1. Introduction: The Green Route Challenge

The International Maritime Organization (IMO) now requires a 40% carbon-intensity cut by 2030 (MEPC.377(80)) (IMO, 2023) while the European Union has extended its Emissions Trading System (EUETS) to ocean shipping, phasing-in 100% coverage for voyages to, from and inside the EU by 2026 (Directive 2023/959). These converging policies expose China Merchants Group (CMG) to rising carbon costs on its bulk and multi-purpose (MPP) services between China and North-west Europe and on a prospective 24k TEU container relaunch after 2028 (China Merchants Port Holdings Company Limited (2023).

The research question is therefore: Which staged adoption of low-/zero-carbon fuels minimises CMG's life-cycle cost while meeting the 2030 ETS/IMO constraints under fuel-price, carbon-price, and technology uncertainties?

We answer this by coupling a feedback-rich system-dynamics (SD) core to a mixed-integer linear programme (MILP). Section 2 outlines the model; Section 3 applies it to CMG's fleet; Section 4 derives industry collaboration mechanisms; Section 5 synthesises strategic recommendations.

2. Method: Hybrid SD-MILP Model

2.1 Architecture

Figure 1 shows a two-layer structure. The SD layer tracks: (i) fleet stock by vintage, (ii) cumulative alternative-fuel power, and (iii) bunkering-infrastructure maturity; endogenous feedback capture learning-curve CAPEX erosion and fuel-infrastructure delay. The MILP layer selects retrofit timing, new-build orders, fuels, and sailing speeds to minimise discounted cost. Stocks at year t act as state constraints for decision variables at t+1, providing full optimisation over the dynamic state space—an advance on static or scenario studies.

Figure 1. SD-MILP Model Architecture

2.2 Key Equations

Fleet stock: \begin{equation} N_{s,t+1} = N_{s,t} + A_{s,t} - R_{s,t} \end{equation}(1)

\begin{equation} N_{s,t+1}  \end{equation}: Number of ships in cohort s at the start of year t+1; unit: vessels; role: state variable. s: Ship cohort index (vintage × size class); set S (e.g., Capesize, MPP, optional 24k TEU container). t: Year index; set T = {2022, …, 2035}; unit: year; role: index.

\begin{equation} N_{s,t} \end{equation}: Number of ships in cohort s at the start of year t; unit: vessels; role: state variable.

\begin{equation} A_{s,t} \end{equation}: Newbuild arrivals into cohort s during year t; unit: vessels/year; role: decisiondependent flow.

\begin{equation} R_{s,t} \end{equation}: Retirements (or removals) from cohort s during year t; unit: vessels/year; role: endogenous/exogenous outflow.
Installed power:\begin{equation} P_{f,t+1} = P_{f,t} + \sum_{s} (\alpha_{s,f,t} + \beta_{s,f,t}) \end{equation}(2)

\begin{equation} P_{f,t+1} \end{equation}: Cumulative installed propulsion power using fuel f at the start of year t+1; unit: MW; role: state variable. f: Fuel/propulsion option index; set F = {VLSFO, LNG, MeOH (methanol), NH3 (ammonia)}; role: index.

\begin{equation} P_{f,t} \end{equation}: Cumulative installed propulsion power using fuel f at the start of year t; unit: MW; role: state variable.

\begin{equation} \alpha_{s,f,t} \end{equation}: Newbuildinstalled propulsion power for fuel f in cohort s during year t; unit: MW/year; role: decision variable.

\begin{equation} \beta_{s,f,t} \end{equation}: Retrofitinstalled propulsion power for fuel f in cohort s during year t; unit: MW/year; role: decision variable.
Infrastructure: \begin{equation} B_{f,t+1} = B_{f,t} + \gamma_f P_{f,t} - \delta_f B_{f,t} \end{equation}(3)

\begin{equation} B_{f,t+1} \end{equation}: Bunkering availability (infrastructure) index for fuel f at the start of year t+1; unit: index (0–1 or 0–B_fmax); role: state variable.

\begin{equation} B_{f,t} \end{equation}: Bunkering availability index for fuel f at the start of year t; unit: index; role: state variable.

\begin{equation} \gamma_f \end{equation}: Learning/scale coefficient linking installed power to infrastructure buildout for fuel f; unit: index units per MW (per year); role: parameter.

\begin{equation} P_{f,t} \end{equation}: Cumulative installed propulsion power using fuel f at the start of year t; unit: MW; role: state variable (reused).

\begin{equation} \delta_f \end{equation}: Depreciation/decay coefficient for fuelspecific infrastructure; unit: fraction/year; role: parameter.
Objective:

\begin{equation}
\begin{aligned}
minZ = \sum_{t=2022}^{2035} \frac{1}{(1 + i)^{t-22}} \Bigg[ &\sum_{s, f} \left( C_{f,t}^{fuel} + p_t^{EUA} EF_f K_r \right) F_{s,f,t} \\
&+ \sum_{s, f} \left( C_{s,f}^{NB} \alpha_{s,f,t} + C_{s,f}^{retro} \beta_{s,f,t} \right) + OPEX_{s,t} \Bigg]
\end{aligned}
\end{equation}(4)

\begin{equation} C_{f,t}^{fuel} \end{equation}: Unit fuel price for fuel f in year t; unit: USD/ton (or USD/GJ if energybased accounting is used consistently); role: parameter.

\begin{equation} p_t^{EUA} \end{equation}: EU Emissions Trading System allowance price in year t; unit: USD per tCO2 (if quoted in EUR, converted at annual average rate); role: parameter.

\begin{equation} EF_f \end{equation}: Welltowake greenhousegas emission factor of fuel f; unit: tCO2 per ton of fuel (or tCO2/GJ if energybased); role: parameter.

\begin{equation} K_r \end{equation}: EUETS coverage coefficient for voyage leg category r (e.g., 0 for nonEU leg, 0.5 for extraEU in/out leg, 1 for intraEU leg). In the compressed formulation \begin{equation} K_r \end{equation} represents the routeaverage coverage factor; unit: dimensionless; role: parameter. r: Voyageleg category index (e.g., EU segment, extraEU segment); set R; role: index (appears only through\begin{equation} K_r \end{equation}).

\begin{equation} F_{s,f,t} \end{equation}: Annual fuel consumption of cohort s using fuel f in year t; unit: tons/year (or GJ/year if energybased); role: endogenous variable derived from speed, power, hours, and efficiency.

\begin{equation} C_{s,f}^{NB} \end{equation}: Specific newbuild capital expenditure for cohort s configured for fuel f, per unit installed power; unit: USD/MW; role: parameter.

\begin{equation} \alpha_{s,f,t} \end{equation}: Newbuildinstalled propulsion power for fuel f in cohort s during year t; unit: MW/year; role: decision variable (reused).

\begin{equation} C_{s,f}^{retro} \beta_{s,f,t} \end{equation}: Specific retrofit capital expenditure for cohort s converting to fuel f, per unit installed power; unit: USD/MW; role: parameter.

\begin{equation} \beta_{s,f,t} \end{equation}: Retrofitinstalled propulsion power for fuel f in cohort s during year t; unit: MW/year; role: decision variable (reused).

\begin{equation} OPEX_{s,t} \end{equation}: Nonfuel operating expenditure for cohort s in year t (e.g., crew, maintenance, insurance, lube oils); unit: USD/year; role: parameter or semiendogenous variable (may depend on speed and technology in implementation).

2.3 Data & Calibration

1. AIS data for fourteen CMG Capesize and MPP ships (2022–2024, 12Hz) yield average China–EU round-trip distance 21,150nm and modal speed 15.2kn.
2. Fuel baselines (2024): VLSFO 620USD t-1; LNG 950; green methanol 1,380; green ammonia 1,590 (Sun et al., 2024).
3. Carbon price: base path 110€/t rising to 150€/t by 2030; shock path to 250€/t after 2028 (Wang et al., 2023) .
4. Discount rate 3.5% (CMG annual report 2023); yard-CAPEX ceiling 80M USD yr-1.
5. Gurobi 10.0 solves the MILP (≈ 7,200 binaries) and exchanges state variables with the SD module at each step.

3. CMG Case Study: Vessel-Fuel Optimisation

3.1 Scenarios

Four pathways are assessed for the existing bulk/MPP fleet plus a hypothetical 24k TEU ship delivered 2028:

• P0 – VLSFO business-as-usual
• P1 – LNG dual-fuel retrofit 2026 → stay LNG
• P2 – LNG 2026 → green methanol 2028
• P3 – Methanol 2028 → ammonia-ready new-build 2030+

All comply with TRL≥8 and CII≤0.60 by 2030.

3.2 Cost & Emission Results

Figure 2 shows discounted cost frontiers. Under the base carbon path, P2 yields a 6% lower net present value (NPV) than P1 and 12% below P0; under the Carbon-Shock path the NPV gap widens to 14%. Cumulative well-to-wake emissions (Figure 3) fall 53% by 2030 in P2 and 61% in P3, exceeding IMO's 40% target.

Figure 2. Discounted Cost Frontiers

Figure 3. Cumulative Well-to-wake Emissions

A sensitivity tornado (Table 1) reveals that EUA price volatility explains 49% of NPV variance, green-methanol bunker price 23%, and retrofit CAPEX 12%. Monte-Carlo runs (10,000 draws) show P2 outperforms P1 in 87% of cases.

Table 1. Drivers of NPV Variance (Tornado Decomposition, 10 000 Monte-Carlo draws)

Rank	Uncertainty Parameter	Range Tested	Contribution to NPV Variance
1	EUA price, 2026-30	90–250€/t (triangular)	49%
2	Green-methanol bunker price	1,100–1,600USD t⁻¹	23%
3	LNG retrofit CAPEX	220–320USDkW⁻¹ (triangular)	12%
4	Discount rate (WACC)	2.5–5.0%	7%
5	Annual demand growth	0–3% p.a.	5%
6	Yard-slot availability	60–100M USD yr⁻¹	4%

Statistical method: Pearson regression on normalised rank-order outputs.
Sum≈100%; minor rounding differences.

3.3 Operational Insights

1. Optimal service speed shifts from 14.8kn (P0) to 15.5kn (LNG phase) and drops to 13.9kn during a simulated LNG price spike—echoing the speed-cost trade-off mapped by Sun et al. (2025).
2. The yard-CAPEX ceiling limits LNG retrofits to three hulls per year; backlog inflates marginal abatement cost by 18€/t CO2 unless CMG coordinates across subsidiaries.
3. If ammonia TRL-8 slips to 2033 ("Tech-Bottleneck"), P2 still beats LNG-only by 4% NPV, confirming the robustness of the methanol bridge fuel.

4. Industry Pathway: Collaboration & Trust

4.1 Shared Infrastructure & R&D

SD feedback shows that bunkering-availability delay critically shapesadoption timing: bringing green-methanol facilities online at Rotterdam, Algeciras and, Ningbo by 2028 reduces CMG's total cost by 7%. We propose a Green-Belt Alliance—CMG plus charterers and fuel producers—to pool demand (≥0.8Mt yr-1) and unlock a 12% CAPEX learning effect, consistent with the retrofit-dominant roadmap in Zhao et al. (2023) and fleet-age optimisation in Wu et al. (2022).

4.2 Risk-Pooling & Carbon-Price Hedging

A group-wide EUA-futures desk could hedge 70% of exposure; simulations cut annual bunker-budget volatility by 40%. A collar-and-swap structure referencing EU Allowances lowers the 90th-percentile NPV downside by 5% (Wang et al, 2023).

4.3 Governance & Trust

Joint verification of well-to-wake life-cycle data, audited to ISO 14083, addresses cargo-owner Scope-3 concerns and trims green-finance spreads by 5bp. Transparent MRV strengthens stakeholder trust and accelerates the learning loop in the SD core.

5. Conclusions & Strategic Recommendations

1. Optimal pathway: LNG retrofit (2026) followed by green-methanol conversion (2028) delivers a 50%+ emission cut and 6-14% NPV gain versus LNG-only, even if ammonia slips beyond 2030.
2. Key uncertainties: EUA price and e-fuel cost account for >70% of value at risk; proactive hedging and offtake contracts are therefore essential.
3. Infrastructure collaboration: A Green-Belt Alliance that co-invests in methanol/ammonia bunkering removes the infrastructure-delay penalty and captures 12% CAPEX learning.
4. Policy message: Stable, forward EU-ETS price corridors and fast-tracked safety codes for ammonia will reduce the discount-rate penalty on zero-carbon assets.
5. Next research: integrate real-time port-congestion dynamics and multi-carrier competition into the SD-MILP platform.

The hybrid framework offers a transferable blueprint for carriers navigating the turbulent 2020s decarbonization landscape while anchoring decisions in rigorous, feedback-aware optimisation.