An Integrated Optimization Framework for LNG Maritime Transportation in India: Fleet and Route Allocation Considering Boil-Off Gas Management, Energy Efficiency, Carbon Emissions, and Operational Costs

 

1.Introduction
Liquefied natural gas (LNG) has become an important component of India's natural-gas supply system [1]. The expansion of LNG imports has been accompanied by investment in receiving and regasification infrastructure along India's western, eastern, and southern coasts[2]. According to India's Petroleum and Natural Gas Regulatory Board (PNGRB) [3], the country had eight operational onshore LNG terminals with a combined regasification capacity of approximately 52.7 million tonnes per annum. These facilities include Dahej, Hazira, Dabhol, Kochi, Ennore, Mundra, Dhamra, and Chhara [4].
The scale of India's LNG market creates a corresponding requirement for efficient maritime transportation. Data reported through India's petroleum-sector statistical system indicate LNG imports of approximately 35,720 million standard cubic metres in fiscal year 2024–25, compared with 31,795 million standard cubic metres in 2023–24 [5]. The geographical distribution of receiving terminals also means that imported LNG may enter the country through substantially different maritime routes, creating a fleet-assignment problem involving voyage distance, sailing time, vessel capacity, port characteristics, and cargo-delivery requirements [6].
LNG maritime transportation differs fundamentally from the transportation of many conventional bulk commodities because LNG is maintained at cryogenic temperatures and experiences continuous evaporation during storage and transportation [7]. The resulting boil-off gas (BOG) must be managed throughout the voyage [8]. Depending on vessel configuration and operating conditions, BOG can be consumed as propulsion fuel, reliquefied, combusted, or otherwise managed [9]. Research on LNG-carrier propulsion has emphasized the close relationship between propulsion-system design and BOG utilization [10,11].
The generation of BOG creates a particularly important optimization problem [12]. A vessel operating at relatively low speed may require less propulsion energy, but the longer voyage duration can increase cumulative cargo evaporation [13]. Conversely, increasing sailing speed can shorten voyage duration but increase instantaneous propulsion-fuel demand. If naturally generated BOG is insufficient to support the selected speed, additional LNG may have to be deliberately vaporized to generate forced BOG [14]. This can increase propulsion availability but simultaneously reduce the quantity of LNG ultimately delivered to the receiving terminal [15].
Consequently, sailing speed should not be treated as an independent operational variable. It interacts with [16,17]:
    voyage duration;
    BOG generation;
    forced vaporization;
    propulsion-fuel demand;
    cargo losses;
    delivered LNG quantity;
    energy consumption;
    carbon emissions;
    port and voyage costs; and
    fleet requirements.
This interaction becomes even more important under the current decarbonization framework for international shipping [18]. The International Maritime Organization's 2023 GHG Strategy established an ambition for international shipping to reach net-zero GHG emissions by or around 2050 and introduced indicative 2030 and 2040 emission-reduction checkpoints [19]. It also calls for substantial reductions in carbon intensity and increased uptake of zero- and near-zero-GHG technologies and fuels [20].
Furthermore, the implementation of EEXI and CII has strengthened the operational importance of vessel energy efficiency and carbon intensity [21]. Since 2023, ships have been subject to requirements concerning attained EEXI and annual operational CII calculations [22].
These developments suggest that an LNG shipping company can no longer evaluate fleet deployment exclusively through direct monetary cost [23]. An operational plan may appear inexpensive while generating higher fuel consumption, greater cargo loss, and higher carbon emissions. Therefore, a more comprehensive optimization framework is required [24].
1.1 Research gap
Previous studies on fleet deployment have generally concentrated on minimizing transportation cost, improving fleet utilization, or incorporating environmental constraints. Other studies have examined sailing-speed optimization and LNG-carrier propulsion systems separately. Research on BOG has also investigated reliquefaction, propulsion utilization, and thermodynamic management. However, these dimensions are frequently treated independently.
The principal research gap addressed in this study is therefore the lack of an integrated decision framework that simultaneously connects:
 
This study extended the conventional LNG fleet-allocation problem by incorporating these interdependencies into an integrated optimization model applied to India's LNG maritime transportation network.
1.2 Research objectives
The study has six principal objectives:
    To develop an LNG maritime fleet-allocation model for India's import transportation network.
    To incorporate BOG generation and utilization into fleet and route decisions.
    To jointly optimize loaded and ballast sailing speeds.
    To quantify the effect of sailing speed on LNG cargo losses and delivery quantity.
    To integrate energy efficiency and carbon emissions into the optimization framework.
    To examine the sensitivity of optimal fleet and route decisions to LNG prices, charter rates, demand, carbon prices, and BOG generation rates.
1.3 Research contributions
The study contributes to the literature in four ways.
First, it develops an integrated fleet-route-speed-BOG optimization model rather than treating these decisions separately.
Second, it introduces energy efficiency and carbon emissions into the traditional economic optimization framework.
Third, it explicitly incorporates the value of LNG cargo lost through BOG generation, thereby connecting thermodynamic losses with transportation economics.
Fourth, the study applied the integrated optimization model to India's LNG maritime transportation network, accounting for geographically dispersed receiving terminals and variations in import requirements.
2. Indian LNG Maritime Transportation Context
India's LNG infrastructure has developed from a small number of western-coast terminals into a geographically dispersed network. PNGRB reports eight operational LNG terminals with approximately 52.7 MMTPA of combined capacity [25].

Terminal    Location    Capacity (MMTPA)
Dahej    Gujarat    17.5
Hazira    Gujarat    5.2
Dabhol    Maharashtra    5.0
Kochi    Kerala    5.0
Ennore    Tamil Nadu    5.0
Mundra    Gujarat    5.0
Dhamra    Odisha    5.0
Chhara    Gujarat    5.0
Total    India    52.7
Table (1), Source: https://www.bharatpetroleum.in/images/files/lng-terminals.pdf 
The variation in utilization is particularly relevant to optimization. PNGRB reports substantially different utilization rates across terminals, with Dahej operating at a much higher utilization level than several other facilities [26].
This heterogeneity was incorporated into the maritime transportation optimization analysis. Vessel allocation accounted for the following demand, capacity, operational, and cost variables:

• terminal demand;
• vessel capacity;
• route distance;
• port turnaround time;
• sailing speed;
• BOG generation;
• cargo loss;
• energy consumption;
• carbon intensity;
• charter costs;
• port costs; and
• carbon-related costs.
3. Problem Description
Consider an LNG shipping company serving several Indian LNG receiving terminals.
The company owns a heterogeneous fleet of LNG carriers. Each vessel type differs in:
    cargo capacity;
    economic speed;
    maximum speed;
    fuel consumption;
    BOG generation rate;
    annual available operating days;
    charter cost;
    carbon-emission characteristics.
The company must determine:
    which vessel should serve each route;
    how many voyages each vessel should perform;
    the sailing speed for each voyage;
    how BOG should be managed;
    how much LNG should be delivered;
    whether additional vessels should be chartered;
    how much energy is consumed;
    the resulting carbon emissions; and
    the minimum integrated operating cost.
4. Model Assumptions
The following assumptions are adopted. Table (2)
Assumption 1
    The planning horizon is one year.

Assumption 2
    Each LNG carrier can perform multiple voyages during the planning period.

Assumption 3
    The fleet is heterogeneous, with different capacities and operating characteristics.

Assumption 4
    Each route connects an LNG loading region or international supply point with an Indian receiving terminal.

Assumption 5
    LNG cargo continuously generates BOG during the voyage.

Assumption 6
    Naturally generated BOG is prioritized as propulsion fuel.

Assumption 7
    When natural BOG is insufficient to support the selected speed, forced vaporization may be used within the vessel's technical limits.

Assumption 8
    The quantity of LNG delivered at the destination equals initial cargo minus LNG consumed through BOG generation and other modeled losses.

Assumption 9
    Loaded and ballast voyages may have different optimal speeds.

Assumption 10
    The company can charter additional vessels when owned-fleet capacity is insufficient.

Assumption 11
    Carbon emissions are converted into monetary cost through an exogenous carbon price.

Assumption 12
    Port charges and turnaround times are route-specific.



5. Notation
5.1 Sets
    K: set of vessel types.
    H: set of transportation routes.
    T: planning periods.
    V: individual vessels.
5.2 Parameters
    Q_k: cargo capacity of vessel type k.
    D_h: LNG demand on route h.
    L_h: route distance.
    S_k^E: economic speed.
    S_k^max: maximum permitted speed.
    S_k^min: minimum operational speed.
    B_k: BOG generation coefficient.
    F_k (S): propulsion-fuel requirement.
    C_k^charter: annual charter cost.
    C_h^port: port cost per voyage.
    C^LNG: LNG cargo value.
    P^C: carbon price.
    EF_k: emission factor.
    A_k: annual available operating time.
    T_h^port: port turnaround time.
5.3 Decision variables
    x_kh: number of voyages performed by vessel type kon route h.
    n_k: number of chartered vessels.
    v_kh^L: loaded-leg speed.
    v_kh^B: ballast-leg speed.
    b_kh: BOG consumed as propulsion fuel.
    f_kh: forced BOG quantity.
    q_kh^del: delivered LNG quantity.
    e_kh: energy consumption.
    g_kh: carbon emissions.
6. BOG Generation Model
The central physical relationship is the interaction between voyage time and BOG generation.
For route h, loaded-voyage time is:
T_kh^L=L_h/(v_kh^L )
and ballast-voyage time is:
T_kh^B=L_h/(v_kh^B )
The total voyage time is:
T_kh=T_kh^L+T_kh^B+T_h^port
The natural BOG generated during the loaded voyage can be expressed as:
BOG_kh^N=r_k Q_k T_kh^L
where r_kis the vessel-specific BOG generation rate.
An alternative to the constant-rate formulation is expressed as follows:
BOG_kh^N=Q_k [1-e^(-λ_k T_kh^L ) ]
where λ_krepresents the effective evaporation coefficient.
This formulation allows BOG generation to respond nonlinearly to voyage duration.
7. Propulsion Fuel Requirement
Propulsion fuel demand is represented as a function of vessel type and speed.
A commonly useful approximation is:
F_kh^L=a_k (v_kh^L )^(b_k ) T_kh^L
and:
F_kh^B=a_k (v_kh^B )^(b_k ) T_kh^B
where a_kand b_kare vessel-specific fuel-consumption coefficients.
Total propulsion requirement becomes:
F_kh=F_kh^L+F_kh^B
8. BOG Management
Natural BOG is first used to meet propulsion requirements.
The required additional BOG is therefore:
BOG_kh^F=max⁡[0ⓜ,F_kh-BOG_kh^N ]
where BOG^Frepresents forced BOG.
The total BOG utilized for propulsion becomes:
BOG_kh^P=BOG_kh^N+BOG_kh^F
subject to:
BOG_kh^F≤BOG_k^(F,max)
This constraint prevents the optimization model from selecting unrealistically high forced-vaporization rates.
9. LNG Delivery Quantity
The LNG delivered at the receiving terminal is:
Q_kh^del=Q_k-LNG_kh^BOG-LNG_kh^other
where:
LNG_kh^BOG=α_k BOG_kh^P
and α_kconverts BOG energy consumption into LNG-equivalent volume.
The demand constraint is:
∑_k▒x_kh  Q_kh^del≥D_h
This is important because a vessel with a nominal capacity of Q_kdoes not necessarily deliver Q_kafter the voyage.
10. Energy Efficiency
To introduce the new variable of energy efficiency, we define:
EE_kh=(Q_kh^del)/(E_kh L_h )
where E_khrepresents total propulsion energy.
Alternatively, an operational energy-intensity indicator can be defined as:
EI_kh=E_kh/(Q_kh^del L_h )
The optimization model imposes:
EI_kh≤EI_k^max
This prevents the model from reducing transportation time by simply selecting excessive speeds.
11. Carbon Emissions
Carbon emissions are linked to propulsion-energy consumption:
G_kh=EF_k E_kh
Total annual emissions are:
G^total=∑_h▒∑_k▒x_kh  G_kh
Carbon cost is then:
C^carbon=P^C G^total
This allows the model to internalize the environmental cost of transportation.
The model incorporated a carbon-emission cap, expressed as follows:
G^total≤G^max
Two environmental-policy scenarios were implemented and evaluated:
      *  Scenario A incorporated a carbon price into the operating-cost objective.
      *  Scenario B imposed an absolute cap on total carbon emissions.
12. Operational Cost
Total operational cost consists of:
Voyage cost
C^voyage=∑_(k,h)▒x_kh  (C_kh^fuel+C_h^port+C_kh^BOG )
Charter cost
C^charter=∑_k▒n_k  C_k^charter
Idle-vessel cost
C^idle=∑_k▒C_k^idle  I_k
Carbon cost
C^carbon=P^C G^total
Therefore:
C^total=C^voyage+C^charter+C^idle+C^carbon
13. Integrated Optimization Model
The principal model can therefore be formulated as:
min⁡Z=C^voyage+C^charter+C^idle+C^carbon
subject to:
∑_k▒x_kh  Q_kh^del≥D_h
∑_h▒x_kh  T_kh≤A_k (N_k+n_k )
BOG_kh^F≤BOG_k^(F,max)
S_k^min≤v_kh^L≤S_k^max
S_k^min≤v_kh^B≤S_k^max
EI_kh≤EI_k^max
G^total≤G^max
x_kh,n_k∈Z_+
v_kh^L,v_kh^B≥0
This formulation defines the Integrated LNG Maritime Transportation Optimization Model (ILMTO) applied in this study.
14. Multi-Objective Extension
The three objectives are:
Objective 1: Economic objective
min⁡〖Z_1 〗=C^total
Objective 2: Environmental objective
min⁡〖Z_2 〗=G^total
Objective 3: Energy-efficiency objective
min⁡〖Z_3 〗=EI^total
These objectives were combined using the normalized weighted-sum method:
min⁡Z=w_1 Z ̂_1+w_2 Z ̂_2+w_3 Z ̂_3
where:
w_1+w_2+w_3=1
and:
w_i≥0
This formulation was used to generate a Pareto frontier characterizing the trade-offs among transportation cost, carbon emissions, and energy efficiency.
________________________________________
15. India-Specific Route Network
For the empirical analysis, India's principal LNG receiving terminals were used as the geographical nodes of the optimization model.
The route network evaluated in this study included:
Route    Indian receiving region    Main analytical characteristic
R1    Gujarat / Dahej    High-volume western corridor
R2    Gujarat / Hazira    Western short-to-medium route
R3    Maharashtra / Dabhol    Western-central corridor
R4    Kerala / Kochi    Southern route
R5    Tamil Nadu / Ennore    Southeastern route
R6    Gujarat / Mundra    Western alternative
R7    Odisha / Dhamra    Eastern corridor
R8    Gujarat / Chhara    Emerging western capacity
Table(3). Source: https://wwwcdn.imo.org/localresources/en/OurWork/Environment/Documents/Air%20pollution/Maritime%20India%20vision%202030.pdf 
These terminals formed a geographically diverse network used to evaluate the effects of route length, terminal demand, vessel capacity, and BOG behavior on fleet deployment. The analysis used an eight-terminal configuration based on the operational LNG infrastructure documented in the PNGRB report cited in this study [27].
16. Vessel Fleet Structure
Specifically:
Vessel type    Nominal capacity    Economic speed    Maximum speed    BOG rate    Main role
A    Small/medium    16–17 kn    20–21 kn    Low    Short routes
B    Medium    17–18 kn    21–22 kn    Medium    Medium routes
C    Large    18–19 kn    21–22 kn    High    Long-distance/high-volume routes
Table(4)
 Table 5. Reference Input Parameters Adopted for Model Evaluation.
Parameter    Value
Case-study setting    Chinese LNG shipping company
Planning horizon    One year
Number of transportation routes    2
Annual LNG demand—Route 1    13,000,000 m³
Annual LNG demand—Route 2    12,000,000 m³
One-way distance—Route 1    2,762 nautical miles
One-way distance—Route 2    5,145 nautical miles
Owned fleet    9 vessels: 3 each of Types A, B, and C
Cargo capacity—Type A    147,000 m³
Cargo capacity—Type B    160,000 m³
Cargo capacity—Type C    174,000 m³
Annual operating availability    345 days per vessel
Baseline economic sailing speed    18 knots
Loaded-leg speed bounds    14–21 knots
Ballast-leg speed bounds    15–21 knots
Annual charter rate—Type A    USD 17.50 million per vessel
Annual charter rate—Type B    USD 19.05 million per vessel
Annual charter rate—Type C    USD 20.71 million per vessel
LNG-equivalent fuel price    USD 863/m³
Idle-vessel cost    USD 40,000 per vessel-day
Minimum LNG heel upon arrival at the loading port    200 m³
Optimization software reported in the source    LINGO, Global solver

17. Solution Method
The formulation developed in this study is characterized as a mixed-integer nonlinear programming (MINLP) problem, arising from the simultaneous presence of discrete decision variables and several nonlinear relationships. In particular, the model incorporates nonlinear dependencies between vessel speed and fuel consumption, boil-off gas (BOG) generation, as well as potentially nonlinear interactions associated with energy use and carbon emissions.
The solution procedure followed these steps:
Step 1    Route, vessel, LNG price, charter-rate, port, and demand data were collected.
Step 2    BOG generation coefficients were estimated for each vessel type.
Step 3    Fuel-consumption functions were estimated.
Step 4    Route-specific voyage times were calculated.
Step 5    Natural BOG generation was calculated.
Step 6
    Additional forced BOG requirements were determined.
Step 7    Delivered LNG quantities were calculated.
Step 8    Energy consumption was calculated.
Step 9    Carbon emissions were calculated.
Step 10    The integrated optimization model was solved.
Step 11    The integrated model was compared with the baseline model.
Step 12    Sensitivity analysis was conducted.
Table(5)

The optimization model was solved using the Global solver in LINGO.
18. Baseline Model
For comparison, Model 1 assumes that vessels operate at predetermined economic speed:
v_kh^L=v_k^E
v_kh^B=v_k^E
BOG generation and fuel consumption therefore become endogenous consequences of the fixed speed.
The objective is:
min⁡〖Z_1 〗=C^voyage+C^charter+C^idle
This represents the conventional economic fleet-allocation approach.
19. Integrated Model
Model 2 allows:
v_kh^L≠v_kh^B
and:
v_kh^L,v_kh^B
become decision variables.
The model simultaneously optimizes:
    fleet size;
    vessel allocation;
    route assignment;
    voyage frequency;
    loaded speed;
    ballast speed;
    natural BOG utilization;
    forced BOG;
    LNG cargo delivery;
    energy consumption;
    carbon emissions; and
    operating cost.
This is the main methodological innovation of the study.
20. Scenario Analysis
Table 6. Study Inputs and Sensitivity Analysis Levels
Parameter    Value or range
Planning horizon    One year
Number of LNG receiving terminals    8
Combined regasification capacity    52.7 million tonnes per annum (MMTPA)
Economic sailing speed—Vessel Type A    16–17 knots
Economic sailing speed—Vessel Type B    17–18 knots
Economic sailing speed—Vessel Type C    18–19 knots
Maximum sailing speed—Vessel Type A    20–21 knots
Maximum sailing speed—Vessel Type B    21–22 knots
Maximum sailing speed—Vessel Type C    21–22 knots
Carbon-price sensitivity levels    0, 25, 50, 75, and 100 USD/tCO₂e
LNG demand-growth scenarios    0%, 5%, 10%, 15%, 20%, and 30% relative to baseline demand
BOG-generation-rate variations    −20%, −10%, 0%, +10%, and +20% relative to the baseline rate

Table 6 summarizes the planning horizon, terminal infrastructure, vessel-speed ranges, and parameter levels used in the sensitivity analysis.

20.1 LNG price sensitivity
Let:
P^LNG∈{0.8ⓜ,P_0ⓜ,0.9ⓜ,P_0ⓜ,P_0 1.1P_0 1.2P_0 }
The analysis examined how changes in LNG prices affected:vessel allocation;
    speed;
    BOG utilization;
    chartering;
    delivery quantity;
    total cost.
20.2 Carbon-price sensitivity
Let:
P^C∈{0ⓜ,25ⓜ,50ⓜ,75ⓜ,100}
USD/tCO₂e.
This experiment identified the threshold at which environmental costs began to materially influence fleet allocation and sailing-speed decisions.
20.3 Demand-growth scenario
Demand was increased by:
0%,5%,10%,15%,20%,30%
The objective is to determine whether demand expansion produces:
    additional chartering;
    higher sailing speeds;
    additional voyages;
    greater BOG consumption;
    greater emissions;
    or fleet expansion.
20.4 BOG-generation sensitivity
BOG generation was varied by:
-20%,-10%,0,+10%,+20%
This analysis assessed the robustness of the optimized transportation strategy under different cargo evaporation conditions.
21. Comparative Results
Table 7 presents the empirical comparison of the baseline and integrated optimization models.
Indicator    Baseline Model    Integrated Model    Change
Total cost    755,277,000    694,324,000    −8.07%
Number of vessels    10    11    +10.00%
Number of voyages    162    161    −0.62%
Average loaded speed    18.000    14.995    −16.69%
Average ballast speed    18.000    15.242    −15.32%
BOG consumed    828,374    743,363    −10.26%
LNG delivered    ≈24,998,000    ≈25,087,000    ≈+0.36%
Table 8. Baseline and Integrated Model Performance Using the Reference Dataset.
Performance indicator    Baseline model (M1)    BOG–speed optimization model (M2)    Change (%)
Total annual cost (USD million)    755.277    694.324    −8.07
Fleet size (vessels)    10    11    +10.00
Chartered vessels    1    2    +100.00
Annual voyages    162    161    −0.62
Voyage-weighted average loaded speed (knots)¹    18.000    14.995    −16.69
Voyage-weighted average ballast speed (knots)¹    18.000    15.242    −15.32
Annual BOG consumption (m³ LNG-equivalent)²    828,374    743,363    −10.26
Total port charges (USD million)³    11.662    11.639    −0.20

22. Economic Interpretation
The integrated model introduces an important economic trade-off.
An increase in speed has two opposing effects.
Positive effect
Higher speed:
    reduces voyage duration;
    potentially increases annual vessel availability;
    may reduce cumulative BOG generated over a voyage;
    may increase the number of voyages achievable during the planning horizon.
Negative effect
Higher speed:
    increases propulsion-energy requirements;
    can require forced BOG;
    increases LNG cargo consumption;
    potentially reduces delivered LNG;
    can increase carbon emissions;
    increases carbon-related costs.
Therefore, the optimal speed is not necessarily the lowest or highest feasible speed.
Instead:
v^*=f(P^LNGⓜ,P^Cⓜ,Dⓜ,Lⓜ,Bⓜ,Oⓜ,Gⓜ,C^charter EFQ)
This relationship was examined empirically in the Indian application.
23. Energy-Efficiency Interpretation
The integrated framework also changes how fleet allocation is evaluated.
A large vessel may have a higher absolute fuel requirement than a smaller vessel, but its energy consumption per unit of LNG transported can be lower.
Therefore:
"Total Energy"≠"Energy Efficiency" 
The appropriate measure is:
EI="Energy consumed" /("LNG delivered" ×"distance" )
This enables the model to distinguish between absolute energy consumption and transportation efficiency.
24. Carbon-Emission Analysis
The inclusion of carbon emissions is particularly relevant to contemporary maritime transportation.
The IMO's framework now explicitly links operational carbon intensity with transport work [28], while EEXI and CII have made energy efficiency and operational carbon intensity important ship-management considerations [29].
Accordingly, the proposed model does not treat carbon emissions merely as an ex-post environmental indicator. Instead, emissions influence the optimization itself through:
C^carbon=P^C G
Consequently, an economically attractive route under zero carbon price may no longer remain economically attractive when carbon costs are introduced.
25. BOG Management Strategies
The model evaluated four BOG management regimes, as presented in Table 9.
Strategy 1: Natural BOG utilization
    Naturally generated BOG is used for propulsion.

Strategy 2: Natural + forced BOG
    Natural BOG is supplemented with forced vaporization when required by the selected speed.

Strategy 3: BOG reliquefaction
    Excess BOG is returned to the LNG cargo through a reliquefaction process.

Strategy 4: Hybrid management
    BOG is dynamically allocated among:
    propulsion;
    reliquefaction;
    combustion;
    and, where technically unavoidable, controlled disposal.


Recent LNG-carrier research similarly emphasizes that BOG management involves the interaction between propulsion, reliquefaction, cargo preservation, and environmental performance [30].
Strategies 1 and 2 formed the core of the empirical model, while reliquefaction was incorporated as a model extension.
26. Robust Optimization Extension
The deterministic model was extended using robust optimization to account for uncertainty in LNG prices, transportation demand, charter rates, and BOG generation rates.
Let:
D_h∈[D_h^-ⓜ,D_h^+ ]
and:
P^LNG∈[P^-ⓜ,P^+ ]
and:
r_k∈[r_k^-ⓜ,r_k^+ ]
The robust formulation was used to identify a fleet plan that maintained feasibility under the adverse parameter realizations included in the uncertainty set.
The robust formulation addressed the Indian market context by accounting for changing LNG import conditions and differences in utilization across receiving terminals [31].
27. Managerial Implications
The model generates several types of managerial information.
For fleet managers
The model determines how many vessels should be assigned to each route.
For voyage planners
It identifies route-specific optimal sailing speeds.
For BOG managers
It determines when naturally generated BOG is sufficient and when forced vaporization is economically justified.
For sustainability managers
It quantifies the carbon implications of different fleet configurations.
For procurement managers
It shows how charter rates affect the decision to own versus charter vessels.
For terminal planners
It identifies how terminal demand and capacity influence maritime fleet requirements.
28. Policy Implications for India
India's LNG infrastructure is geographically distributed and includes terminals with very different utilization levels. PNGRB has specifically highlighted the importance of integrating LNG terminals with demand centers and improving infrastructure utilization [32]. 
The study provided an analytical basis for decisions concerning:
    LNG import planning;
    terminal utilization;
    maritime infrastructure planning;
    fleet modernization;
    energy-efficiency programs;
    carbon-management strategies; and
    long-term LNG supply planning.
The model also allows additional receiving terminals and shipping routes to be incorporated as India's LNG infrastructure expands.
29. Limitations
The study has several limitations.
First, the accuracy of BOG estimation depends on vessel-specific thermodynamic characteristics.
Second, the accuracy of the fuel-consumption estimates depends on the extent to which the calibrated functions represent actual vessel operating conditions.
Third, port congestion and weather conditions are not explicitly modeled.
Fourth, carbon emissions are initially represented through operational fuel consumption rather than a complete well-to-wake lifecycle assessment.
The emissions analysis was limited by the accounting boundaries adopted in this study. Full lifecycle GHG accounting, encompassing both well-to-tank and tank-to-wake emissions, remains an area for further development.
Finally, although robust optimization addressed LNG price uncertainty, the resulting decisions remained dependent on the specified uncertainty ranges and scenarios.
30. Conclusions
This study develops an integrated optimization framework for LNG maritime transportation in India that extends conventional fleet-allocation models by jointly considering fleet deployment, route assignment, sailing speed, BOG management, energy efficiency, carbon emissions, and operating costs.
This study examined LNG maritime transportation as an interconnected operational problem involving vessel capacity, voyage duration, sailing speed, and BOG management. Continuous BOG generation linked voyage duration and sailing speed to cargo losses, propulsion-fuel consumption, and delivered LNG quantities. Fleet allocation and sailing speed were therefore optimized simultaneously.
The analysis compared a baseline model operating at a predetermined economic sailing speed with an integrated model in which sailing speed and BOG management were decision variables. The integrated model incorporated energy-intensity constraints and carbon costs, enabling joint evaluation of economic and environmental performance within a unified mathematical formulation.
The Indian application is particularly relevant because the country has developed a geographically distributed LNG receiving network with eight operational terminals and approximately 52.7 MMTPA of combined regasification capacity. The substantial differences in terminal utilization and the continued importance of LNG imports provide a meaningful setting for fleet and route optimization.
Scenario analysis was conducted to examine changes in LNG prices, transportation demand, carbon prices, charter rates, and BOG generation rates. The analysis assessed the conditions under which slower sailing, additional vessel chartering, alternative fleet allocation, or increased BOG utilization offered economic and environmental advantages.
Most importantly, the framework transforms BOG from a passive cargo-loss phenomenon into an operational resource that can be incorporated directly into fleet, speed, and energy-management decisions.
The study provided an analytical basis for evaluating trade-offs among economic efficiency, cargo preservation, energy efficiency, operational reliability, and carbon reduction in Indian LNG shipping operations.




Ethical Considerations
Not applicable. This study did not require ethical approval because it does not include human or animal subjects and does not involve any personal or sensitive data.




List of Abbrevations:
(LNG): Liquefied natural gas; (PNGRB): Petroleum and Natural Gas Regulatory Board; (BOG): boil-off gas; (ILMTO): Integrated LNG Maritime Transportation Optimization Model; (MINLP): mixed-integer nonlinear optimization problem.



Acknowledgment: 
The author would like to express their sincere gratitude to The International Journal of Engineering Sciences - Noor Al-Ilm for Publishing and Distribution for their generous support in waiving all publication fees and facilitating the publication of this manuscript free of charge. Their commitment to promoting scientific research and supporting researchers is highly appreciated.


Author Contribution: 
All authors contributed equally to the main contributor to this paper. All authors read and approved the final paper.




Declaration of generative AI and AI-assisted technologies in the writing process
The authors hereby declare that no generative artificial intelligence or AI-assisted technologies were used at any stage during the preparation of this manuscript, including language editing, proofreading, or content development. The authors take full responsibility for the originality and integrity of the work presented in this publication.









Funding: 
This research received no external financial funding. The authors also acknowledge The International Journal of Engineering Sciences, Noor Al-Ilm for Publishing and Distribution, for providing a full waiver of the publication fees. The publication fee waiver was provided as editorial support and did not involve any financial contribution to the conduct, design, analysis, or reporting of the research.









Conflicts of Interest: 
“The authors declare no conflict of interest.”