_{op}}{T_{{cycle}_{bsws}}}}\right)$$

(29)

$$N_{{charger}_{{bsws}_{battery}}}\ge \left(1+10\%\right)·{\displaystyle \frac{N_{ev}·N_{{charge}_{{per}_{{day}_{bsws}}}}}{\frac{24}{B_{{ev}_{bsws}}·\frac{{SOC}_{ev}}{P_{bsws}}}}}$$

(30)

P_bsws is the charging power provided by BSWSs to EVs, which is the same value as P_fcs.

$$N_{{charger}_{{bsws}_{battery}}}\ge max \left(N_{ev}·{\displaystyle \frac{T_{{ev}_{charging}}}{T_{{ev}_{op}}}},N_{{charge}_{{per}_{{day}_{bsws}}}}·{\displaystyle \frac{T_{{ev}_{charging}}}{T_{op}}}\right)$$

(31)

For the bi-objective optimization problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) performs exceptionally well. Wietheger et al. [33] demonstrate its effectiveness in solving bi-objective problems, while Rahimi et al. [34] highlight its strong performance in multi-objective scheduling tasks, including production and personnel scheduling. Therefore, this model framework employs NSGA-II to efficiently solve the bi-objective optimization problem.

2.4. Model Solution Process

The solution process for the model involves several key steps to efficiently optimize both economic and environmental objectives. Initially, the relevant parameters, such as vehicle operational characteristics, charging station capacities, and emission factors, are defined. Next, NSGA-II is employed to solve the bi-objective optimization problem. This algorithm iteratively evaluates potential solutions, ranks them based on Pareto dominance, and selects the best trade-offs between carbon emissions and NPV. The process is repeated across multiple generations, with the algorithm refining the solutions until the Pareto fronts are fully optimized. The result is a set of Pareto-optimal solutions that balance the trade-off between environmental impact and economic viability, enabling informed decision-making regarding the deployment of mobile charging stations.

The framework operates through two distinct comparative models:

i.

MCSs–FCSs Comparative Model: Evaluates MCSs against FCSs by calculating the relative Net Present Value (Δ_NPV = NPV_mcs − NPV_fcs) and carbon emission differentials (Δ_Emissions = C_{total_fcs} − C_{total_mcs});

ii.

MCSs–BSWSs Comparative Model: Assesses MCSs’ performance relative to BSWSs through analogous relative metrics (Δ_NPV = NPV_mcs − NPV_bsws; Δ_Emissions = C_{total_bsws} − C_{total_mcs}).

Initially, the relevant parameters are defined through scenario-specific configurations:

i.

For MCSs–FCSs comparisons: Vehicle dwell time patterns, fixed infrastructure CAPEX, and grid emission intensity;

ii.

For MCSs–BSWSs comparisons: Battery inventory costs, swapping time thresholds, and lithium-ion degradation factors.

The NSGA-II is then independently applied to both comparative models to solve their respective bi-objective optimization problems. This dual implementation enables parallel exploration of MCSs’ competitiveness relative to different baseline technologies. The algorithm iteratively evaluates potential solutions through three-phase optimization:

i.

Scenario Encoding: Generates population matrices representing charging station deployment schemes, with distinct gene structures for FCSs and BSWSs comparison scenarios;

ii.

Fitness Evaluation: Calculates Δ_NPV using discounted cash flow analysis and Δ_Emissions through life-cycle assessment (LCA) coefficients;

iii.

Constraint Handling: Applies dynamic penalty functions to maintain feasible solutions across both models’ operational constraints.

Dual Pareto fronts emerge from the optimization process: one quantifying the trade-offs between MCSs and FCSs, and another mapping the compromises between MCSs and BSWSs. The optimization employs the NSGA-II algorithm with a population size of 500 evolved over 200 generations. This study used simulated binary crossover with a probability of 0.8 and distribution index of 20.0, and polynomial mutation with a probability of 0.2, distribution index of 20.0, and independent mutation probability per attribute of 0.1. The evolutionary strategy follows the eaMuPlusLambda variant with μ = λ = 500. These parameter settings were determined through preliminary sensitivity analysis across adaptive crossover (0.6–0.9) and mutation rates (0.01–0.2) to maintain solution diversity and convergence. The models converge to optimized solution sets in which no objective (Δ_NPV or Δ_Emissions) can be improved without degrading the other.

To verify the stability of the optimization results, this study performed multiple independent runs of the NSGA-II algorithm with different random seeds. Across these runs, the overall shape, extent, and key trade-off characteristics of the obtained Pareto fronts were found to be consistent. While minor stochastic variations in the exact positioning of individual non-dominated solutions were observed, they did not alter the fundamental conclusions regarding the performance comparison of MCSs, FCSs, and BSWSs, or the identification of the critical reuse ratio threshold.

Cross-model validation is subsequently performed by comparing the relative positioning of MCSs in both Pareto spaces. This dual perspective enables a comprehensive assessment of MCSs deployment strategies across varying port operational paradigms, ultimately providing decision-makers with quantified evidence for technology selection based on specific environmental and economic priorities.

3. Results

The simulation results, derived from real-world operational data from Shenzhen Mawan Port, demonstrate the environmental and economic superiority of the MCSs system over FCSs and BSWSs. The ecological and economic performance of the MCSs system was evaluated under varying parameter combinations for both the MCSs–FCSs and MCSs–BSWSs comparative models. Key parameters, including the MCSs deployment ratio (ratio), MCSs unit cost (C_mcs), revenue per TEU (R_teu), and carbon trading price (R_{carbon_trading}), were systematically adjusted to assess their impacts on carbon emissions and net present value (NPV). Key findings are summarized below, supported by quantitative analysis and verification of Pareto optimality.

3.1. For the MCSs–FCSs Model

The shape of each front in Figure 3 is a downward-sloping trade-off between emissions and NPV. At low ratios (0–0.1), the front is long, allowing significant reductions in emissions at the expense of NPV. As the ratio increases, the front shifts upward (to a higher NPV for a given emission) and shortens. In particular, the ratio of 1.0 front collapses into a small set of high-NPV, high-emission points. This indicates that higher reuse tends to dominate lower-ratio solutions in a Pareto sense: for any given emission level within their overlap, a higher-ratio solution yields greater NPV. For example, at zero emissions, increasing the ratio from 0.1 to 0.5 raises the NPV from 6.6 × 10⁸ to 7.0 × 10⁸ CNY. Thus, the higher-ratio fronts enclose or outrank the lower ones in the trade-off space, except that full reuse yields no low-emission alternatives. In essence, increasing the ratio improves Pareto-optimal NPV across the board, demonstrating a substantial efficiency gain at the cost of higher emissions.

When the ratio is ≥10%, the optimal solution set for MCSs compared to the FCSs solution is positive in both NPV and carbon emission reduction, demonstrating overall superiority. Even when the ratio is zero (i.e., no reuse of queuing time for charging), most optimal MCSs solutions still show a positive NPV compared to the FCSs solution. This suggests that MCSs solution has a clear economic and carbon advantage.

3.2. For the MCSs–BSWSs Model

The simulation results are as follows:

As shown in Figure 4, the BSWSs fronts depicted in Figure 4 exhibit a consistent decrease. The fronts for 0.75–0.8 enclose those for 0–0.5: at any fixed emissions level, the higher-ratio front attains a higher NPV. The 1.0 ratio case again forms a tight cluster of high-emission, high-NPV points, effectively eliminating the trade-off. The shapes are comparable, though the BSWSs’ fronts are steeper due to the smaller NPV range. Overall, in both models, the Pareto fronts for larger ratios consistently dominate those for smaller ratios, indicating that reusing idle time is Pareto-improving for the economic objective (given higher emissions).

When the ratio is 80% or higher, the optimal MCSs solution outperforms the BSWSs solution across both NPV and carbon emission reduction, indicating overall superiority. When the ratio is 0 (meaning no reuse of queuing time for charging), most optimal MCSs solutions, compared to the BSWSs solution, display negative NPVs, suggesting their profitability is relatively limited.

3.3. Normalized Output Metrics

To facilitate a fair and transparent comparison between different configurations (MCSs, FCSs, BSWSs), the output metrics—specifically Net Present Value (NPV) and carbon emissions—are normalized based on the total TEU handling capacity. This ensures that the performance of each configuration is assessed on a per-unit basis (per TEU), providing more meaningful comparisons in large-scale port operations (see

Table 2. Normalized Results: MCSs–FCSs and MCSs–BSWSs.

System Comparison	ratio	Max Normalized ΔNPV (CNY/TEU)	Corresponding ΔEmissions (kg/TEU)	Max Normalized ΔEmissions (kg/TEU)	Corresponding ΔNPV (CNY/TEU)
MCSs vs. FCSs	0	5.4440	−0.0884	1.3625	0.9630
	0.25	5.4456	−0.0870	1.3783	0.8226
	0.5	5.7380	−0.0858	1.3699	2.6790
	0.75	6.0083	−0.0755	1.3625	4.5226
	1	6.4592	1.3416	1.3833	6.1218
MCSs vs. BSWSs	0	0.9889	3.6003	10.2675	−26.2053
	0.25	2.3152	3.6221	10.2621	−17.8831
	0.5	3.7149	3.6155	10.2765	−9.7459
	0.75	5.1160	3.6081	10.2557	−1.2597
	1	7.0639	10.2525	10.2718	6.9267

). By normalizing these metrics, the study allows for an objective evaluation of the trade-offs between environmental and economic performance across different system configurations.

The analysis of the normalized outputs reveals distinct trade-off patterns. In the MCSs vs. FCSs comparison, a critical finding is that prioritizing the maximum decarbonization benefit (Max Normalized Δ_Emissions) consistently yields a positive Δ_NPV across all reuse levels (0.82 to 6.12 CNY/TEU). This indicates that the operational configuration which makes MCSs most superior to FCSs in emission reduction is also economically beneficial, presenting a strong case for synergistic environmental and economic gains. When prioritizing maximum economic performance (Max Normalized Δ_NPV), MCSs maintain a decarbonization advantage (positive Δ_Emissions) only at the highest reuse level (ratio = 1). At lower reuse levels, maximum economic gain involves a slight emission penalty versus FCSs, though the economic benefit remains substantial.

The MCSs vs. BSWSs comparison demonstrates that MCSs hold a consistent and significant decarbonization advantage, with all Max Normalized Δ_Emissions values being strongly positive (~10.26–10.28 kg/TEU). However, achieving concurrent economic superiority is contingent upon the reuse level. A clear threshold exists between ratio 0.5 and 0.75. Below this threshold, the configuration yielding the greatest emission reduction results in a negative Δ_NPV, indicating an economic trade-off. Above this threshold, specifically at ratio = 1, the system achieves solutions where both primary objectives are positively met (e.g., Δ_Emissions = 10.27 kg/TEU, Δ_NPV = 6.93 CNY/TEU), enabling MCSs to outperform BSWSs comprehensively.

To assess the robustness of the model and identify key leverage points, a sensitivity analysis was performed to evaluate the influence of key economic and policy parameters on the relative performance of MCSs. The analysis focused on the capital expenditure (C_cap), the daily operational time of EVs (T_op), and the carbon trading price (R_{carbon_trading}). The results, presented in

Table 3. Sensitivity analysis of C_cap T_op and R_{carbon_trading} for the MCSs–FCSs model.

Parameter	Sensitivity Level	Normalized ΔNPV (CNY/TEU)	Normalized ΔEmissions (kg/TEU)
Ccap (+50%)	Low impact	−0.27%	+0.43%
Ccap (−50%)	Low impact	+0.74%	−0.03%
Top (+50%)	Medium impact	−6.45%	+3.65%
Top (−50%)	Medium impact	+11.52%	−9.49%
Rcarbon_trading (+50%)	Medium impact	+6.05%	+3.65%
Rcarbon_trading (−50%)	Medium impact	−6.10%	−4.58%

, quantify the impact of a ±50% variation in each parameter on the normalized Δ_NPV and Δ_Emissions of MCSs relative to the FCS baseline.

The analysis reveals distinct response patterns. The model exhibits low sensitivity to the capital expenditure (C_cap). A substantial ±50% change in upfront costs results in minimal fluctuations (≤1%) in both economic and environmental performance metrics. This suggests that the long-term viability and competitive advantage of MCSs are not predominantly determined by the initial investment but are more dependent on operational factors.

Conversely, the system demonstrates moderate sensitivity to operational intensity and carbon policy. A 50% increase in daily EV operational time (T_op) reduces the relative economic benefit (Δ_NPV) of MCSs by 6.45% and slightly diminishes their emission advantage (Δ_Emissions changes by +3.65%, indicating a reduction in the emission reduction benefit). This highlights that under extremely high utilization scenarios, the operational efficiency gains of MCSs may be partially offset. Most notably, the model is significantly responsive to the carbon trading price (R_{carbon_trading}). A 50% increase in the carbon price enhances the relative economic attractiveness of MCSs (Δ_NPV) by 6.05%, concurrently strengthening their emission reduction advantage (Δ_Emissions increases by 3.65%). This symmetric response confirms that carbon pricing mechanisms effectively internalize the environmental benefit of MCSs, translating lower emissions directly into improved financial performance.

In summary, the normalized metrics and sensitivity analysis collectively demonstrate the context-dependent advantages of MCSs. Compared to FCSs, MCSs can achieve both decarbonization and economic gains, especially under configurations that prioritize emission reduction. Against BSWSs, MCSs consistently offer a definitive emissions reduction benefit, with economic competitiveness becoming robust once operational reuse efficiency exceeds a critical threshold. Furthermore, the economic-environmental performance of MCSs shows low sensitivity to capital cost variations but is significantly influenced by operational parameters and carbon pricing. These quantified insights provide a clear, scenario-aware evidence base for port infrastructure planning.

4. Discussion

The findings demonstrate that the reuse ratio of crane idle time emerges as a decisive factor shaping both environmental and economic outcomes of MCSs deployment. On the one hand, higher reuse consistently improves financial performance, particularly in the MCSs–FCSs model, where net present values are maximized under full utilization. On the other hand, the same strategy drives the systems into a high-emission regime, eliminating low-carbon alternatives and reducing operational flexibility. This dual effect highlights a fundamental trade-off: efficiency gains and profitability are achieved at the expense of sustainability. Moreover, the nonlinear response, where system performance changes little at low reuse ratios but shifts dramatically once reuse exceeds 50%, underscores the importance of careful calibration rather than simple reuse maximization.

4.1. Main Findings and Mechanism Explanation

Across both models (MCSs–FCSs and MCSs–BSWSs), a clear trade-off emerges between environmental and economic performance as the reuse ratio of crane idle time increases. On the ecological side, higher reuse ratios consistently increase total carbon emissions. For MCSs–FCSs, emissions range from 4.23 × 10⁶ kg CO₂ at low reuse (0–0.1) to a uniform level of about 8.24 × 10⁶ kg CO₂ at full reuse, eliminating low-emission solutions. A similar trend appears in MCSs–BSWSs: emissions increase from nearly zero to 1.10 × 10⁷ kg CO₂ at low reuse, rising to approximately 1.38 × 10⁷ kg CO₂ at full reuse. In both cases, greater reuse compresses the Pareto fronts into a high-emission region.

Economically, the opposite pattern holds. For MCSs–FCSs, NPV increases substantially with reuse: from a maximum of 6.60 × 10⁸ CNY at low ratios to 7.94 × 10⁸ CNY at full reuse. At the same time, the minimum attainable NPV also rises, indicating consistently more substantial returns. The MCSs–BSWSs model shows the same direction of change, though at much lower magnitudes: from 0.30 × 10⁸ CNY at a ratio of 0 to 1.88 × 10⁸ CNY at full reuse. The scale difference is striking: even with full reuse, BSWSs’ NPVs remain one order of magnitude smaller than FCSs-based outcomes.

Taken together, these findings indicate a fundamental mechanism: maximizing idle-time reuse drives the system toward uniformly higher emissions while yielding larger and more stable economic gains. Between the two designs, MCSs–FCSs is markedly more profitable than MCSs–BSWSs at comparable environmental cost. This trade-off motivates the sensitivity analysis that follows.

The binding constraints within the system shift distinctly with the reuse ratio. At low reuse ratios (e.g., <0.5), the limiting factor is the available charging time during vehicle queues, activating the charging demand coverage constraint. In this scenario, more MCS units or larger EV batteries are often needed to meet the charging demand. In contrast, at high reuse ratios (e.g., >0.75), the system becomes constrained by the MCS’s own energy supply. The battery capacity and charging power limits of the MCS become the bottleneck, as MCSs must frequently return for recharging, limiting their ability to continue servicing EVs despite the improved scheduling efficiency.

4.2. Sensitivity Analysis

4.2.1. Small vs. Large Changes

The Pareto fronts are largely insensitive to small changes in the ratio. In MCSs–FCSs, increasing the ratio from 0 to 0.10 scarcely alters the frontier: the three curves almost coincide, indicating that performance remains essentially unchanged until the ratio rises substantially. A similar pattern appears in MCSs–BSWSs: the fronts for ratios of 0 and 0.5 are still comparable. However, once the ratio crosses a threshold (0.5–0.75), the fronts shift noticeably upward.

4.2.2. Nonlinear Effect

The jump from medium ratios (0.5–0.8) to full reuse (1.0) is dramatic. The diversity of solutions collapses, and NPV peaks sharply. This suggests a diminishing sensitivity in the mid-range: most of the gain occurs after a certain point. Thus, the objectives exhibit a nonlinear response: small increases in reuse have little effect, but high reuse greatly improves NPV (and raises emissions). Decision-makers should note this threshold effect.

Cross-Model Comparison: Both models exhibit this sensitivity, where low ratios (0–0.1) and high ratios (0.5–1.0) produce two distinct regimes. However, MCSs–FCSs shows a larger absolute jump in NPV as the ratio increases. The BSWSs model exhibits a steady rise from 0.5 to 0.8, followed by a spike at 1.0. In summary, Pareto fronts are relatively stable at low reuse levels but become much more favorable (economically) once reuse exceeds 50–75%.

4.2.3. Depth-of-Discharge (DoD) Sensitivity

To assess the robustness of MCSs’ performance, a sensitivity analysis was conducted by varying the allowable Depth-of-Discharge (DoD) from 40% to 60%. This analysis examines how DoD influences the relative economic and environmental advantages of MCSs over FCSs and BSWSs under five reuse-ratio scenarios (0, 0.25, 0.5, 0.75, and 1). Results are summarized in

Table 4. Sensitivity analysis of DoD (40–60%) for the MCSs–FCSs model.

DoD (%)	ratio	ΔNPV (×108 CNY)	ΔEmissions (×106 kg)
40	0	5.95	3.92
	0.25	6.30	3.96
	0.50	6.66	4.00
	0.75	7.03	4.08
	1	7.54	7.70
50	0	5.20	4.15
	0.25	5.56	4.19
	0.50	5.92	4.21
	0.75	6.29	4.25
	1	6.81	8.02
60	0	6.33	4.23
	0.25	6.70	4.26
	0.50	7.06	4.30
	0.75	7.43	4.35
	1	7.94	8.24

and

Table 5. Sensitivity analysis of DoD (40–60%) for the MCSs–BSWSs model.

DoD (%)	ratio	ΔNPV (×108 CNY)	ΔEmissions (×106 kg)
40	0	1.40	8.00
	0.25	1.77	8.03
	0.50	2.14	8.18
	0.75	2.50	8.20
	1	3.01	12.20
50	0	0.85	8.75
	0.25	1.23	8.77
	0.50	1.58	8.80
	0.75	1.95	8.92
	1	2.46	13.00
60	0	0.30	9.30
	0.25	0.66	9.31
	0.50	1.03	9.32
	0.75	1.39	9.40
	1	1.88	13.80

.

In the MCSs–FCSs comparison (shown in Table 4), increasing DoD from 40% to 60% has mixed effects on Δ_NPV. At lower ratios (0, 0.25), Δ_NPV fluctuates, while at higher ratios (0.5, 0.75, 1), Δ_NPV increases, especially at ratio = 1.0 (7.54 × 10⁸ to 7.94 × 10⁸ CNY, a 5.3% improvement). In contrast, Δ_Emissions consistently increase with higher DoD values. For example, at ratio = 0.5, emissions rise from 4.00 × 10⁶ kg (DoD = 40%) to 4.30 × 10⁶ kg (DoD = 60%), indicating a 7.5% increase.

In the MCSs–BSWSs comparison (shown in Table 5), a clear inverse relationship is seen between DoD and Δ_NPV. As DoD increases, Δ_NPV decreases, with a 52% drop at ratio = 0.5 (from 2.14 × 10⁸ to 1.03 × 10⁸ CNY). However, it is important to note that while Δ_NPV does decrease, MCSs still outperform BSWSs economically at all DoD levels, but the magnitude of this advantage narrows as DoD increases. For instance, at ratio = 0, emissions rise from 8.00 × 10⁶ kg (DoD = 40%) to 9.30 × 10⁶ kg (DoD = 60%), reflecting a 16% increase, indicating that deeper discharge cycles impact environmental outcomes more strongly than economic ones in this scenario.

The negative impacts of higher DoD are partially mitigated by increasing reuse ratios. For instance, in the MCSs–BSWSs model, at DoD = 60%, increasing the ratio from 0 to 1.0 improves Δ_NPV from 0.30 × 10⁸ CNY to 1.88 × 10⁸ CNY, demonstrating that optimal time utilization can compensate for the negative economic effects of deeper discharge cycles.

This analysis suggests that the optimal DoD setting depends on the specific context and objectives. In the MCSs–FCSs context, DoD = 60% generally improves both economic and environmental outcomes, particularly at higher reuse ratios. In contrast, in the MCSs–BSWSs context, lower DoD values (40–50%) tend to favor economic performance (Δ_NPV), while DoD = 60% may be acceptable when the priority is carbon reduction (Δ_Emissions), although it results in a decrease in economic advantage.

Overall, this sensitivity analysis highlights the importance of considering both economic and environmental trade-offs when selecting DoD values, as well as the role of higher reuse ratios in mitigating some of the economic impacts associated with deeper discharge cycles.

4.3. Limitations and Social-Governance Aspects

This study focused on the environmental and economic dimensions of port electrification, establishing a carbon-efficiency trade-off framework. A recognized limitation is the exclusion of social (S) and governance (G) assessments from the ESG triad, due to current data and modeling scope constraints. A qualitative consideration of these dimensions suggests potential influences on our findings:

4.3.1. Social (S) Factors

Social factors, such as the health benefits from reduced local emissions and improved worker safety, could be monetized as positive externalities. If incorporated, they would enhance the economic attractiveness of low-carbon MCSs solutions, potentially shifting the Pareto frontier in their favor.

4.3.2. Governance (G) Factors

Governance factors, such as stakeholder coordination costs and new regulatory compliance, could introduce additional implementation burdens. Internalizing these costs may marginally increase the upfront cost of MCSs adoption, possibly affecting short-term technology choices.

While these S&G factors could modulate the precise position of the critical reuse ratio threshold identified in this study, the fundamental trade-off structure remains robust. Future research should aim to integrate quantified S&G indicators to provide a holistic sustainability assessment of port electrification pathways.

5. Conclusions

This study proposes a unified bi-objective framework that compares MCSs, FCSs, and BSWSs under a carbon-efficient recharging paradigm, integrating operational electricity and embedded battery emissions with NPV within a single port-specific decision system. The analysis shows that MCSs outperform FCSs once idle-time reuse is available and rises quickly with higher reuse; against BSWSs, MCSs deliver conditional advantages that emerge only at sufficiently high reuse. A salient, nonlinear threshold around reuse 0.5–0.75 shifts the system from carbon-conserving to profit-maximizing regimes, where low-emission solutions rapidly disappear, revealing an intrinsic efficiency-carbon trade-off that should be tuned rather than maximized.

Furthermore, the sensitivity analysis underscores that key parameters like the Depth-of-Discharge (DoD) introduce additional trade-offs, emphasizing the need for context-specific calibration of operational strategies.

To provide actionable decision rules for port authorities, this study defines the reuse ratio thresholds at which MCSs deliver superior performance on both economic (Δ_NPV > 0) and environmental (Δ_Emissions > 0) fronts compared to baseline solutions. Against FCSs, MCSs achieve dual-objective dominance at a reuse ratio of ≥10%. At and above this threshold, the Pareto-optimal solutions for MCSs yield both higher NPV and greater carbon reduction than FCSs. For instance, at a reuse ratio of 0.5, typical Δ_NPV and Δ_Emissions values are on the order of 7.0 × 10⁸ CNY and 4.0 × 10⁶ kg CO₂, respectively (see Section 4.2.3). Against BSWSs, a higher reuse ratio of ≥80% is required for MCSs to dominate on both objectives. As the results indicate, beyond this point, MCSs outperform BSWSs in both net present value and emissions reduction. At a reuse ratio of 0.8, representative Δ_NPV and Δ_Emissions can reach ~2.5 × 10⁸ CNY and ~8.2 × 10⁶ kg CO₂, respectively. These specific thresholds (10% and 80%) offer clear operational guidance: ports capable of reusing even a small fraction (≥10%) of crane idle time for charging should prefer MCSs over FCSs; to also surpass BSWSs, a greater commitment to operational integration (≥80% reuse) is needed.

In practice, our framework produces deployable configurations. It provides a clear basis for selecting among MCSs/FCSs/BSWSs based on priorities of carbon versus profit, land/grid constraints, and achievable reuse. It can be ported to other terminals to support transparent, carbon-informed electrification decisions.

To support the practical application and portability of this framework, it is important to acknowledge its principal abstractions, which include assuming a stable grid supply, simplified vehicle energy consumption profiles, and the exclusion of stochastic operational disturbances. To rerun the NSGA-II optimization experiments for another port terminal and obtain site-specific insights, key inputs are required: (1) operational data (e.g., vehicle routes, speeds, task schedules, and effective daily hours); (2) technical parameters (e.g., EV energy consumption, available battery capacities, and charging efficiencies); and (3) local economic and environmental factors (e.g., equipment costs, electricity price, grid carbon factor, and carbon trading price). Providing these inputs enables the reproduction of the Pareto-front analysis and the generation of deployable configurations, thereby offering a transparent and adaptable decision-support tool for carbon-efficient electrification planning across diverse port environments.

Looking ahead, this research opens several pathways for extension. Future work could explore hybrid infrastructures that incorporate direct grid-connected charging systems (e.g., overhead catenaries or conductive rails), which theoretically enable in-motion or queue-time charging. Evaluating the trade-offs between such capital-intensive fixed infrastructures and the flexible MCSs solution presented here, particularly in terms of upfront investment, operational adaptability, and integration into existing port ecosystems, represents a critical next step for the field of port electrification.