An Integrated Optimisation Model for LNG Supply Chain Planning and Infrastructure Under FOB Scheme with Time-Dependent Demand

Abstract

Background: Liquefied natural gas (LNG) distribution in archipelagic regions involves complex trade-offs between transportation, infrastructure investment, and contractual arrangements. While most optimisation studies focus on seller-managed Delivery Ex-Ship (DES) schemes, limited research addresses buyer-managed Free on Board (FOB) frameworks that extend decision responsibility upstream. Methods: This study develops a two-stage integrated optimisation model for long-term LNG supply chain planning under an FOB contractual scheme with time-dependent deterministic demand. Stage 1 determines hub selection, port clustering, vessel sizing, fleet configuration, and endogenous infrastructure capacities using a genetic algorithm, while Stage 2 optimises cluster-level routing sequences. Robustness is assessed through multiple independent runs and sensitivity analysis. Results: A case study of the Nusa Tenggara region identifies Sumbawa as the optimal hub. The upstream segment consistently selects a 65,000 m³ vessel under terminal service capacity constraints, while downstream clusters are served by 3500 m³ and 10,000 m³ vessels depending on distance and demand aggregation. Infrastructure requirements are derived from peak-demand conditions, and the resulting levelised logistic cost is 4.66 USD/MMBtu. Conclusions: The findings demonstrate that FOB arrangements fundamentally reshape network configuration, fleet segmentation, and infrastructure sizing, providing a robust strategic planning framework for buyer-managed LNG supply chains in archipelagic contexts.

1. Introduction

Liquefied natural gas (LNG) is essential for supporting the energy transition for regions where pipeline-based gas distribution is impractical. This is particularly relevant in archipelagic and developing countries with spatially dispersed demand nodes and evolving market demands. In such contexts, the design of the LNG supply chain requires simultaneous consideration of maritime transportation, network configuration, and long-term infrastructure investment decisions.

Recent studies have demonstrated that the performance and cost efficiency of LNG supply chains are strongly influenced by network configuration, fleet deployment, and infrastructure design, especially in small-scale and emerging LNG markets [1,2,3,4,5,6,7]. However, most existing models adopt simplified contractual structures and assume constant demand over time, which limits their applicability for long-term strategic planning in emerging LNG markets. LNG transactions are commonly structured under various contractual regimes that govern the allocation of transportation risks and obligations between sellers and buyers. Under seller-managed delivery arrangements, such as Delivery Ex-Ship (DES), upstream transportation from the source terminal is handled by the seller, and the buyer’s planning scope is largely confined to downstream distribution and receiving infrastructure. In contrast, under FOB arrangements, buyers assume responsibility for transportation once the LNG is loaded at the source terminal, thereby expanding the logistics decision space to include upstream fleet deployment and source terminal operation [8].

Recent global LNG market assessments indicate a growing prevalence of flexible contractual structures and buyer-managed shipping arrangements. Industry reports highlight that FOB contracts increasingly dominate new LNG trade volumes, driven by market liberalisation, portfolio optimisation strategies, and the need for greater transportation flexibility under uncertain demand and regulatory conditions [9,10]. In parallel, contractual analyses emphasise that LNG buyers are progressively exposed to shipping risk, fleet availability, and terminal operability considerations, particularly in volatile market environments [11]. Furthermore, evolving regulatory frameworks, such as methane emission regulations and environmental compliance requirements, are expected to reinforce buyer involvement in logistics and transportation decisions, thereby further strengthening the relevance of FOB-based planning perspectives [12].

The implications of this shift in logistics responsibility have become increasingly relevant in recent years as LNG markets have liberalised and greater emphasis has been placed on transportation flexibility and fleet configuration. Recent research demonstrates that vessel size selection and fleet composition play a significant role in determining LNG transportation performance and cost structures under evolving market conditions [2]. These findings suggest that planning frameworks implicitly aligned with seller-managed delivery regimes may not be directly applicable to buyer-managed FOB contexts, where upstream logistics decisions interact with downstream network design.

From a modelling perspective, a substantial body of LNG supply chain optimisation literature focuses on strategic network design, hub-and-spoke configurations, and infrastructure planning, often treating upstream transportation as exogenous or fixed. Such assumptions are reasonable in DES-oriented settings but become structurally limited when buyers are responsible for end-to-end logistics coordination. Several studies addressing LNG supply chains in archipelagic and regional contexts—particularly those examining clustering strategies, routing structures, and small-scale LNG distribution—primarily emphasise downstream logistics and infrastructure implications [13,14,15,16,17,18]. While these studies provide valuable insights, they do not explicitly capture the expanded decision scope and operational constraints that arise under FOB arrangements.

These considerations are particularly relevant for archipelagic regions such as Indonesia, where LNG distribution is characterised by dispersed demand nodes, limited port infrastructure, and increasing reliance on small-scale LNG to support power generation and energy transition objectives. Recent studies on Indonesia’s LNG supply chains highlight the effectiveness of hub-and-spoke configurations and clustering approaches in improving cost efficiency and the robustness of logistics systems [1,5,19,20,21]. At the same time, long-term planning in such contexts must account for demand growth and phased capacity expansion, as infrastructure requirements are often driven by peak throughput rather than average demand levels [3,5].

Against this background, this study develops an integrated optimisation framework for LNG supply chain planning under an FOB contractual scheme with time-dependent deterministic demand. Formulated from a buyer-managed logistics perspective, the framework simultaneously determines hub selection, port clustering, upstream and downstream vessel size classes, fleet sizing, and routing configuration over a long-term planning horizon.

A key distinguishing feature of the proposed framework is that infrastructure capacities are not treated as independent decision variables but are derived endogenously as consequences of logistics configuration and peak-demand implications. Storage, jetty, and regasification capacities are determined based on the selected hub location, vessel size classes, clustering structure, and demand evolution, reflecting practical planning logic in small-scale LNG systems.

In addition, the framework explicitly incorporates a source terminal service capacity constraint, which limits the maximum number of vessel calls that can be accommodated at the LNG source terminal. This constraint directly links upstream fleet-size selection to terminal operability, thereby capturing a realistic trade-off faced by buyers under FOB arrangements: smaller vessels increase call frequency and may violate terminal service limits, while larger vessels reduce call frequency but may suffer from underutilization and higher charter costs.

By integrating these features into a unified strategic planning model, the proposed framework provides logistics-oriented insights into how buyer-managed FOB arrangements reshape network configuration, vessel segmentation, and the resulting infrastructure requirements in archipelagic LNG supply chains.

The framework is demonstrated through a case study of the Nusa Tenggara region of Indonesia, representing an archipelagic LNG supply chain with dispersed demand and incremental growth over a long-term planning horizon. By contrasting the logistics implications of buyer-managed FOB planning with those reported in seller-managed DES-oriented studies in the literature, this study provides logistics-oriented insights into how contractual regimes shape network configuration, vessel deployment, routing structures, and derived infrastructure requirements in LNG supply chains.

2. Literature Review

2.1. LNG Supply Chain Planning and Small-Scale LNG Logistics

The strategic planning of LNG supply chains has received sustained attention due to the growing role of LNG in supporting energy transition, particularly in regions where pipeline-based gas distribution is impractical. Existing studies emphasise that LNG supply chains are capital-intensive and highly dependent on logistics configurations, particularly in maritime transportation and port-based infrastructure design [1,2,3,4,5,6,7].

In emerging and small-scale LNG (SS-LNG) markets, transportation structure and fleet composition play a critical role in determining system performance. Yuan et al. [2] demonstrate that fleet size and vessel composition significantly affect LNG transportation efficiency under liberalised market conditions. Similarly, El Ghazi et al. [6] highlight that midstream infrastructure coordination and transportation decisions are key determinants of cost competitiveness in merging LNG markets. Recent vulnerability analyses of LNG maritime networks further reveal that structural characteristics, such as network topology and capacity concentration, substantially influence system robustness and exposure to disruption risks [7].

SS-LNG logistics has been widely studied as a practical solution for supplying dispersed demand centres in coastal and island regions. Optimisation-based studies along coastlines and archipelagic settings show that coordinated planning of shipping operations, vessel deployment, and supporting infrastructure is essential to ensure reliable and cost-efficient LNG distribution under fragmented demand conditions [17,18,21]. More recent contributions extend this perspective by optimising LNG transport and storage for multimodal and maritime operators, further underscoring the importance of integrated logistics planning in LNG systems [22].

2.2. Hub-and-Spoke Network and Archipelagic LNG Distribution Networks

Hub-and-spoke configurations are commonly adopted in archipelagic LNG distribution systems to aggregate demand and exploit economies of scale in maritime transportation. A substantial body of literature demonstrates that hub selection, clustering strategies, and port assignment decisions significantly influence transportation efficiency, infrastructure utilisation, and overall system cost [15,16,17,19].

In the Indonesian context, several studies confirm the relevance of hub-and-spoke structures for LNG distribution to power plants located across multiple islands. These works combine clustering analysis, routing evaluation, and cost assessment to identify efficient logistics configurations under geographical dispersion and infrastructure constraints [5,16,19,20,23]. Comparative analyses of hub-and-spoke and milk-run schemes further show that the optimal network structure depends on demand distribution, vessel characteristics, and service frequency requirements rather than on geographical proximity alone [19].

Recent studies also emphasise that LNG logistics planning in archipelagic environments prioritises structural efficiency and demand aggregation over localised routing considerations, particularly at the strategic planning level [24]. These findings provide important foundations for hub-based LNG distribution but often assume a predefined upstream logistics structure or fixed supply-side operations.

2.3. Optimisation Framework for LNG Transportation and Infrastructure Design

Mathematical optimisation has been widely applied to support LNG supply chain planning decisions. Mixed-integer linear programming (MILP) and related formulations have been used to determine optimal network structures, fleet composition, routing schemes, and infrastructure investments, typically with the objective of minimising total system cost or unit supply cost [17,18,21].

More recent studies extend classical formulations by integrating transportation and infrastructure investment decisions within unified planning frameworks. Turan and Flamand [3] present a model that jointly addresses natural gas transportation and infrastructure investment, while Pratama et al. [24] develop an MILP framework that endogenously determines logistics schemes for gas supply chain infrastructure planning. These approaches improve model realism by capturing interactions between transportation and infrastructure decisions.

Nevertheless, most existing optimisation models focus primarily on downstream logistics and infrastructure design, treating upstream transportation either as exogenous or implicitly unconstrained. As a result, the expanded decision scope that arises when buyers assume responsibility for end-to-end logistics coordination remains insufficiently explored in LNG supply chain optimisation.

2.4. Contractual Arrangements and Buyer-Controlled LNG Logistics

Contractual arrangements play a fundamental role in shaping LNG supply chain planning by determining how transportation responsibilities and risks are allocated between sellers and buyers. Khalilpour & Karimi [8] analyse LNG contract selection from a procurement perspective and show that contract terms directly affect the supply chain cost structure and operational flexibility.

Recent industry and policy-oriented studies document a structural shift toward buyer-managed LNG logistics. Market reports by the International Gas Union and GIIGNL confirm that FOB contracts have become increasingly prominent in global LNG trade, reflecting buyers’ preference for greater control over shipping, fleet deployment, and delivery scheduling [9,10]. From a contractual and regulatory perspective, Sharples [11] notes that market turbulence and portfolio diversification have intensified buyers’ exposure to transportation and logistics risks. In parallel, evolving regulatory frameworks, such as methane emission regulations, are expected to further influence contractual choices and reinforce buyer involvement in logistics and transportation decisions [12].

In line with these market developments, recent optimisation studies have begun to explicitly examine LNG shipping network design, fleet deployment, and routing decisions at a global scale. For example, global LNG shipping network optimisation models demonstrate that fleet composition and routing strategies significantly affect system-wide performance and cost efficiency [25]. However, such studies typically focus on large-scale international networks and abstract from regional infrastructure constraints, hub-and-spoke configurations, and port-level operational considerations that are critical in fragmented, infrastructure-limited contexts.

Despite these developments, optimisation-based LNG supply chain models rarely translate contractual regimes into explicit planning logic. Most models implicitly assume seller-managed delivery, such as DES, by treating upstream transportation from the source terminal as fixed or unconstrained. Consequently, the operational and infrastructural implications of buyer-managed FOB arrangements remain underrepresented in the optimisation literature.

2.5. Long-Term Planning and Demand Evolution in LNG Supply Chains

Long-term LNG supply chain planning requires careful consideration of demand growth and phased capacity expansion. Several studies demonstrate that infrastructure sizing based on average demand can underestimate capacity requirements, as storage, jetty, and regasification investments are typically driven by peak-throughput conditions rather than average demand levels [3,7].

Recent analyses of LNG maritime supply chains further reveal the vulnerability of logistics networks to capacity bottlenecks under increasing demand and limited infrastructure flexibility [7]. These findings reinforce the importance of explicitly linking long-term demand evolution with transportation capacity, fleet configuration, and infrastructure implications in strategic planning models. Deterministic demand profiles are commonly adopted in this context to assess capacity adequacy and investment requirements over long planning horizons, particularly when the focus is on strategic rather than operational decision-making.

2.6. Research Gap and Contribution Positioning

The reviewed literature demonstrates substantial progress in LNG supply chain optimisation, hub-and-spoke network design, and small-scale LNG logistics, particularly in archipelagic contexts. However, three key limitations remain evident. First, most existing studies implicitly assume seller-managed delivery and focus primarily on downstream logistics, leaving upstream transportation decisions and source terminal operability outside the scope of optimisation. Second, infrastructure capacities are often treated as independent decision variables rather than as endogenous outcomes derived from logistics configuration and vessel characteristics. Third, contractual regimes, particularly FOB arrangements, are rarely incorporated explicitly into long-term LNG supply chain planning models.

Building on DES-oriented LNG supply chain optimisation frameworks reported in the literature [13,17,18,21], this study addresses these gaps by developing an integrated optimisation framework for LNG supply chain planning under a buyer-managed FOB contractual scheme with time-dependent deterministic demand. The proposed framework explicitly incorporates upstream transportation decisions, source terminal service capacity constraints, and bathymetry-based infrastructure sizing logic, thereby linking logistics configuration, vessel segmentation, and infrastructure requirements within a unified strategic planning model. This positioning allows the framework to provide logistics-oriented insights into how shifting the logistics control boundary upstream reshapes network configuration, vessel deployment, routing structures, and derived infrastructure requirements in archipelagic LNG supply chains.

Table 1. Comparison of related LNG supply chain optimisation studies and this study.

Related Literature	Contract Scheme	Demand Treatment	Upstream Logistics	Hub-and-Spoke	Infrastructure Endogeneity	Terminal Capacity Constraint	Solution Approach	Real Case Study
Jokinen et al. [16]	DES	Static	Exogenous	☑	☒	☒	MILP	☒
Bittante et al. [17]	DES	Static	Exogenous	☑	☒	☒	MILP	☒
Bittante & Saxén [18]	DES	Multi-period	Exogenous	☑	☒	☒	MILP	☒
Machfudiyanto et al. [15]	DES	Static	Exogenous	☑	☒	☒	MILP + Risk	☑
Rahmanta et al. [5]	DES	Static	Exogenous	☑	☒	☒	MILP	☑
Yuan et al. [2]	FOB	Static	Exogenous	☒	☒	☒	Fleet Optimisation	☑
Mei et al. [7]	FOB	Static	Exogenous	☒	☒	☒	Network Analysis	☑
Pratama et al. [24]	DES	Multi-period	Exogenous	☑	☑ (Partial)	☒	MILP
This Study	FOB	Time-dependent deterministic	Endogenous	☑	☑ (Fully derived)	☑	Two-Stage: MILP + TSP	☑

Note: ☑: Included ☒: Excluded.

positions the proposed framework within the existing literature on LNG supply chain optimisation. Unlike most previous studies, which implicitly assume seller-managed delivery and treat upstream transportation as exogenous, this study explicitly models buyer-managed logistics under an FOB contractual scheme. In addition, infrastructure capacities are not treated as independent decision variables; they are derived endogenously from network configuration, vessel selection, clustering structure, bathymetric conditions, and peak-demand considerations. The inclusion of a source terminal service capacity constraint further distinguishes this work by capturing an operational mechanism that directly influences vessel segmentation and network feasibility, a topic that has received limited attention in prior optimisation-based LNG studies.

Recent developments in AI-driven supply chain optimisation, including deep reinforcement learning and transformer-based architectures, have demonstrated promising results in dynamic routing and inventory management contexts [26,27,28]. However, these approaches typically focus on operational decision layers rather than long-term strategic infrastructure investment under deterministic multi-period demand. Therefore, the present study maintains a structured optimisation framework aligned with strategic planning objectives.

Therefore, the principal novelty of this article resides in its endogenous, contract-aware, and infrastructure-coupled optimisation framework, which provides a structurally consistent basis for long-term LNG logistics planning beyond the scope of conventional exogenous network formulations.

3. Problem Description and Decision Framework

3.1. System Description

The system investigated in this study comprises a single LNG source terminal and a set of destination ports, with one port selected as a hub and the remaining ports as spokes. The system operates under a buyer-managed FOB contractual scheme, whereby the buyer assumes full responsibility for transportation from the source terminal to the final delivery ports. This arrangement enables an end-to-end optimisation of logistics and infrastructure planning decisions within a unified framework.

The logistics network is structured into two interconnected segments. The upstream segment transports LNG from the source terminal to the selected hub port using large-capacity LNG carriers, while the downstream segment distributes LNG from the hub to multiple destination ports using smaller vessels organised into clusters. This end-to-end structure enables the consolidation of upstream flows and allows flexible downstream delivery, making it particularly suitable for archipelagic regions.

A critical characteristic of the problem is the interaction between fleet selection and source terminal operability. While the FOB scheme grants the buyer flexibility in determining vessel sizes, the framework explicitly accounts for source terminal service capacity limitations, defined by a maximum allowable vessel call frequency. This constraint reflects physical berth availability and loading limitations, thereby creating a dependency between upstream fleet configuration and terminal accessibility.

Each destination port represents a demand node associated with power plants participating in Indonesia’s diesel-to-gas conversion program. LNG demand at each port follows a deterministic but time-dependent profile over a 20-year planning horizon, reflecting projected electricity demand growth and gradual capacity expansion.

The central problem addressed in this study is to determine an integrated LNG logistics configuration that minimises the total annualised unit cost while ensuring that demand at all ports is satisfied throughout the planning horizon.

3.2. Decision Variables and Planning Scope

The proposed optimisation framework simultaneously determines the following key decision variables:

• Hub selection: Identifying the most cost-efficient destination port to serve as the regional LNG hub.
• Port clustering: Assigning each non-hub port to a downstream cluster served from the hub, ensuring that each port is exclusively assigned to a single cluster.
• Fleet configuration: Determining vessel capacity and fleet size for both upstream and downstream transportation segments.
• Routing: Optimising sailing routes within each downstream cluster.

While infrastructure sizing—encompassing storage tanks, jetties, and regasification capacities—is a critical key planning component, these capacities are not treated as independent decision variables in this framework. Instead, infrastructure requirements at hub-and-spoke ports are derived endogenously as a function of the selected hub location, vessel size classes, clustering structure, and peak-demand implications.

The objective of the model is to minimise the annualised unit cost of LNG distribution, defined as the total annualised logistics costs (transportation and infrastructure investment) normalised by the total LNG demand over the planning horizon.

3.3. Model Positioning: Strategic Versus Operational Planning

The proposed model is positioned as a strategic planning tool for long-term LNG supply chain design rather than a detailed operational scheduling model. The primary focus is on identifying robust logistics configurations—such as hub selection, vessel size classes, and infrastructure capacities—that remain cost-efficient under evolving demand conditions.

Operational-level details, such as daily scheduling, berth time windows, weather-related disruptions, and short-term fleet dispatching, are intentionally abstracted to maintain tractability and to emphasise long-term investment and network design decisions. This modelling choice is consistent with prior LNG supply chain planning studies that prioritise strategic-level insights over operational micro-scheduling.

3.4. Model Assumptions and Justification

To enable an integrated and computationally tractable formulation, the following assumptions are adopted:

• Single LNG source terminal: LNG supply availability is assumed to be unconstrained, while operational service capacity is explicitly limited in terms of vessel call frequency.
• FOB contractual scheme: All transportation responsibilities and associated costs from the source terminal to the destination ports are borne by the buyer, enabling full end-to-end optimisation.
• Deterministic time-dependent demand: Demand at each port is assumed to be known and varies deterministically over time, allowing for the systematic evaluation of capacity adequacy over a long-term planning horizon.
• Hub-and-spoke network structure: One destination port is selected as a hub to consolidate upstream shipments and redistribute LNG to spoke ports as well as to meet local demand.
• Exclusive clustering: Each non-hub port is assigned to only one downstream cluster to avoid fragmented logistics operations.
• Uniform vessel size per segment: The upstream segment and each downstream cluster are served by vessels of identical capacity. This assumption reflects long-term time-charter practises and avoids excessive fleet fragmentation at the strategic level.
• Continuous annual operations: The logistics system is assumed to operate continuously throughout the year. As justified in Section 3.3, stochastic interruptions and maintenance downtime are abstracted to preserve model tractability.
• Neglect of boil-off gas: Boil-off gas (BOG) dynamics are not explicitly modelled, as their impact on strategic network configuration and infrastructure sizing is considered secondary relative to dominant transportation and investment cost drivers. In several maritime supply chain models, BOG is implicitly treated as an operational parameter rather than a separate material flow, and in some cases, the vaporised LNG is assumed to be used for onboard power generation. Consequently, the direct financial impact of BOG is absorbed into aggregated operating cost parameters rather than modelled explicitly as an independent cost component [29,30].

These assumptions balance model realism with analytical transparency, allowing the proposed framework to generate meaningful strategic insights while remaining computationally manageable.

4. Model Formulation and Solution Approach

4.1. Overview of the Optimisation Framework

Based on the literature review, existing LNG supply chain optimisation studies predominantly treat infrastructure capacity, contractual arrangements, and upstream transportation decisions as either exogenous inputs or independently defined components. Many prior works assume seller-managed delivery structures and fixed infrastructure parameters, thereby limiting their ability to capture the systemic interdependencies between network configuration, vessel selection, contractual schemes (e.g., FOB), and evolving demand characteristics. As a result, a significant research gap persists in integrating endogenous infrastructure determination with buyer-managed logistics and upstream transportation decisions within a unified strategic planning framework.

To address these limitations, the present study proposes an integrated modelling approach that embeds contractual structure, infrastructure sizing, and upstream logistics decisions into a coherent optimisation architecture. The proposed model extends the authors’ previously developed DES-based framework by broadening the decision boundary to explicitly incorporate upstream logistics and by relaxing constant-demand assumptions. This enhancement enables a more realistic and comprehensive representation of long-term LNG supply chain planning under a buyer-managed FOB contractual scheme.

Accordingly, the study adopts an integrated two-stage optimisation framework that couples strategic network and infrastructure investment decisions with operational routing optimisation. This hierarchical structure allows strategic infrastructure sizing, fleet configuration, and network design decisions to be evaluated simultaneously with routing feasibility and service capacity constraints. The overall decision logic and interaction between the strategic and operational components are illustrated in Figure 1.

As depicted in Figure 1, the framework begins by defining the study’s physical, economic, and institutional boundaries using key input parameters, including time-dependent demand profiles, vessel characteristics, bathymetric conditions, and the FOB contractual structure. The optimisation process is then decomposed into two interconnected stages. Stage 1 (Strategic Planning) employs a mixed-integer programming (MIP) formulation to simultaneously determine the optimal network configuration, including hub location, port clustering, and fleet sizing for both upstream and downstream segments. Crucially, this stage endogenously derives infrastructure requirements—such as storage tanks, jetties, and regasification units—ensuring that capital investment is directly consistent with the selected logistics configuration and source terminal constraints.

Subsequently, Stage 2 (Routing Optimisation) addresses operational efficiency within the established network structure. For each downstream cluster, a travelling salesman problem (TSP)-based formulation is applied to minimise sailing distances and travel times, ensuring that short-term operational routing aligns with the long-term strategic design. The outputs from both stages are then integrated into a comprehensive cost evaluation module, where transportation OPEX and annualised infrastructure CAPEX are aggregated to minimise the total annualised unit cost of LNG distribution.

Finally, the framework concludes with post-optimisation analyses, including sensitivity and robustness assessments, to evaluate the solution’s stability under parameter variations. This hierarchical structure—separating strategic design from operational routing while maintaining a unified cost framework—provides a transparent and tractable decision-support tool for long-term LNG supply chain planning in archipelagic regions.

4.2. Symbol Explanation

The sets, indices, parameters, and variables used in the mathematical formulation, along with their meanings, are defined in

Table 2. Definition and description of model parameters.

Category	Symbol	Description
Set and Indices	P	Set of destination ports
	H	Set of candidate hub ports, $\mathrm{H}\subseteq \mathrm{P}$
	K	Set of downstream clusters
	T	Set of time periods (years)
	V	Set of vessel size classes
	i, j	Indices for destination ports
	h, k, t, v	Indices for hub, cluster, time, and vessel
Parameters	${\mathrm{C}}_{\mathrm{t}}^{\mathrm{trans}}$	Total transportation cost in year t
	${\mathrm{I}}^{\mathrm{infra}}$	Total infrastructure investment (CAPEX)
	A	Capital recovery factor (CRF)
	r	Discount rate
	${\mathrm{D}}_{\mathrm{t}}^{\mathrm{total}}$	Total regional LNG demand in year t
	${\mathrm{D}}_{\mathrm{i},\mathrm{t}}$	Demand at destination port i in year t
	${\mathrm{Q}}_{\mathrm{v},\mathrm{h}}$	Net cargo capacity of vessel class v for the upstream segment
	${\mathrm{Q}}_{\mathrm{v},\mathrm{k}}$	Net cargo capacity of vessel class v for cluster k
	${\mathrm{F}}_{\mathrm{t},\mathrm{v},\mathrm{h}}$	Upstream call frequency for vessel v required in year t
	${\mathrm{F}}_{\mathrm{t},\mathrm{v},\mathrm{k}}$	Downstream voyage frequency for vessel v in cluster k in year t
	${\mathrm{F}}^{\mathrm{source}}$	Maximum allowable vessel call frequency at the source
	${\mathrm{d}}_{\mathrm{i},\mathrm{j}}$	Distance between port i and j
Decision Variables	${\mathrm{x}}_{\mathrm{h}}$	1 if port h is selected as hub, 0 otherwise
	${\mathrm{y}}_{\mathrm{i},\mathrm{k}}$	1 if port i is assigned to cluster k, 0 otherwise
	${\mathrm{z}}_{\mathrm{v},\mathrm{h}}$	1 if vessel v is assigned to serve hub h (upstream), 0 otherwise
	${\mathrm{z}}_{\mathrm{v},\mathrm{k}}$	1 if vessel v is assigned to serve cluster k (downstream), 0 otherwise
	${\mathrm{w}}_{\mathrm{i},\mathrm{j}}$	1 if vessel travels directly from port i to j, 0 otherwise
Auxiliary variables	${\mathrm{u}}_{\mathrm{i}},{\mathrm{u}}_{\mathrm{j}}$	Sequence variable for port visits in the routing sub-problem

.

4.3. Stage 1: Strategic-Level Optimisation

4.3.1. Network Structure

The study models the LNG supply chain as a buyer-managed FOB hub-and-spoke network. The system comprises an upstream segment using large-capacity LNG carriers to transport LNG to an endogenously selected hub, and a downstream segment utilising smaller vessels to distribute LNG to clustered spoke ports. In this stage, the optimisation focuses on strategic decision variables—specifically, hub selection and cluster formation—to balance transportation distances and distribution efficiency. To maintain computational tractability and prioritise structural efficiency, detailed operational constraints are intentionally abstracted, providing a coherent foundation for integrating strategic logistics decisions with long-term infrastructure implications.

4.3.2. Vessel Class Representation and Fleet Configuration

Vessels are represented by discrete size classes, characterised by capacity, draft, speed, and charter rates derived from market-data regression [10]. At this stage, the model determines the optimal vessel class and fleet size for both segments. To reflect long-term time-charter practices and avoid fleet fragmentation, a uniform vessel size is enforced within the upstream segment and within each downstream cluster. This selection is driven by a trade-off between economies of scale and operational flexibility: downstream selection favours smaller vessels to serve dispersed demand, while upstream selection is heavily influenced by source terminal constraints.

4.3.3. Source Terminal Service Capacity Constraint

A critical feature of the framework is the explicit inclusion of a source terminal service capacity constraint, modelled as the maximum allowable annual vessel-call frequency. This constraint captures physical realities such as berth availability and prevents the unrealistic assumption of unlimited access. It fundamentally drives upstream fleet sizing: while smaller vessels offer flexibility, they require higher call frequencies that may violate terminal limits, thereby compelling the selection of larger vessels despite their higher charter rates. This mechanism ensures that the resulting fleet configuration is not only cost-optimal but also operationally feasible within the physical limits of the source facility.

4.3.4. Infrastructure Sizing Logic

Infrastructure capacities are derived endogenously from the logistics configuration and peak-demand requirements. Storage capacity is calculated to bridge the time between vessel arrivals, explicitly accounting for the maximum projected demand, safety buffers, and unpumpable volumes. Regasification capacity is dimensioned to meet the daily peak load (assumed at 135% of the average) to accommodate fluctuations. Finally, jetty and trestle requirements are determined using a bathymetry-based approach; rather than imposing rigid depth constraints, the model calculates the trestle length required to reach the necessary water depth for the selected vessel class. This links vessel selection directly to CAPEX, capturing the realistic trade-off between maritime efficiency and port infrastructure investment.

4.3.5. Mathematical Model

The objective of the strategic optimisation is to determine an integrated LNG logistics configuration that minimises the equivalent uniform annualised unit cost of LNG distribution over the planning horizon. This metric is derived by first calculating the specific unit cost for each year t (i.e., annual transportation expenditures plus the annualised equivalent of infrastructure investment, divided by annual demand), discounting these annual unit costs to their present value, and finally re-annualising the total using the Capital Recovery Factor (CRF). Formally, the objective function is expressed as follows:

$$\min \mathrm{Z}=\mathrm{A}\sum _{\mathrm{t}\in \mathrm{T}}\left[{\displaystyle \frac{{\mathrm{C}}_{\mathrm{t}}^{\mathrm{trans}}+\left({\mathrm{I}}^{\mathrm{infra}}\mathrm{A}\right)}{{\mathrm{D}}_{\mathrm{t}}^{\mathrm{total}}}}{\left(1+\mathrm{r}\right)}^{-\mathrm{t}}\right]$$

(1)

where ${\mathrm{C}}_{\mathrm{t}}^{\mathrm{trans}}$ represents the total transportation cost in year t for both upstream and downstream segments, $\left({\mathrm{I}}^{\mathrm{infra}}\mathrm{A}\right)$ denotes the annualised capital cost of infrastructure (where ${\mathrm{I}}^{\mathrm{infra}}$ is the total CAPEX and $\mathrm{A}$ is the CRF), and ${\mathrm{D}}_{\mathrm{t}}^{\mathrm{total}}$ is the total regional LNG demand in year t. The term in the brackets represents the present value of the unit cost in year t. The summation aggregates these present values over the planning horizon T, and the final multiplication by A converts the aggregate present value into a uniform annual equivalent. This formulation ensures that the cost efficiency metric accounts for the time-varying nature of demand while providing a consistent single-value indicator for comparison.

The strategic optimisation simultaneously determines:

• The selection of a single hub port from a set of candidate destination ports.
• The assignment of non-hub ports into downstream clusters served from the hub.
• Vessel size classes and fleet sizes for upstream (source-hub) and downstream (hub-spoke) transportation.
• The resulting infrastructure capacity requirements at hub and spoke ports.

The model is subject to the following structural and operational constraints:

$$\sum _{\mathrm{h}\in \mathrm{H}}{\mathrm{x}}_{\mathrm{h}}=1$$

(2)

$$\sum _{\mathrm{k}\in \mathrm{K}}{\mathrm{y}}_{\mathrm{i},\mathrm{k}}=1, \forall \mathrm{i}\in \mathrm{P}\backslash \mathrm{h}$$

(3)

$$\sum _{\mathrm{h}\in \mathrm{H}}{\mathrm{z}}_{\mathrm{v},\mathrm{h}}=1, \forall \mathrm{v}\in \mathrm{V}$$

(4)

$$\sum _{\mathrm{k}\in \mathrm{K}}{\mathrm{z}}_{\mathrm{v},\mathrm{k}}=1, \forall \mathrm{v}\in \mathrm{V}$$

(5)

$$\sum _{\mathrm{h}\in \mathrm{H}}{\mathrm{Q}}_{\mathrm{v},\mathrm{h}}{\mathrm{F}}_{\mathrm{t},\mathrm{v},\mathrm{h}}{\mathrm{z}}_{\mathrm{v},\mathrm{h}}\ge {\mathrm{D}}_{\mathrm{t}}^{\mathrm{total}}, \forall \mathrm{t}\in \mathrm{T}$$

(6)

$$\sum _{\mathrm{k}\in \mathrm{K}}{\mathrm{Q}}_{\mathrm{v},\mathrm{k}}{\mathrm{F}}_{\mathrm{t},\mathrm{v},\mathrm{k}}{\mathrm{z}}_{\mathrm{v},\mathrm{k}}\ge \sum _{\mathrm{k}\in \mathrm{K}}\sum _{\mathrm{i}\in \mathrm{P}\backslash \mathrm{h}}{\mathrm{D}}_{\mathrm{i},\mathrm{t}}, \forall \mathrm{t}\in \mathrm{T}$$

(7)

$${\mathrm{F}}_{\mathrm{t},\mathrm{v},\mathrm{h}}\le {\mathrm{F}}^{\mathrm{source}}, \forall t\in T$$

(8)

$$x_h,y_{i,k},z_{v,h},z_{v,k}\in \left\{\mathrm{0,1}\right\}$$

(9)

Equation (2) ensures that exactly one destination port is selected as the hub. Equation (3) stipulates that each non-hub port is assigned to exactly one downstream cluster, preventing fragmented logistics operations. Regarding fleet configuration, Equation (4) imposes a uniformity constraint requiring the upstream segment to be served by a single vessel class, while Equation (5) applies a similar constraint to each active downstream cluster.

To ensure supply sufficiency, Equation (6) verifies that the upstream vessel capacity is adequate to meet the total regional demand, while Equation (7) ensures that the fleet capacity allocated to each downstream cluster satisfies the aggregate demand of its member ports. Crucially, Equation (8) guarantees that the upstream vessel calls frequency remains within the source terminal’s allowable operational limits. This constraint imposes a trade-off among vessel size, call frequency, utilisation, and charter costs, thereby explicitly linking upstream fleet configuration to terminal operability. Finally, Equation (9) defines the domain of all decision variables as binary.

4.4. Stage 2: Operational Routing Optimisation

As illustrated in Figure 1, operational routing optimisation constitutes the second stage of the framework. While Stage 1 determines the strategic configuration (hub selection, clustering, and fleet sizing), Stage 2 addresses the operational-level problem of determining efficient sailing routes within each established downstream cluster.

Routing optimisation is performed independently for each cluster k identified in Stage 1. Given a fixed hub location, assigned spoke ports, and vessel speed, the problem aims to determine the port-visit sequence that minimises the total sailing distance for a single delivery cycle. Formally, this is modelled as a travelling salesman problem (TSP). For a specific cluster k comprising a set of ports ${\mathrm{P}}_{\mathrm{k}}$ (including the hub), the optimisation problem is formulated as follows:

$$\min {\mathrm{Z}}_{\mathrm{k}}=\sum _{\mathrm{i}\in {\mathrm{P}}_{\mathrm{k}}}\sum _{\mathrm{j}\in {\mathrm{P}}_{\mathrm{k}},\mathrm{j}\ne \mathrm{i}}\left[{\mathrm{d}}_{\mathrm{ij}}{\mathrm{w}}_{\mathrm{ij}}\right]$$

(10)

Subject to:

$$\sum _{\mathrm{j}\in {\mathrm{P}}_{\mathrm{k}},\mathrm{j}\ne \mathrm{i}}{\mathrm{w}}_{\mathrm{ij}}=1, \forall \mathrm{i}\in {\mathrm{P}}_{\mathrm{k}}$$

(11)

$$\sum _{\mathrm{i}\in {\mathrm{P}}_{\mathrm{k}},\mathrm{i}\ne \mathrm{j}}{\mathrm{w}}_{\mathrm{ij}}=1, \forall \mathrm{j}\in {\mathrm{P}}_{\mathrm{k}}$$

(12)

$${\mathrm{u}}_{\mathrm{i}}-{\mathrm{u}}_{\mathrm{j}}+\left|{\mathrm{P}}_{\mathrm{k}}\right|{\mathrm{w}}_{\mathrm{ij}}\le \left|{\mathrm{P}}_{\mathrm{k}}\right|-1$$

(13)

$${\mathrm{w}}_{\mathrm{ij}}\in \left\{0,1\right\}$$

(14)

where ${\mathrm{d}}_{\mathrm{ij}}$ represents the maritime distance between port i and port j, and ${\mathrm{w}}_{\mathrm{ij}}$ is a binary decision variable equal to 1 if the vessel travels directly from i to j. Constraints (11) and (12) ensure that each port is visited exactly once (i.e., once for each arrival and once for each departure). Constraint (13) represents the standard subtour elimination constraint to prevent disconnected loops.

The separation between strategic and operational decisions reflects the planning logic adopted in this study. Strategic decisions define the network structure that remains fixed over long planning horizons, while routing decisions serve to quantify operational performance indicators—such as round-trip distance and cycle time—based on that structure. By solving the routing problem sequentially, the framework prevents computational feedback loops while ensuring that cost calculations in the subsequent stage are based on optimised operational parameters rather than rough estimates. The resulting sailing times directly inform the calculation of annual delivery frequencies and voyage-related variable costs in the cost evaluation stage.

4.5. Cost Evaluation Framework

The economic evaluation is conducted after strategic and operational decisions have been determined. As depicted in Equation (1), the total system cost comprises two primary categories: infrastructure-related costs and transportation operating expenditures (OPEX). All costs are evaluated on an annualised basis to ensure consistency across components and comparability among alternative configurations.

4.5.1. Infrastructure-Related Costs

Infrastructure costs consist of capital expenditures (CAPEX) and recurring operating and maintenance expenditures (O&M).

• Infrastructure CAPEX: Includes initial investments in storage tanks, jetties, including trestles, and regasification units at both hub and non-hub ports. As described in Section 4.3.4, these capacities are derived endogenously based on the selected logistics configuration, vessel characteristics, bathymetric conditions, and peak demand requirements. To integrate with annual expenses, CAPEX is converted to an equivalent uniform annual cost using the capital recovery factor (CRF).
• Infrastructure O&M: Represents annual upkeep costs, modelled as a fixed percentage of the total infrastructure investment. This pragmatic assumption captures recurring facility expenses without introducing excessive operational complexity.

4.5.2. Transportation Costs (OPEX)

Under the FOB contractual scheme, transportation costs are classified as operational expenditures, reflecting long-term time charter arrangements. These are divided into fixed and variable components:

• Time Charter Costs (Fixed): Correspond to the annual cost of fleet deployment, determined by the number of vessels (upstream and downstream) selected in Stage 1 and the market charter rates for the respective vessel classes.
• Voyage Costs (Variable): Include fuel consumption, port charges, and anchorage fees. Fuel consumption is calculated across distinct operating states: (i) loading, (ii) discharging, (iii) sailing, and (iv) idle/anchorage. Port charges depend on call frequency, while anchorage costs are driven by accumulated idle time. These variables are directly derived from the routing outcomes in Stage 2.

4.5.3. Unit Cost Aggregation

The total annual system cost is obtained by summing transportation OPEX, annualised infrastructure CAPEX, and infrastructure O&M costs. The annualised unit cost (USD/MMBtu) is then derived by normalising these costs against the annual LNG demand. Since demand evolves over time, the model calculates the unit cost for each year, discounts it to a present value, and re-annualises it by using the CRF to produce a uniform performance metric, as defined in the objective function (Equation (1)).

The detailed mathematical formulations for each specific cost component are provided in Appendix A.

4.6. Solution Approach

The integrated optimisation problem—combining network design, fleet configuration, operational routing, and infrastructure investment under time-dependent demand—constitutes a large-scale combinatorial search space. Given the complexity of the underlying sub-problems (specifically the Facility Location Problem and Travelling Salesman Problem), exact MIP-based solution methods become computationally prohibitive for realistic problem instances. Therefore, a Genetic Algorithm (GA) is adopted as the solution method. This metaheuristic approach is implemented in Palisade Evolver, an Excel-based optimisation add-in, enabling the simultaneous optimisation of discrete and continuous variables while prioritising solution robustness and scalability over exact optimality.

The GA parameters were selected based on established evolutionary computation literature. Population size, crossover rate, and mutation rate were determined to balance exploration capability and computational efficiency.

Previous studies in evolutionary optimisation indicate that moderate population sizes (30–100 individuals) provide adequate genetic diversity for medium-scale combinatorial problems while maintaining computational efficiency [31,32]. Accordingly, a population size of 50 individuals was selected as a balanced intermediate setting.

The crossover rate was set at 0.5 to promote effective recombination of high-quality candidate solutions without overly disrupting promising structures. The mutation rate was set to 0.1 to maintain genetic diversity and prevent premature convergence, particularly given the discrete clustering and vessel-class decision structure. Convergence was assessed using a progress-based stopping criterion rather than a fixed time limit. The optimisation process was terminated when the improvement in the objective function value fell below 0.1% over 20,000 consecutive trials (solution evaluations).

These parameter settings were further evaluated through convergence and sensitivity analyses. To evaluate the stability of the solution, 20 independent GA experiments were performed using different random seeds while consistently applying the same parameter settings. Additionally, sensitivity analysis was conducted by varying population size (30, 50, and 100 individuals) while keeping other GA parameters unchanged.

4.7. Model Scope and Limitations

The proposed framework is intended as a strategic decision-support tool for long-term LNG supply chain planning under a buyer-managed FOB contractual scheme, particularly within archipelagic regions. By focusing on key economic and structural trade-offs, the model provides a robust and tractable approach for identifying cost-efficient network configurations, fleet segmentation, and infrastructure implications. However, to maintain computational manageability and to emphasise strategic insights, several abstractions and limitations are adopted:

• Deterministic Demand: LNG demand at each destination port is represented using a deterministic, time-dependent profile. This approach enables the systematic evaluation of capacity adequacy and infrastructure requirements under peak-demand conditions, which are critical drivers of long-term investment decisions. While demand uncertainty is not explicitly modelled, the robustness of the resulting network configuration is examined through sensitivity analysis, as discussed in Section 6.6.
• Exclusion of Boil-off Gas (BOG): BOG losses during transportation and storage are not explicitly incorporated into the cost formulation. As justified in Section 3.4, this simplification is consistent with the study’s strategic objective. Given that BOG costs are secondary to dominant transportation and infrastructure (CAPEX) cost drivers, excluding them helps isolate the structural effects of logistics configuration without significantly altering the optimal network topology. Advanced studies on BOG dynamics demonstrate that an accurate representation requires nonlinear thermal modelling and dynamic simulation [33,34]. Incorporating such non-linear and ship-specific thermodynamic behaviour into the supply chain optimisation framework would significantly increase computational complexity and reduce model tractability.
• Operational Abstraction: The model abstracts from detailed operational constraints such as daily berth scheduling, specific time windows, weather-related disruptions, maintenance downtime, and short-term fleet dispatching. These factors are more relevant to operational-level optimisation and vessel performance analysis than to long-term network design. By excluding such constraints, the framework preserves analytical clarity and focuses on decisions with long-term, irreversible economic implications.
• Solution Optimality: Regarding the solution methodology, it is acknowledged that the Genetic Algorithm (GA)-based approach identifies the best solution found within the search space rather than a mathematically proven global optimum. This limitation is common in strategic logistics optimisation studies employing metaheuristics for large-scale combinatorial problems. Future research may address this by comparing GA-based solutions against exact Mixed-Integer Programming (MIP) formulations (for smaller instances), decomposition-based methods, or alternative metaheuristics to further validate solution quality.

Overall, these modelling choices reflect a deliberate balance between realism and tractability. The framework is not intended to replace detailed operational scheduling models but to complement them by providing a coherent, physically grounded basis for strategic LNG supply chain planning. Within this scope, the proposed model offers meaningful insights into how contractual arrangements, terminal operability constraints, and infrastructure consequences jointly shape LNG logistics systems in archipelagic regions.

5. Case Study and Data

The proposed framework is applied to the LNG supply chain serving the Nusa Tenggara region of Indonesia, an archipelagic area characterised by geographically dispersed demand, long inter-island distances, and limited port infrastructure. This case study is designed to evaluate the model’s applicability and robustness under logistics conditions that differ significantly from those of continental or pipeline-connected systems examined in previous studies.

5.1. Case Study Background

The Nusa Tenggara region was selected as the focal case due to its strategic importance in Indonesia’s national diesel-to-gas power generation conversion program. This initiative is mandated by the Decree of the Minister of Energy and Mineral Resources of the Republic of Indonesia No. 13 K/13/MEM/2020 [35] and its subsequent amendment No. 249.K/MG.01/MEM/2022 [36], which designates several regions in Eastern Indonesia as priority zones for LNG-based power supply development.

Within this region, eight locations—Lombok (LOM), Sumbawa (SBW), Bima (BIM), Flores (FLO), Maumere (MAU), Alor (ALO), Kupang (KPG), and Waingapu (WAI)—are identified as target demand nodes. Each location exhibits a distinct LNG demand profile that evolves over the planning horizon, consistent with electricity demand growth projections from the state-owned electricity company, PT PLN (Persero).

The Tangguh LNG Plant (TGU), located in West Papua, serves as the single source terminal for this study. This selection aligns with the official LNG supply allocation specified in the aforementioned ministerial decrees. By fixing the supply source, the study concentrates on optimising the logistics network design, fleet configuration, and infrastructure implications under a buyer-managed FOB contractual scheme, rather than addressing upstream supply availability issues. The geographical distribution of the source terminal and destination ports is illustrated in Figure 2.

5.2. Demand Profile and Growth Assumptions

The LNG demand profiles employed in this study are based on Indonesia’s national diesel-to-gas conversion program, with the Nusa Tenggara region designated as a priority area for implementation. The demand projections are derived from the Electricity Supply Business Plan (RUPTL) of PT. PLN (Persero) [37]. While the overall regional electricity demand is projected to grow at an average annual rate of approximately 8.7% until 2030, the targeted power plants account for 14.5% of the region’s total installed capacity. Consequently, the weighted average growth rate for LNG demand specifically associated with these converted plants is estimated at approximately 1.26% per year.

The primary demand data used in this study is expressed in m³/day. Given that official RUPTL projections extend only to 2020, the derived annual growth rate of 1.26% is extrapolated to persist throughout the remainder of the 20-year planning horizon. For the optimisation model and cost evaluation, these daily demand rates were aggregated into total annual demand (MMBtu/year). Selecting a 20-year horizon aligns with the typical economic lifetime of LNG infrastructure and reflects the strategic nature of the planning problem, in which long-term investment decisions are driven by the cumulative evolution of demand.

Table 3. Projected annual LNG demand (m³/day) for destination ports in Nusa Tenggara over the planning horizon. Details of the annual LNG demand for each location throughout the planning horizon are provided in Appendix C.

Port Name	Port Code	Year 1	Year 5	Year 10	Year 15	Year 20
Lombok	LOM	1013.70	1065.76	1134.62	1207.93	1285.97
Kupang	KPG	141.42	148.69	158.29	168.52	179.41
Maumere	MAU	213.59	224.56	239.07	254.51	270.96
Sumbawa	SBW	1078.60	1134.00	1207.26	1285.26	1368.30
Bima	BIM	458.18	481.71	512.83	545.96	581.24
Flores	FLO	106.07	111.52	118.72	126.39	134.56
Alor	ALO	65.38	68.74	73.18	77.91	82.95
Waingapu	WAI	168.55	177.20	188.65	200.84	213.82
Total	Region	3245.49	3412.18	3632.63	3867.33	4117.19

and Figure 3 summarise the projected annual LNG demand for each port at representative intervals over the planning horizon. The data reveal significant heterogeneity in demand across the region. Lombok (LOM) and Sumbawa (SBW) emerge as dominant load centres due to their larger installed power generation capacities, collectively accounting for most of the initial regional demand. In contrast, eastern peripheral nodes, such as Alor (ALO) and Waingapu (WAI), exhibit lower baseload requirements.

The adoption of a deterministic, time-dependent demand profile is crucial for the systematic assessment of infrastructure adequacy. As emphasised in the model formulation, logistics decisions and infrastructure sizing—including storage tanks, jetties, and regasification units—are driven by maximum observed demand (peak load) over the planning horizon rather than average throughput. This approach ensures that the irreversible infrastructure investments remain adequate to support the gradual capacity expansion required throughout the system’s lifecycle.

5.3. Vessel Sizes and Cost Parameters

To accommodate the hierarchical demand structure, the study considers two distinct sets of vessel classes. The upstream segment is served by large-capacity LNG carriers ranging from 30,000 m³ to 145,000 m³, capable of handling bulk shipments from the source terminal to the hub. The downstream segment utilises a fleet of smaller vessels, with capacities ranging from 3500 m³ to 20,000 m³. This specific range is selected to align with the relatively low, dispersed demand profiles of the destination ports, thereby enabling appropriate delivery frequencies and ensuring high vessel capacity utilisation within the cluster-based distribution network.

The technical specifications and economic parameters for these vessel classes are derived from operational data provided by a national oil and gas company. To respect commercial confidentiality while ensuring model realism, the cost parameter—including time charter rate and fuel consumption profiles—is presented as a representative market value applicable to the Indonesian maritime logistics context.

Table 4. Characteristics of candidate vessel classes of upstream and downstream segments.

Segment	Vessel Class (m3)	Speed (Knots)	Charter Rate (USD/Day) *	Draft (m)	Disch Rate (m3/h)	Fuel Consumption (MT/Day) *
						Loading	Discharging	Sailing	Idle
Downstream	3500	8.40	11,000	4.45	1000	2.14	3.42	7.62	1.46
	5000	8.40	13,000	5.07	1000	2.52	3.93	9.09	1.71
	6500	8.40	16,100	5.54	2000	2.84	4.34	10.34	1.93
	7500	9.10	17,000	5.81	2000	3.03	4.59	11.10	2.05
	10,000	9.10	20,800	6.37	2000	3.46	5.13	12.79	2.34
	15,500	9.10	27,100	7.30	5100	4.25	6.07	15.87	2.85
	18,500	9.10	29,500	7.71	5100	4.59	6.50	17.32	3.09
	20,000	9.10	30,500	7.89	5100	4.79	6.70	18.00	3.20
Upstream	30,000	10.50	39,400	8.91	5100	5.73	7.83	21.98	3.84
	45,000	11.00	49,900	10.06	5100	6.90	9.16	26.84	4.61
	65,000	13.00	63,700	11.21	5100	8.17	10.56	32.18	5.45
	125,000	14.00	94,600	13.58	5100	11.03	13.58	44.42	7.32
	135,000	14.50	98,800	13.89	5100	11.43	13.99	46.14	7.58
	145,000	14.50	102,900	14.18	5100	11.81	14.38	47.79	7.83

* Charter rates and fuel consumption figures are based on representative operational data from industry sources.

summarises the characteristics of the candidate vessel classes. The fuel consumption rates are modelled for four distinct operating states: sailing, loading, discharging, and idle/anchorage, reflecting the vessels’ detailed operational profile.

5.4. Logistics Infrastructure Parameters

The calculation of infrastructure CAPEX is governed by location-specific conditions and equipment sizing logic derived from the optimisation results, as explicitly summarised in

Table 5. Infrastructure sizing parameters and cost function.

Category	Parameter/Component	Value/Formula	Unit/Note
Storage Facility	Hub port (Flat-Bottom tank)	1000	USD/m3
	Spoke ports (Bullet tank)	2,420,000	USD/unit (1000 m3)
	Heel (unpumpable)	10	% of capacity
	Safety Buffer	3	Days of daily demand
Marine Infrastructure	Jetty CAPEX	See Appendix A.2	Function of vessel size
	Trestle CAPEX	Function of length	Driven by bathymetry
Regasification	Regas Unit CAPEX	See Appendix A.2	Function of peak load
	Peak load factor	135	% of daily demand
Operational	Infrastructure O&M	5	% of total CAPEX/year
	Annual operating days	355	Days/year

. The table outlines the parameter values and functional relationships used to dimension each infrastructure component, ensuring that investment costs are directly linked to network configuration and vessel selection outcomes.

5.4.1. Storage Facilities

For the selected hub port, large-scale flat-bottom tanks are assumed to have a unit cost of 1100 USD/m³. For non-hub (spoke) ports, which generally handle smaller volumes, modular bullet tanks are utilised. These are modelled as discrete units of 1000 m³, with a unit cost of USD 2.42 million. The required storage capacity at each port is calculated to accommodate daily demand, plus a 10% unpumpable (heel) allowance and a 3-day safety buffer.

5.4.2. Marine Infrastructure (Jetty and Trestle)

Marine infrastructure CAPEX comprises two distinct components: the jetty head (berth) and the trestle. The jetty investment is modelled as a function of vessel size (deadweight tonnage, DWT) and the required number of berths. This formulation reflects the need for stronger mooring and breasting structures for larger carriers. The trestle cost is driven by the distance from the shoreline required to reach the necessary water depth (draft) for the selected vessel class. The distance from the shoreline is determined using location-specific bathymetric profiles. The full bathymetric data used for all ports and depth intervals are provided in Appendix D.

5.4.3. Regasification and O&M

Regasification unit CAPEX is calculated as a function of peak send-out capacity, assumed to be 135% of the average daily load to accommodate hourly fluctuations. Finally, annual operating and maintenance (O&M) costs for all infrastructure components are estimated at 5% of the total initial investment.

Overall, as consolidated in Table 5, infrastructure CAPEX in this study is not treated as an exogenous input but is endogenously determined by demand levels, vessel class selection, bathymetric conditions, and operational design margins. By differentiating technology assumptions between hub and spoke ports and scaling marine and regasification facilities according to functional requirements, the model ensures that capital investment decisions remain fully consistent with the optimised network configuration and long-term supply chain structure.

5.5. Economic and Operational Settings

The economic evaluation and strategic optimisation are formulated using a set of global parameters applicable to the entire supply chain. A planning horizon of 20 years is established, consistent with the typical economic lifetime of the primary infrastructure assets such as storage tanks, jetties, and regasification units. For the cost analysis, a 9.5% discount rate is applied to calculate the capital recovery factor (CRF) and the present value of annual expenditures. This rate reflects the weighted average cost of capital (WACC) typically associated with infrastructure projects in Indonesia.

With respect to vessel operational costs, a fuel price of 960 USD/MT is assumed for all vessel classes, corresponding to the domestic fuel pricing structure. To capture realistic long-term cost dynamics, the model incorporates a uniform annual cost escalation. A constant inflation rate of 2% per annum is applied to all operational expenditure components—including fuel price, time charter rate, port charges, and infrastructure O&M costs—throughout the planning horizon. This assumption reflects long-term expectations of macroeconomic stability and ensures that future cash flows are adjusted for purchasing power parity.

The logistics system is assumed to operate 355 days per year, allowing for a standard allocation of downtime for dry-docking and system-wide maintenance. These parameters are summarised in

Table 6. Global economic and operational parameters.

Parameter	Symbol	Value	Unit
Planning Horizon	T	20	Years
Discount Rate (WACC)	r	9.5	%
Annual Inflation Rate	i	2	%
Operating Days	${\mathrm{T}}^{\mathrm{ops}}$	355	Days/year

.

6. Results

6.1. Optimal Network Configuration

Across 20 independent GA runs as presented in Appendix F, Sumbawa (SBW) consistently emerges as the selected hub location, indicating strong robustness of the strategic configuration. In the best-performing configuration, the downstream ports are grouped into three clusters, with SBW serving as both the redistribution hub and a demand node:

• Cluster 1: LOM
• Cluster 2: BIM, FLO
• Cluster 3: KPG, MAU, ALO, WAI

Alternative near-optimal solutions observed in several runs redistribute certain peripheral nodes between clusters; however, hub selection and upstream vessel class segmentation remain invariant.

The selection of SBW is primarily driven by two key factors: its proximity to the LNG source terminal and its relatively great local demand. As highlighted in Table 3, only LOM and SBW exhibit substantial demand levels among the candidate ports. Compared with LOM, SBW is located closer to the source terminal, resulting in shorter upstream transportation distances and lower transportation costs. Furthermore, SBW’s simultaneous role as a hub and a consuming node allows a significant portion of the incoming LNG volume to be absorbed locally, thereby reducing idle storage capacity and re-handling requirements relative to alternative hub candidates.

In addition, SBW is geographically closer to the eastern destination ports than LOM, thereby further improving downstream distribution efficiency. This spatial advantage contributes to shorter average sailing distances and more balanced routing structures for downstream delivery.

These outcomes indicate that the model prioritises structural cost efficiency over simple geographical proximity, consistent with principles of strategic LNG logistics planning. As illustrated in Figure 4, the selected hub at Sumbawa (SBW) anchors three operationally distinct downstream clusters—Cluster 1 (red), Cluster 2 (blue), and Cluster 3 (green)—each defined not merely by spatial adjacency but by optimised sailing sequences, demand aggregation patterns, and vessel capacity alignment. The routing structure demonstrates how peripheral, lower-demand ports are consolidated within shared service loops to improve vessel utilisation, while higher-demand nodes are configured to justify dedicated or higher-frequency service cycles. The visual representation confirms that the clustering logic emerges from an integrated cost–distance–capacity trade-off rather than from purely geographic grouping.

6.2. Vessel Configuration and Operational Performance

The best-performing configuration identified across 20 independent GA runs exhibits a clear segmentation between upstream and downstream vessel classes, reflecting the fundamentally different logistical roles and operational constraints governing each transportation segment. Convergence analysis confirms that upstream vessel selection remains invariant across all runs, while downstream fleet composition adapts to demand distribution within a narrow objective-value band.

6.2.1. Upstream Fleet Selection

For the upstream segment connecting the Tangguh (TGU) source terminal to the Sumbawa hub, the model consistently selects a 65,000 m³ vessel class across all GA runs. This robustness reflects the structural influence of the source terminal service capacity constraint, which limits the maximum allowable annual vessel calls.

Using smaller vessels would require a higher call frequency to satisfy aggregate demand, potentially exceeding terminal service capacity. Conversely, larger vessels reduce call frequency but result in lower utilisation levels and higher unit transportation costs due to higher charter rates. The selected 65,000 m³ vessel thus represents a cost-efficient equilibrium between call frequency, vessel utilisation, and charter cost under the imposed terminal capacity constraint.

This mechanism explains the emergence of a single dominant upstream vessel class rather than a mixed fleet configuration and highlights the structural role of terminal operability in shaping fleet segmentation under the FOB framework.

6.2.2. Downstream Fleet Configuration

In the downstream segment, the fleet configuration exhibits a distinct demand-consolidation pattern:

• Cluster 1 (LOM) is served by a 3500 m³ vessel class. Despite Lombok’s relatively high demand, its short sailing distance from the SBW hub enables high service frequency with smaller vessels while maintaining acceptable berth utilisation and transportation cost efficiency.
• Cluster 2 (BIM and FLO) is also served by 3500 m³ vessels. The combined demand of these two ports does not justify the deployment of larger vessels when evaluated against sailing distances and charter costs. The model prioritises maintaining high utilisation levels while avoiding excess capacity.
• Cluster 3 (MAU, ALO, KPG, and WAI) is served by a 10,000 m³ vessel class. Although individual demand levels at these eastern ports are relatively moderate, their geographic dispersion and longer sailing distances from the hub increase round-trip cycle time. Aggregating these nodes into a single cluster with a larger vessel reduces required voyage frequency and improves cost efficiency over long-haul downstream distribution.

This configuration illustrates that vessel sizing is driven not solely by demand magnitude, but by the interaction between demand aggregation, sailing distance, and cycle time. The resulting segmentation reflects an economic balance between charter cost, utilisation, and route length.

6.2.3. Dynamic Fleet Expansion

To accommodate projected demand growth, the fleet size is adjusted dynamically. The staggered expansion timing reflects differentiated demand growth trajectories and route-cycle characteristics rather than uniform system-wide scaling.

The optimal fleet configuration and its operational metrics over the 20-year planning horizon are presented in

Table 7. Optimal fleet configuration and operational metrics over the 20-year horizon.

Segment	Cluster	Vessel Class (m3)	Fleet Size (Unit)	Annual Freq. [Min]–[Max]	Fleet Utilisation [Min]–[Max]
Upstream	TGU ⟶ SBW	65,000	Year 1–20 (1 unit)	21–26	47.09–59.74%
Downstream	Cluster 1	3500	Year 1–12 (1 unit) Year 13–20 (2 units)	118–150	50.56–99.86%
	Cluster 2	3500	Year 1–14 (1 unit) Year 15–20 (2 units)	66–83	50.59–99.92%
	Cluster 3	10,000	Year 1–20 (1 unit)	24–31	62.86–79.74%

, while detailed operational performance indicators are provided in Appendix E. As shown in Table 7, the upstream segment (TGU–SBW) is consistently served by a single 65,000 m³ vessel throughout the entire horizon, with annual voyage frequency increasing from 21 voyages/year in Year 1 to 26 voyages/year in Year 20 (

Table A5. Voyage frequency evolution (20-year horizon).

Indicator	Year 1	Year 5	Year 10	Year 15	Year 20
Upstream voyages/year	21	22	23	25	26
Cluster 1 voyages/year	118	124	132	140	150
Cluster 2 voyages/year	66	69	74	78	83
Cluster 3 voyages/year	24	26	27	29	31

). Correspondingly, upstream vessel utilisation improves progressively from 47.09% to 59.74% (

Table A7. Vessel utilisation rates.

Indicator	Year 1	Year 5	Year 10	Year 15	Year 20
Upstream	47.09%	49.51%	52.71%	56.12%	59.74%
Cluster 1	87.01%	91.48%	97.39%	51.84%	55.19%
Cluster 2	83.82%	89.27%	93.82%	50.59%	53.86%
Cluster 3	62.86%	66.08%	70.35%	74.90%	79.74%

), reflecting demand growth absorbed through higher sailing frequency rather than fleet expansion.

In contrast, the downstream configuration demonstrates adaptive fleet scaling. Cluster 1 and Cluster 2 initially operate with one 3500 m³ vessel each but expand to two vessels in Years 13 and 15, respectively (

Table A6. Fleet sizing dynamics.

Indicator	Year 1	Year 5	Year 10	Year 15	Year 20
Upstream vessel (65,000 m3)	1	1	1	1	1
Cluster 1 vessel (3500 m3)	1	1	1	2	2
Cluster 2 vessel (3500 m3)	1	1	1	2	2
Cluster 3 vessel (10,000 m3)	1	1	1	1	1

). This expansion accommodates increasing annual voyage requirements, which rise from 118 to 150 voyages/year in Cluster 1 and from 66 to 83 voyages/year in Cluster 2 over the planning horizon (Table A5). The temporary decline in vessel utilisation rates after Year 10 (e.g., Cluster 1 drops from 97.39% in Year 10 to 51.84% in Year 15) reflects this fleet expansion, which redistributes cargo volumes across two vessels to maintain service reliability under higher demand. Cluster 3, serving geographically dispersed eastern ports, maintains a stable configuration with one 10,000 m³ vessel over the entire horizon, while voyage frequency increases moderately from 24 to 31 voyages/year and utilisation improves steadily from 62.86% to 79.74%.

Operationally, loading and discharging times remain stable across the planning horizon (

Table A8. Loading and discharging time per shipment (days).

Indicator	Year 1	Year 5	Year 10	Year 15	Year 20
Upstream vessel (65,000 m3)
Loading time at source	0.79	0.79	0.80	0.80	0.80
Discharging time at the hub	1.09	1.09	1.10	1.10	1.10
Cluster 1 vessel (3500 m3)
Loading time at the hub	0.69	0.69	0.69	0.69	0.69
Discharging time at LOM	0.76	0.76	0.76	0.76	0.76
Cluster 2 vessel (3500 m3)
Loading time at the hub	0.69	0.69	0.69	0.69	0.69
Discharging time at BIM	0.73	0.73	0.73	0.73	0.73
Discharging time at FLO	0.65	0.65	0.65	0.65	0.65
Cluster 3 vessel (10,000 m3)
Loading time at the hub	0.81	0.81	0.81	0.81	0.81
Discharging time at MAU	0.69	0.69	0.69	0.69	0.69
Discharging time at ALO	0.65	0.65	0.65	0.65	0.65
Discharging time at KPG	0.67	0.67	0.67	0.67	0.67
Discharging time at WAI	0.68	0.68	0.68	0.68	0.68

), indicating that terminal service capacity is not a bottleneck under the optimal configuration. Furthermore, storage turnover ratios (

Table A9. Storage linkage with demand dynamics.

Indicator	Year 1	Year 5	Year 10	Year 15	Year 20
Storage turnover Upstream	17.38	16.59	15.87	14.60	14.04
Storage turnover Cluster 1	3.09	2.94	2.77	2.61	2.43
Storage turnover Cluster 2	5.53	5.29	4.93	4.68	4.40
Storage turnover Cluster 3	15.21	14.04	13.52	12.59	11.77

) gradually decline over time—e.g., upstream turnover decreases from 17.38 to 14.04—reflecting improved supply frequency and fleet scaling rather than excess storage capacity. Because storage infrastructure is dimensioned for peak-year demand, later-year reductions in turnover indicate operational stabilisation rather than oversizing.

Overall, Table 7 and Appendix E demonstrate that the optimisation framework achieves structural stability at the upstream level while allowing controlled fleet expansion downstream. Demand growth is primarily absorbed through frequency adjustments and phased vessel addition, confirming that the solution balances utilisation efficiency, service reliability, and long-term infrastructure constraints within the proposed two-stage optimisation framework.

6.3. Operational Routing Optimisation Results

Following the strategic fleet allocation, the operational routing optimisation (Stage 2) determines the optimal port visiting sequence for each cluster to minimise sailing distance. The resulting route structure, visualised in Figure 4, demonstrates efficiency gains achieved through the TSP-based optimisation.

6.3.1. Route Efficiency and Sailing Distances

The optimisation yields distinct routing loops for each cluster, as summarised in

Table 8. Optimal routing sequences and round-trip distances.

Segment/Cluster	Optimal Port Sequence	Round-Trip Distance (nm)
Upstream	TGU ⟶ SBW ⟶ TGU	2086
Cluster 1	SBW ⟶ LOM ⟶ SBW	238
Cluster 2	SBW ⟶ BIM ⟶ FLO ⟶ SBW	500
Cluster 3	SBW ⟶ MAU ⟶ ALO ⟶ KPG ⟶ WAI ⟶ SBW	1240

.

• Upstream route: The dedicated shuttle service between the Tangguh source and Sumbawa hub covers a round-trip distance of 2086 nm. Given the long-haul leg, a large 65,000 m³ carrier is necessary to ensure economic viability while meeting the service capacity constraint at the source terminal.
• Cluster 1: As cluster 1 comprises only a single port, the routing problem is trivial; therefore, explicit sailing distance minimisation is not required for this cluster.
• Cluster 2: The route SBW ⟶ BIM ⟶ FLO ⟶ SBW covers 500 nm. Although longer than Cluster 1, this medium-range loop remains compatible with the 3500 m³ vessel class, balancing sailing time and cargo aggregation without requiring larger parcel sizes.
• Cluster 3: The eastern cluster SBW ⟶ MAU ⟶ ALO ⟶ KPG ⟶ WAI ⟶ SBW forms the longest downstream loop (1240 nm). The extended sailing distance and dispersed geography justify deployment of the 10,000 m³ vessel class, which reduces required voyage frequency and improves cost efficiency over long-haul distribution.

6.3.2. Operational Implications

The routing optimisation does not alter hub selection, clustering structure, or vessel size classes, which are determined exclusively at the strategic planning stage. Instead, routing results provide operationally consistent performance measures that bridge strategic network design and cost evaluation. Sailing distances and travel times obtained from this stage are subsequently used to improve the cost in the cost assessment stage.

The routing optimisation results demonstrate that the proposed two-stage framework ensures internal consistency between the long-term logistics configuration and the short-term operational performance, while preserving a clear separation between the strategic and operational decision layers.

6.4. Infrastructure Implications and Capacity Sizing

The optimisation results demonstrate the LNG infrastructure requirements at each port—whether hub or non-hub—emerge as direct consequences of network configuration, vessel segmentation, and long-term demand evolution, rather than being determined in isolation.

Table 9. Derived infrastructure capacities and operational metrics.

Port	Role	Storage		Trestle Length (m)	BOR * [Min]–[Max]	Regas (m3/Day)
		Capacity (m3)	Type
Sumbawa	Hub	76,000	Flat-Bottom tank	270	46.38–58.75%	1847.20
Lombok	Spoke	8000	Bullet tank	500	24.43–31.04%	1736.06
Bima	Spoke	5000	Bullet tank	180	13.21–16.63%	784.67
Flores	Spoke	2000	Bullet tank	1090	11.74–14.77%	181.65
Alor	Spoke	2000	Bullet tank	130	4.25–5.48%	111.98
Waingapu	Spoke	4000	Bullet tank	130	4.46–5.75%	288.65
Maumere	Spoke	5000	Bullet tank	390	4.55–5.87%	365.79
Kupang	Spoke	3000	Bullet tank	780	4.46–5.75%	242.20

* BOR = Berth (Jetty) Occupancy Ratio.

details the required capacities for storage tanks, jetties (including trestles), and regasification units at the hub-and-spoke ports.

6.4.1. Storage Capacity

As the selected hub, SBW requires significantly greater storage capacity than other ports due to its dual role as both a redistribution and a demand node. To accommodate the large parcels delivered by the upstream 65,000 m³ carrier and buffer the outflows to three downstream clusters, SBW requires a storage capacity of 76,000 m³ implemented as a flat-bottom tank. In contrast, spoke ports utilise modular bullet tanks with significantly smaller capacities (2000–8000 m³), proportioned to their local peak demand and delivery frequency. Lombok, as the largest demand node in Cluster 1, requires the largest spoke storage (8000 m³), while smaller nodes like Alor and Flores operate sufficiently with a minimal 2000 m³ buffer.

6.4.2. Marine Infrastructure (Jetty and Trestle) and Bathymetric Impact

The explicit modelling of bathymetry reveals striking variations in marine infrastructure investment. While vessel sizes for spoke ports are identical (Cluster 2 & 3), the required trestle lengths vary dramatically due to local seabed profiles. For instance, Flores requires a 1090 m trestle to reach the necessary depth, whereas Alor and Waingapu require only 130 m. This highlights the model’s ability to capture location-specific CAPEX drivers that would be missed by generic distance-based cost models.

Furthermore, the Berth Occupancy Ratio (BOR) analysis confirms operational feasibility. The hub experiences the highest utilisation, ranging from 46.38% to 58.75%, which remains safely below the typical congestion threshold of 60–70% [38], validating the decision to construct a single jetty.

6.4.3. Regasification Units

Regasification units are dimensioned for the year-20 peak load, with capacities ranging from 107.5 MMSCFD in Alor to over 1770 MMSCFD in Sumbawa, ensuring long-term supply reliability.

Overall, these results underscore that infrastructure investment decisions in small-scale LNG systems cannot be decoupled from the network configuration and fleet selection. The resulting infrastructure sizing does not represent a locally minimised solution, but rather one that is systematically consistent with operational requirements and peak demand over the planning horizon. This approach reinforces the model’s relevance as a strategic planning tool, particularly in archipelagic regions characterised by infrastructure constraints and long-term demand dynamics.

6.5. Cost Structure Analysis

The economic performance of the optimised supply chain is evaluated through a comprehensive lifecycle cost analysis. This assessment integrates the upfront infrastructure CAPEX, recurring infrastructure O&M, and transportation OPEX over the 20-year planning horizon.

6.5.1. Lifecycle Cost Composition

To facilitate comparative analysis, all cost components are evaluated on a Net Present Value (NPV) basis. As illustrated in Figure 5, the total lifecycle cost of the system is estimated at USD 940.2 million. Infrastructure-related expenditures constitute the largest share of this total. The initial infrastructure CAPEX amounts to USD 333.9 million, while the lifecycle operating and maintenance (O&M) costs accumulate to an NPV of USD 146.5 million. Combined, these infrastructure costs reach USD 480.5 million, representing 51.1% of the total lifecycle cost. Transportation OPEX, including vessel operations and voyage-related costs, account for the remaining USD 459.7 million, or 48.9% of the total.

This distribution indicates that, in archipelagic LNG logistics systems, the economic burden is nearly evenly split between maritime operations and infrastructure lifecycle costs. Such cost parity highlights the importance of an integrated optimisation approach that simultaneously considers fleet efficiency and infrastructure investment decisions to achieve long-term economic sustainability.

6.5.2. Infrastructure Cost Breakdown

Within the initial investment component (CAPEX),

Table 10. Breakdown of initial infrastructure CAPEX by cluster and component.

Port/Cluster	Storage (USD)	Jetty + Trestle (USD)	Regas (USD)	Total CAPEX (USD)	Share (%)
Hub (SBW)	76,000,000	6,648,251	31,392,456	114,040,707	34.1%
Cluster 1	19,360,000	5,337,742	38,148,822	62,846,564	18.8%
LOM	19,360,000	5,337,742	38,148,822	62,846,564
Cluster 2	16,940,000	11,806,028	26,947,489	55,693,517	16.7%
BIM	12,100,000	3,997,838	14,842,511	30,940,349
FLO	4,840,000	7,808,190	12,104,977	24,753,167
Cluster 3	33,880,000	21,930,999	45,557,170	101,368,169	30.4%
MAU	12,100,000	5,618,834	12,660,380	30,379,214
ALO	4,840,000	4,530,162	7,744,715	17,114,877
KPG	7,260,000	7,251,842	13,224,820	27,736,661
WAI	9,680,000	4,530,162	11,927,256	26,137,418
TOTAL	146,180,000	45,723,020	142,045,937	333,948,957	100%

details the distribution. The hub (Sumbawa) accounts for approximately 34% of the regional investment (USD 114 million), driven by high-capacity storage and regasification units. Across the region, storage tanks constitute the largest single CAPEX component (≈44%), exceeding investment in regasification units (≈43%) and marine infrastructure (≈14%).

6.5.3. Levelized Unit Cost

Finally, the system performance is synthesised into a single economic metric. The calculation considers the time-varying nature of demand: annual unit costs are first computed for each year (by dividing the sum of annual transport costs, annualised infrastructure CAPEX, and annual infrastructure O&M costs by the respective annual demand), and then discounted and re-annualised to derive a uniform measure.

This rigorous calculation yields a levelized unit cost of 4.66 USD/MMBtu. This value represents the break-even logistics cost required to support the diesel-to-gas conversion program in the Nusa Tenggara region, accounting for both initial capital intensity and long-term operational dynamics.

To enhance transparency and reproducibility, detailed operational performance indicators—including annual voyage frequencies, fleet sizing evolution, vessel utilisation rates, and loading/discharging durations—are provided in Appendix E. These data allow independent verification of the reported cost decomposition and confirm capacity adequacy across the 20-year planning horizon.

6.6. Sensitivity Analysis

To evaluate the robustness of the proposed LNG supply chain configuration, a sensitivity analysis was conducted by systematically varying aggregated demand levels while observing changes in network topology, fleet segmentation, and unit cost outcomes. Demand uncertainty represents the primary long-term planning risk in small-scale LNG systems, particularly in government-driven diesel-to-gas conversion programs where commissioning schedules and electricity growth projections may deviate from baseline assumptions.

It is important to distinguish robustness analysis under identical demand conditions from structural sensitivity analysis under perturbed demand scenarios. While repeated GA runs under base-case demand confirmed convergence stability, changes in aggregate demand may lead to different optimal fleet configurations due to structural capacity constraints.

Demand levels at all destination ports were uniformly perturbed by ±20% relative to the base-case projections over the planning horizon. This range reflects plausible deviations arising from forecast uncertainty, phased power plant implementation, or macroeconomic fluctuations. Each demand scenario was evaluated using identical GA parameter settings to ensure methodological consistency and comparability across structural configurations.

The results indicate that the optimal network topology remains stable under moderate variations in demand (±20%). However, under extreme demand contraction (−50%), the model identifies a different clustering configuration, indicating that topology adjustments may occur when demand falls significantly below the baseline projection. Hub selection exhibits invariance, confirming that spatial configuration and terminal operability constraints dominate long-term network design decisions. The model adapts to demand variations primarily through fleet sizing rather than network topology reconfiguration.

Under reduced demand (−20%), the upstream vessel class remains at 65,000 m³, indicating that terminal service capacity constraints continue to govern upstream segmentation even under lower throughput conditions. In the downstream segment, Cluster 1 (LOM) and Cluster 2 (BIM, FLO) remain served by 3500 m³ vessels, while Cluster 3 adjusts from 10,000 m³ to 7500 m³ to maintain economic efficiency under reduced volume and long sailing distances. The resulting levelised unit cost increases to 5.35 USD/MMBtu.

Under moderate demand growth (+10%), the upstream vessel class increases to 125,000 m³, reflecting the interaction between aggregate throughput and terminal call limitations. In this scenario, Cluster 2 is served by 5000 m³ vessels while Cluster 3 maintains the 10,000 m³ class. The corresponding unit cost is 5.31 USD/MMBtu.

Under higher demand (+20%), the upstream 125,000 m³ vessel remains optimal. Downstream resizing occurs in Clusters 1 and 2, both selecting 5000 m³ vessels, whereas Cluster 3 continues to operate 10,000 m3 vessels due to route-length and demand-aggregation effects. The unit cost under this scenario decreases to 5.02 USD/MMBtu.

Table 11. The implications of demand variations on the network configuration and fleet segmentation over the planning horizon.

Scenario	Ports	Vessel Class (m3)	Unit Cost (USD/MMBtu)
Base-case	Hub (SBW)	65,000	4.66
	Cluster 1 (LOM)	3500
	Cluster 2 (BIM, FLO)	3500
	Cluster 3 (MAU, ALO, KPG, WAI)	10,000
Demand −20%	Hub (SBW)	65,000	5.35
	Cluster 1 (LOM)	3500
	Cluster 2 (BIM, FLO)	3500
	Cluster 3 (MAU, ALO, KPG, WAI)	7500
Demand −10%	Hub (SBW)	65,000	4.97
	Cluster 1 (LOM)	3500
	Cluster 2 (BIM, FLO)	3500
	Cluster 3 (MAU, ALO, KPG, WAI)	10,000
Demand +10%	Hub (SBW)	125,000	5.31
	Cluster 1 (LOM)	3.500
	Cluster 2 (BIM, FLO)	5000
	Cluster 3 (MAU, ALO, KPG, WAI)	10,000
Demand +20%	Hub (SBW)	125,000	5.02
	Cluster 1 (LOM)	5000
	Cluster 2 (BIM, FLO)	5000
	Cluster 3 (MAU, ALO, KPG, WAI)	10,000

summarises the optimal network configuration and fleet segmentation under different demand scenarios.

To further examine structural breakpoints beyond moderate perturbation, extreme demand scenarios of −50% and +50% were additionally evaluated. This extended analysis reveals asymmetric structural behaviour across contraction and expansion regimes.

Extreme contraction (−50%) demand scenario triggers structural consolidation. While SBW remains the selected hub, the downstream configuration shifts from three clusters to two: Cluster 1 merges LOM and BIM (5000 m³ vessel); Cluster 2 aggregates FLO, MAU, ALO, KPG, and WAI (7500 m³ vessel); and upstream vessel capacity reduces to 45,000 m³.

This consolidation reflects insufficient demand density to sustain three independent downstream loops economically. Under severe contraction, demand aggregation becomes necessary to preserve vessel utilisation and cost efficiency. The resulting unit cost increases significantly to 6.88 USD/MMBtu due to reduced scale economies.

In contrast, under a +50% demand scenario, the hub selection (SBW) and three-cluster structure remain invariant. Scaling is accommodated through fleet resizing: upstream vessel capacity increases to 125,000 m³, Cluster 2 vessel increases to 5000 m³, Cluster 3 vessel increases to 15,500 m³, while Cluster 1 remains unchanged. The network absorbs higher demand through capacity expansion rather than topological restructuring. The resulting unit cost decreases slightly to 4.49 USD/MMBtu, reflecting improved economies of scale.

These results indicate strong structural robustness under growth conditions. The topology remains stable even under substantial expansion, while scaling occurs through adjustments to vessel segmentations.

From a cost perspective, unit costs exhibit gradual and structurally consistent adjustments under moderate demand variation, while extreme contraction introduces topology consolidation. Although fleet segmentation adapts across scenarios, hub selection and clustering remain stable, indicating that the base-case configuration is not located at a knife-edge optimum but within a structurally stable region of the solution space.

Overall, the sensitivity analysis demonstrates that the long-term LNG supply chain structure in the studied archipelagic context is primarily governed by spatial configuration and terminal operability constraints, while fleet sizing serves as the principal adjustment mechanism under demand uncertainty. These findings reinforce the suitability of the proposed optimisation framework for strategic planning under buyer-managed FOB arrangements. Extensions incorporating stochastic demand modelling or robust optimisation approaches are identified as future research directions.

7. Discussion

The optimisation results presented in Section 6 provide quantitative evidence of how contractual structure, terminal operability constraints, and spatial demand distribution interact in shaping the LNG logistics system in archipelagic regions. While the case study focuses on the Nusa Tenggara region of Indonesia, the structural insights derived from the model extend beyond the specific geographical context examined in this study. This section discusses the theoretical contributions of the proposed optimisation framework, its implications for LNG supply chain planning and energy infrastructure policy, and the limitations that define the scope of the current research.

7.1. Implications for Theory

The findings of this study contribute to the theoretical development of LNG supply chain optimisation by highlighting how contractual structures influence logistics system design. Most existing LNG logistics models implicitly assume seller-managed DES arrangements, in which upstream transportation from the source terminal is treated as an external service provided by the LNG supplier. Under such assumptions, optimisation frameworks typically focus on downstream distribution planning and terminal allocation decisions, while upstream transportation remains outside the decision space.

In contrast, the framework proposed in this study explicitly models buyer-managed logistics under an FOB contractual scheme. By internalising upstream transportation decisions within the optimisation model, the framework reveals how source terminal operability constraints interact with vessel sizing and network configuration. The optimisation results demonstrate that the service capacity limitation at the source terminal plays a decisive role in determining upstream fleet configuration. Across repeated genetic algorithm runs under identical demand conditions, the model consistently selects a single dominant upstream vessel class, reflecting the structural interaction between vessel capacity, call frequency constraints, and charter cost efficiency.

The results also provide theoretical insights into the mechanisms that govern fleet segmentation in small-scale LNG distribution networks. Vessel sizing decisions are shown to emerge not solely from local demand magnitude but from the interaction between spatial demand distribution, sailing distance, and voyage cycle time. Ports located within short sailing distances from the hub can be served efficiently by smaller vessels operating at higher frequencies, while geographically dispersed ports with longer route cycles require larger vessel capacities to maintain transportation efficiency. This interaction between spatial structure and fleet configuration illustrates how maritime logistics constraints shape optimal network design in geographically fragmented energy systems.

Another theoretical contribution of this study lies in the endogenous representation of infrastructure requirements. Instead of treating port infrastructure capacity as an independent decision variable, the proposed framework derives infrastructure sizing directly from the logistics configuration generated by the optimisation model. Storage capacity, jetty requirements, and regasification infrastructure emerge as consequences of fleet configuration, routing structure, and demand evolution over the planning horizon. This approach provides a more structurally integrated representation of LNG logistics systems compared with traditional formulations in which infrastructure and transportation decisions are optimised separately.

Finally, the sensitivity analysis presented in Section 6 shows that the optimal network topology remains stable under moderate demand variations. While fleet segmentation adjusts under varying throughput levels, the hub location remains unchanged across all evaluated scenarios. Under extreme demand reductions, however, the cluster structure adapts to maintain transportation efficiency, indicating that fleet configuration and cluster composition serve as the primary adjustment mechanisms when demand deviates substantially from the baseline projections.

7.2. Implications for Practice and Policy

From a practical perspective, the proposed optimisation framework provides a decision-support tool for governments, energy planners, and LNG logistics operators involved in small-scale LNG deployment in geographically fragmented regions.

First, the optimisation results demonstrate that infrastructure investment represents a structurally dominant component of LNG supply chain economics in low-demand archipelagic systems. Cost decomposition analysis shows that total infrastructure capital expenditure amounts to USD 333.9 million, with storage (USD 146.2 million; 43.8%) and regasification facilities (USD 142.0 million; 42.5%) constituting the largest shares, while marine infrastructure accounts for USD 45.7 million (13.7%). These figures indicated that infrastructure development, rather than maritime transportation, represents the primary cost driver in small-scale LNG distribution systems serving dispersed demand centres.

The spatial distribution of infrastructure investment further reveals a high concentration of capital at the selected hub location. The Sumbawa (SBW) hub alone accounts for USD 114.0 million, representing approximately 34.1% of the total infrastructure investment. This concentration reflects the strategic role of the hub terminal in aggregating regional LNG demand and supporting downstream distribution operations. At the same time, downstream clusters serving geographically dispersed ports also require substantial infrastructure investment. Cluster 3, which serves eastern ports with relatively long sailing distances, contributes USD 101.4 million (30.4%) of the total infrastructure cost, largely driven by the need to develop receiving infrastructure across multiple locations.

These findings highlight the sensitivity of LNG supply chain economics to infrastructure scale and utilisation, particularly in geographically fragmented regions where infrastructure capacity must be dimensioned to accommodate peak demand projections over long planning horizons. As a result, infrastructure planning becomes a critical determinant of system-wide economic performance in emerging LNG distribution networks.

Second, the robustness of hub selection across multiple optimisation runs and sensitivity scenarios provides important guidance for long-term infrastructure planning. Even under substantial demand variations, the Sumbawa hub consistently emerges as the optimal aggregation point for regional LNG distribution. This structural stability suggests that infrastructure investment decisions at strategically located hub terminals can remain economically viable even under uncertain demand conditions.

Third, the endogenous infrastructure sizing approach adopted in this study provides a practical method for estimating long-term investment requirements for LNG receiving terminals. By linking storage capacity and jetty utilisation directly to vessel operations and demand trajectories, the model supports more consistent infrastructure planning for small-scale LNG systems in emerging gas markets.

Finally, the results provide policy-relevant insights for government-led energy transition programmes, particularly those aimed at replacing diesel-based electricity generation with natural gas in remote island regions. In such contexts, the economic feasibility of LNG distribution systems depends not only on transportation efficiency but also on the coordination of infrastructure development across multiple ports. Integrated planning approaches that simultaneously consider fleet configuration, infrastructure capacity, and spatial demand distribution can therefore play a critical role in supporting the successful implementation of regional gasification programmes.

7.3. Limitations of the Study and Future Research Directions

While the proposed optimisation framework provides valuable insight into LNG supply chain planning under a buyer-managed FOB contractual structure, several limitations should be acknowledged.

First, the model focuses on long-term strategic planning and therefore assumes deterministic time-dependent demand projections over the planning horizon. Although sensitivity analysis demonstrates that the network configuration remains robust under moderate demand variations, real-world LNG demand may exhibit stochastic fluctuations due to electricity demand growth, delays in power plant commissioning, or broader economic uncertainty. Future research may therefore benefit from incorporating stochastic demand modelling or robust optimisation approaches to better capture uncertainty in long-term LNG demand projections.

Second, the model abstracts from several operational factors that may influence LNG logistics performance, including detailed berth scheduling, weather-related disruptions, and short-term vessel dispatching decisions. These aspects are typically addressed at the operational level and are therefore beyond the scope of the strategic optimisation framework developed in this study. Integrating operational scheduling models with long-term logistics optimisation represents a promising direction for future research.

Third, boil-off gas (BOG) dynamics are not explicitly represented in the optimisation model. Incorporating BOG behaviour would require modelling cargo losses as a function of voyage duration and unloading sequence, which would significantly increase model complexity and require adjustment to the cargo allocation formulation. While simplified estimates suggest that BOG-related cargo losses represent a relatively small share of total logistics costs in the examined system, future research could incorporate detailed modelling of BOG behaviour for operational-level analyses.

To quantitatively assess the potential structural impact of BOG, an upper-bound volumetric estimation was conducted based on the model’s first year operational results. Assuming a conservative evaporation rate of 0.10–0.12% per day and using the round-trip durations generated by the optimisation model, the estimated BOG losses per voyage remain limited. For the upstream segment (65,000 m³ vessel; 8.09 round-trip days), estimated losses range between 0.81% and 0.97% of transported volume per voyage. For downstream clusters, estimated losses are approximately 0.26–0.32% (Cluster 1; 2.63 days), 0.46–0.55% (Cluster 2; 4.55 days), and 0.92–1.10% (Cluster 3; 9.18 days) per voyage.

Even under the conservative upper-bound assumption, these losses remain below approximately 1% of transported volume per cycle. At the annual level, the upstream volumetric deviation is below 1% of the total transported volume. While explicit modelling of BOG would require reformulation of the unloading allocation mechanism—since cargo availability becomes path-dependent along multi-port routes—the magnitude of the deviation is sufficient to materially alter hub selection, clustering structure, vessel segmentation, or infrastructure sizing within the deterministic planning horizon considered. Therefore, BOG exclusion does not affect the structural validity of the strategic configuration results, although it may influence detailed operational scheduling under short-term stochastic conditions.

Finally, the solution approach employs a Genetic Algorithm to address the large-scale combinatorial structure of the optimisation problem. Although convergence analysis confirms stable results across multiple independent runs, future studies may explore hybrid metaheuristic or decomposition-based solution methods to further improve computational efficiency for larger LNG distribution networks.

8. Conclusions

This study develops an integrated optimisation framework for designing LNG supply chains under an FOB contractual scheme, where transportation responsibility is transferred from the seller to the buyer. The proposed model simultaneously determines hub selection, port clustering, vessel configuration, routing structure, and supporting infrastructure requirements within a unified optimisation framework. By internalising both upstream and downstream logistics decisions, the model provides a more comprehensive representation of LNG distribution planning compared to conventional approaches that treat upstream transportation as exogenous.

The results of the case study demonstrate that terminal operability at the LNG source plays a critical role in shaping upstream fleet configuration. The optimisation consistently identifies a single dominant vessel class for the upstream segment, reflecting the interaction between vessel capacity, call frequency limitations, and transportation cost efficiency. At the downstream level, fleet segmentation emerges from the interaction between spatial demand distribution, sailing distance, and route cycle time, resulting in differentiated vessel classes across service clusters.

Sensitivity analysis indicates that the overall network structure exhibits a high degree of robustness under moderate demand variations. Hub selection remains stable across all evaluated scenarios, confirming that spatial configuration and terminal service capacity constraints dominate long-term network design decisions. Under more extreme demand deviations, the model adapts primarily by adjusting fleet size and cluster composition rather than by making fundamental changes to hub location. These results suggest that LNG supply chain systems in geographically dispersed regions can maintain structural stability across a wide range of demand conditions while adjusting operational parameters to accommodate demand fluctuations.

A key contribution of this study lies in treating infrastructure capacity as an endogenous outcome rather than an exogenous decision variable. Storage, jetty including trestle, and regasification capacities are derived directly from the selected hub location, vessel size classes, clustering structure, and long-term demand evolution. In particular, the integration of bathymetry-based infrastructure sizing captures the realistic interaction between vessel draft requirements and jetty investment, providing a physically grounded representation of port development costs in archipelagic environments.

The inclusion of a source terminal service capacity constraint further strengthens the framework’s realism by explicitly linking upstream vessel size selection to terminal operability. The results show that this constraint plays a critical role in vessel segmentation: smaller vessels increase call frequency and may violate terminal service limits, while larger vessels reduce call frequency but suffer from underutilisation and higher charter costs. The optimal selection of a 65,000 m³ upstream vessel reflects trade-offs and underscores the importance of terminal accessibility constraints in buyer-managed LNG logistics.

Although the model captures key strategic planning decisions, several extensions may further enhance its applicability. Future research may incorporate stochastic demand representations, explicit modelling of boil-off gas losses, and operational uncertainties such as weather-related port accessibility and charter market volatility. Incorporating these elements would provide a more comprehensive representation of real-world LNG logistics operations while preserving the strategic planning insights generated by the present framework.