A Hybrid Integrated Multi-Objective Optimization Framework for Sustainable International Road Logistics Networks: Integrating Transportation Models and Pythagorean Aggregation Decision Methods

Abstract

The Greater Mekong Subregion (GMS) has emerged as a strategic logistics hub due to rapid economic integration and the expansion of cross-border road transportation. However, international road logistics networks in the region must address several competing objectives, including minimizing transportation costs, reducing delivery times, and balancing transport distances among trading partners. To overcome these challenges, this study proposes an innovative hybrid computational framework that integrates the classical Transportation Problem with the Pythagorean methodology (TPPM). The proposed approach consolidates multiple transportation objectives into a unified performance metric based on the Pythagorean concept, thereby enabling simultaneous optimization under practical constraints. In addition, geographic inputs derived from Google Maps and Google Earth via web platforms, which are reliable open-source GIS tools, are incorporated into the transportation model to improve spatial accuracy. A simulated dataset comprising 35 suppliers and 42 customers, representing major logistics nodes in the GMS, is developed to evaluate the proposed method. The computational results indicate that the TPPM approach outperforms the conventional single-objective Classical Transportation Problem (CTP) by producing higher solution quality and more balanced performance. Overall, the findings demonstrate that the proposed hybrid method is a robust decision-support tool for sustainably enhancing the resilience of international logistics planning in emerging economic regions.

1. Introduction

Within the Greater Mekong Subregion (GMS), smallholder agriculture remains the principal livelihood base for more than 60% of the population, out of an estimated regional total of approximately 340 million. This sector is central to the livelihood security of over 200 million people across the subregion [1,2]. Consequently, efforts to improve trade efficiency, which are intrinsically linked to freight transport performance, cannot be pursued solely within domestic policy frameworks. Rather, they must be advanced through an integrated regional approach that explicitly addresses cross-border logistics connectivity and network coordination. Strengthening international logistics linkages is therefore essential not only for enhancing trade facilitation, but also for expanding market access and supporting the economic development of agricultural enterprises throughout the Greater Mekong Subregion.

Although maritime transport accounts for more than 80% of global international trade flows [3,4], intra-regional transportation connectivity in the GMS continues to rely predominantly on terrestrial freight modes. This structural dependence is largely attributable to the region’s contiguous geographic configuration, particularly the southern territory of China and its borders with Myanmar and the Lao PDR, both of which are connected by multiple overland corridors to Thailand, Cambodia, and Viet Nam. In addition, road transport has become the dominant channel for international freight movement across the subregion. This dominance is evidenced by the substantial expansion of road networks along major economic corridors, namely the North–South, Southern, and East–West corridors, which serve as the primary axes of transport integration within the regional logistics system [5,6]. In this context, the application of transportation problem formulations to the design of direct full-truckload delivery strategies for small consignments offers a mathematically rigorous approach with considerable potential to improve distribution efficiency and support small- and medium-sized enterprises operating in the GMS.

The Transportation Problem (TP) is a standard optimization framework concerned with allocating commodities from supply nodes to demand nodes in a manner that minimizes total transportation cost. Over time, this model has become an important tool in transportation analysis and logistics decision-making. In its classical form, TP is typically framed as a single-objective cost minimization problem, in which the primary aim is to reduce the expense of direct deliveries [7,8,9]. However, real-world transportation environments are considerably more complex and cannot be adequately represented by cost considerations alone. In operational practice, decision-makers must often account for multiple competing factors simultaneously, such as demand satisfaction, route length, transit time, and system constraints. For example, the least-cost route may differ from the shortest-distance route or the fastest one. Likewise, congestion and heavy traffic may force drivers to take detours, thereby increasing both travel distance and delivery time. These additional burdens, in turn, affect vehicle utilization, equipment deployment, labor requirements, and related activities, ultimately increasing operational workload and generating further indirect costs.

A promising approach for integrating multiple dimensions is the Pythagorean methodology (PM), which is based on the Pythagorean theorem, a classical geometric principle associated with right-angled triangles. From a theoretical perspective, when two evaluated quantities are measured relative to a common origin but expressed along different axes, their squared values may be summed and then transformed using the square root operator to generate a composite measure that captures both dimensions simultaneously. This composite measure provides a unified indicator of the combined effect of the two variables [10,11,12,13]. Accordingly, the adoption of the Pythagorean methodology for integrating multiple objectives in a single-stage transportation problem may represent a meaningful advancement in transportation planning, as it enables the concurrent evaluation of multidimensional criteria.

In the GMS, international road-based logistics networks have expanded rapidly in response to economic corridor development and rising cross-border trade, thereby increasing operational complexity. As a result, decision-makers must simultaneously balance multiple conflicting objectives, including transportation cost, delivery reliability, and capacity utilization. However, conventional transportation problem formulations typically optimize cost alone and are therefore insufficient for international logistics systems that require the simultaneous consideration of multiple performance criteria. Moreover, although the demand for integrated multi-objective decision-making frameworks is growing, the literature remains limited in its development of models that explicitly capture trade-offs among competing logistics objectives.

To address the limitations of conventional cost-centric models in managing multi-objective integration in international road logistics within the Greater Mekong Subregion (GMS), this study proposes a novel decision-support framework that integrates the classical Transportation Problem (TP) with a Pythagorean Methodology (PM). To highlight the academic and practical advancements of this work, the main contributions are threefold:

First, from a methodological standpoint, this study develops a hybrid TPPM framework that employs a right-angled geometric transformation to synthesize competing objectives namely cost, distance, and transit time into a single composite function, thereby eliminating the need for subjective priority-weighting schemes.

Second, in terms of context-specific empirical modeling, this study constructs and validates a realistic simulated dataset that captures the operational realities and cross-border corridor networks of the GMS, thus establishing a domain-tailored benchmark for future regional freight research.

Third, with regard to practical decision support, this study delivers quantified scenario analyses that equip GMS logistics providers and agricultural SMEs with a mathematically grounded tool for optimizing full-truckload fleet routing and enhancing regional market access.

The remainder of this paper is organized as follows. Section 2 reviews the literature on the Transportation Problem and multi-objective optimization, and introduces the proposed hybrid TP–Pythagorean methodology. Section 3 details the simulated GMS dataset, mathematical formulation, and computational experiments. Section 4 presents the comparative analysis and outlines avenues for future research. Finally, Section 5 concludes the study.

2. Materials and Methods

2.1. Literature Review

The classical transportation problem (CTP) has long been regarded as a foundational model for minimizing distribution costs in logistics and supply chain planning. By determining optimal shipment allocations across multiple destinations, it provides a structured basis for the efficient movement of resources in alignment with production and delivery requirements. More recently, research has increasingly extended the CTP to incorporate multiple transportation objectives, reflecting the growing operational complexity of contemporary logistics systems and the need for more flexible decision-making frameworks.

Early contributions emphasized the integration of diverse information requirements into transportation-related data acquisition processes in order to improve system performance. For example, ref. [14] showed that embedding real-time data within computational frameworks enhances data accuracy and supports cost reduction in transportation operations. Similarly, ref. [15] highlighted the importance of technological readiness and contextual user-demand analysis, demonstrating that the adoption of advanced technologies can significantly improve operational efficiency. In a related study, ref. [16] illustrated that computer-based tools are effective in addressing the complexity of transportation problems by simplifying data processing and facilitating the identification of optimal solutions. Collectively, these studies underscore the growing role of digital and computational innovations in strengthening international logistics and supply chain efficiency.

Within multi-destination transportation research, ref. [17] proposed a unified formulation that integrates Euclidean distance and transportation cost to obtain optimal solutions. Their results indicate that distance-based considerations can simultaneously reduce transportation cost and improve routing efficiency. Likewise, ref. [18] developed polynomial-time algorithms for transportation optimization, with subsequent support provided by ref. [19]. However, these studies remain primarily at the level of computational formulation, and their validation has largely relied on simulation, offering promising but limited evidence of cost efficiency.

During the same period, refs. [20,21] addressed multi-objective transportation problems by incorporating environmental and weighted-objective considerations into their models. Nevertheless, both studies remain largely exploratory, as they are confined to simulation-based analysis. Ref. [20] has yet to achieve full computational maturity due to the absence of empirical data for validation, whereas ref. [21] relied on synthetic datasets to test its approach. In addition, both studies treated the objectives separately rather than within an integrated framework, thereby limiting the possibility of a holistic assessment of system-wide performance.

Ref. [22] developed time-dependent algorithms based on polynomial formulations to solve transportation problems with temporal structure, demonstrating the effectiveness of such formulations in deriving optimal solutions. Likewise, ref. [23] introduced a computational framework that leverages time-series data to address transportation problems under temporal constraints, yielding efficient solutions. In a complementary contribution, ref. [24] applied game-theoretic analysis to dynamic interactions among transportation service providers within a single parent organization, showing that this approach supports cost-minimizing decision-making. Collectively, these studies indicate that the integration of polynomial, temporal, and game-theoretic methods can substantially enhance the analytical and computational treatment of transportation optimization problems.

Recent scholarship in transportation research has progressively moved beyond deterministic, single-objective network models toward integrative frameworks that explicitly account for uncertainty, multi-stakeholder behavior, and environmental externalities. This paradigmatic shift reflects a growing recognition that transportation systems—particularly those embedded within international logistics and supply chain networks—operate under highly variable conditions, including fluctuating travel times, divergent commercial interests among supply chain actors, and mounting pressure to decarbonize freight movement across global trade corridors. The six studies reviewed herein exemplify these converging research trajectories, collectively illustrating how the field is advancing toward more realistic, adaptive, and sustainability-oriented approaches to transportation and logistics optimization.

A central concern in contemporary network design lies in travel-time uncertainty, particularly when variance is non-uniform across spatial and temporal dimensions of the network. Ref. [25] address this challenge directly, proposing a simulation-based robust and adaptive optimization method tailored to heteroscedastic transportation problems—that is, contexts in which uncertainty varies systematically by location and time rather than conforming to a single, fixed distribution. Their adaptive framework enables decision-makers to hedge against volatility without resorting to the overly conservative solutions that often characterize classical robust optimization. This heteroscedasticity-aware perspective constitutes a meaningful departure from earlier robust models premised on homogeneous uncertainty, offering a more faithful representation of the irregular disruption patterns that typify real-world logistics networks, particularly those operating across heterogeneous international corridors.

Complementing this adaptive orientation, ref. [26] incorporate both the mean and standard deviation of travel time into the classical Network Design Problem (NDP). Rather than optimizing solely for expected travel time, their formulation explicitly penalizes variability, thereby capturing traveler risk-aversion and reliability concerns that are especially salient in time-sensitive freight and supply chain operations. To manage the computational complexity introduced by this dual-moment objective, the authors propose a hybrid algorithm integrating Column Generation and Lagrangian Relaxation, thereby achieving tractable solutions even for large-scale networks. Read together, these two studies signal a discernible trajectory in the field: robust transportation optimization is evolving from mean-based cost minimization toward variance-sensitive, adaptive frameworks capable of responding to heterogeneous and dynamically evolving uncertainty—an evolution with direct implications for the design of resilient international supply chains.

Beyond purely physical network optimization, freight-route decisions are further shaped by strategic interactions among stakeholders with divergent, and at times competing, incentives. Ref. [27] examine this dimension through a multi-stage evolutionary game framework involving shippers, carriers, and government actors during the promotion of new freight routes. Their model demonstrates how policy incentives and behavioral adaptation jointly shape route adoption over time, revealing that the success of route promotion initiatives depends not merely on cost-efficiency but on the alignment of incentives across all three actor groups. This behavioral lens meaningfully complements the mathematical optimization literature by illustrating that technically optimal routes may nonetheless fail in practice if strategic stakeholder dynamics—an especially critical consideration in multi-actor international logistics systems—are left unaccounted for.

In a related vein, within the domain of transit and freight line planning, ref. [28] investigate how differing optimization objectives, such as minimizing operator cost versus maximizing user welfare, yield substantially divergent network outcomes. Their sensitivity analysis underscores that the selection of an objective function is not a neutral technical decision but one bearing significant distributional consequences for both operators and users across the supply chain. This finding reinforces a broader disciplinary theme: transportation and logistics planning increasingly demands multi-objective, stakeholder-sensitive evaluation rather than singular, cost-based optimization—an imperative that becomes especially pronounced in globally interconnected freight systems.

Environmental considerations further complicate freight-route decision-making, particularly in light of the disproportionate carbon footprint associated with heavy-duty trucking within international logistics operations. Ref. [29] contribute a spatially granular model of heavy-duty truck CO₂ emissions derived from detailed travel activity data. By linking micro-level driving behaviors—such as speed variation and idling—to corresponding emission outputs, their spatial analysis identifies specific corridors and operational patterns responsible for disproportionately high carbon output. This activity-based approach signals a broader methodological shift in freight emissions research, moving from aggregate, macro-level estimates toward fine-grained spatial diagnostics that enable more precisely targeted decarbonization strategies within global supply chains.

Beyond structural network design, freight routing and line planning are inherently multi-actor processes shaped by competing economic, operational, and regulatory interests. At the operational execution level, ref. [30] addressed cross-border logistics through an extended Traveling Salesman Problem (TSP) incorporating strict distance–time constraints. By integrating symmetry-based algorithms with real-time Google Maps API data, their model enables continuous dynamic rerouting for international land logistics, solving schedule adherence issues in volatile environments.

Taken collectively, these six recent studies reveal a field increasingly attentive to the interplay between uncertainty, stakeholder behavior, and environmental impact within transportation and logistics systems. Robust optimization methods refs. [25,26] furnish the mathematical foundation necessary for managing travel-time variability, while behavioral and objective-sensitivity studies refs. [27,28] demonstrate that network performance cannot be meaningfully evaluated in isolation from stakeholder incentives and planning priorities. Meanwhile, refs. [29,30] illustrate the growing necessity of embedding spatially explicit emissions analysis into freight planning processes. Future research would benefit from integrating these three analytical strands—adaptive robust optimization, multi-agent behavioral modeling, and spatially explicit carbon accounting—toward the design of freight and international supply chain networks that are simultaneously resilient, strategically viable, and environmentally sustainable.

Overall, the reviewed literature indicates that research on the classical transportation problem has primarily focused on obtaining cost-minimizing solutions. To improve model realism and operational robustness, recent studies have incorporated additional constraints such as time, distance, and other relevant informational parameters into standard formulations. These enhanced models are then implemented using computational methods and algorithmic procedures to derive solutions that more accurately reflect practical logistics conditions. The evidence further suggests that combining advanced computational techniques with problem-specific constraints can substantially improve solution efficiency, thereby enhancing decision quality and reducing transportation costs.

Despite substantial progress in transportation research including the introduction of additional constraints, multi-objective formulations, and advanced computational methods relatively few studies have addressed multiple operational objectives within a single coherent framework. In practical transportation systems, decisions are inherently multi-criteria and typically involve trade-offs among time, cost, and distance. However, treating these criteria separately may obscure important system-level performance characteristics. Although the literature has examined multiple transportation objectives, these have often been analyzed in isolation rather than in an integrated manner. Accordingly, an important methodological challenge is to consolidate heterogeneous real-world objectives into a unified evaluative measure. The proposed algorithm is designed to address this challenge by explicitly incorporating such considerations into its formulation.

Moreover, a critical review of the literature reveals that no prior study has integrated transportation modeling with the Pythagorean methodology to develop a decision support system for solving multi-objective, single-stage transportation problems. Accordingly, there is a clear need for advanced research that formulates a hybrid computational framework to support the optimization of multi-dimensional transportation problems in international road logistics networks.

2.2. Methodology

2.2.1. Problem Statement

Transportation models have long been fundamental tools for optimizing logistics and supply chain systems. More recently, the classical framework has been extended to multi-objective transportation problems (MOTPs), which are solved using a range of optimization paradigms, including weighted-sum formulations, goal programming, and aggregation decision-making models. By contrast, the conventional transportation problem (CTP) is typically limited to minimizing transportation expenditure. Although such formulations remain effective in deterministic and highly structured environments, they are insufficient for capturing the operational complexity of contemporary international logistics networks, where cost, distance, and delivery time often arise as simultaneous and competing criteria that must be optimized in an integrated manner. In light of these considerations, the international road logistics network can be formulated accordingly, and the corresponding indices and objective functions are presented in

Table 1. Definitions of indices and objective functions. Source: The Authors.

Notation	Definition
$i$	Each supplier location which individually responses for suppliable capacity.
$j$	Each customer location which identically generates the demand quantity.
$C_{ij}$	Each transport cost along the international road linkage from $i$ to $j.$
$D_{ij}$	Each transport distance along the international road linkage from $i$ to $j.$
$T_{ij}$	Each transport time along the international road linkage from $i$ to $j.$

.

As shown in Table 1, each direct international shipment is characterized by transportation objectives represented by $C_{ij}$, $D_{ij}$ and $T_{ij}$. In this context, the Pythagorean methodology (PM) offers an effective framework for integrating multiple criteria into a single composite index. By measuring the Euclidean distance from an ideal reference solution, PM enables a systematic and balanced assessment of competing transportation objectives. Accordingly, the proposed transportation problem with Pythagorean methodology (TPPM) is designed to support the simultaneous minimization of transportation distance, delivery time, and cost, thereby enhancing decision-making in international logistics and supply chain planning.

2.2.2. Classical Transportation Problem (CTP)

This problem concerns the allocation of resources from production origins, including manufacturing plants, raw material suppliers, and warehouses, to terminal destinations for subsequent use. Its objective is to minimize the total associated cost, which classifies it as a classical minimization problem [8,9,31]. In international road freight transport supporting overseas production facilities, direct shipments are typically carried out using full-truckload (FTL) vehicles to deliver intermediate goods to customers. The indices and parameters used in the CTP calculation are presented in

Table 2. Additional definitions of indices and parameters in CTP. Source: The Authors.

Notation	Definition
$S_i$	The number of the trucks with the full truck load available at supplier $i.$
$O_j$	The demand of the trucks with the full truck load required to be delivered to customer $j.$
$C_{ij}$	The transportation cost representing by the fuel consumption for each shipping by the truck with the full truck load from the origin node $i$ to the destination node $j.$
$X_{ij}$	Decision variable indicates the number of the full loading trucks shipments from the origin node $i$ to the destination node $j.$
$CTP$	Parameter objectively indicates the total transport cost when internationally transfers goods by the trucks with the full truck load per planning period.

.

CTP is typically formulated to determine an optimal direct-shipping plan from origin nodes to destination nodes by selecting routes that minimize transportation costs over a given planning horizon, subject to the availability of full-truckload vehicles. In essence, it provides a direct freight-planning framework designed to minimize total logistics costs, with each shipment assigned to a single truck at full capacity. Under these assumptions, the problem can be formulated as follows.

• Objective function

CTP seeks to minimize the total transportation cost of international freight movements using full-truckload vehicles within each planning period.

$$Minimize CTP={\displaystyle \sum _{i=1}^m}{\displaystyle \sum _{j=1}^n}{C}_{ij}{X}_{ij}$$

(1)

2.

Constraint functions

The total full-truck-load shipments across all routes shall not exceed the full-truck-load trucks available at origin node $i$.

$${\displaystyle \sum _{j=1}^n}{X}_{ij}=S_i , \forall i (i\in 1,2,3,\dots .m)$$

(2)

The total number of full truckloads transported across all routes shall not exceed the required full truckloads at destination nodes $j$.

$${\displaystyle \sum _{i=1}^m}{X}_{ij}=O_j , \forall j (j\in 1,2,3,\dots .n)$$

(3)

Under the least-cost criterion, each selected international direct-delivery route shall minimize the transportation cost of full-truck-load shipments from domestic supplier $i$ to overseas customer $j$.

$${\sum }_{j=1}^n{X_{ij}C}_{ij}\le C_{ik}+M\left(1-X_{ik}\right), \forall i,k$$

(4)

where: $X_{ij}$ is the decision variable for selecting arc ($i,j$), $C_{ij}$ is the cost coefficient for arc ($i,j$), and $M$ is a sufficiently large constant.

The number of shipment trucks allocated to each transportation route must be nonnegative.

$$X_{ij}\ge 0$$

(5)

$X_{ij}$ $\ge$ 1 if a full-truckload shipment is dispatched from domestic supplier $i$ to overseas customer $j$, $X_{ij}$ = 0 otherwise.

2.2.3. Combination of Transportation Problem and Pythagorean Methodology (TPPM)

This study examines a class of transportation problems that integrate multiple objectives within a unified decision-making framework. To this end, the classical Transportation Problem is combined with the Pythagorean Method, resulting in a hybrid model referred to as the Transportation Problem with Pythagorean Method (TPPM). The Pythagorean theorem offers a systematic approach for aggregating multidimensional information into a single composite measure, namely the square root of the sum of squared components [32,33,34]. By contrast, the transportation problem aims to minimize distribution costs by efficiently allocating shipments between supply and demand nodes and identifying optimal delivery routes [35,36].

Within this framework, manufacturers and suppliers employ full truckload (FTL) shipments to transport goods to international destinations while simultaneously evaluating multiple decision criteria, including travel distance, transit time, transportation cost, and other operational factors. This integrated approach ensures that all relevant objectives are incorporated into a single decision-making structure, thereby overcoming the limitations associated with route selection based on only a limited number of metrics. Accordingly, each fully loaded truck is assigned a route from the country of origin to an overseas destination that minimizes the aggregated value of the selected objectives. The proposed model therefore optimizes distance, time, and cost concurrently as key performance indicators under a unified formulation.

In addition, the model explicitly incorporates the relationship between vehicle speed and fuel consumption, recognizing that fuel efficiency is strongly influenced by freight vehicle operating speed. This feature enables a more realistic representation of transportation performance in international freight operations. The TPPM formulation extends the CTP model and provides a more comprehensive and flexible framework for multi-objective international logistics planning, simultaneously accounting for cost, distance, and time. The additional indices and parameters used in the TPPM formulation are presented in

Table 3. Additional definitions of indices and parameters in TPPM. Source: The Authors.

Notation	Definition
$V_{ij}$	The transportation speed for shipments from origin location $i$ in the primary country to destination location $j$ in the foreign country is expressed in kilometers per hour.
$F_{ij}$	The transportation energy efficiency at speed $V_{ij}$ for shipment from origin $i$ in the home country to destination $j$ in the foreign country is expressed in kilometers per liter.
$P_{ij}$	The Pythagorean distance was evaluated over controlled dimensions to facilitate the simultaneous optimization of multiple objectives in a single-stage transportation model, in which goods are dispatched from origin node $i$ in the source country to destination node $j$ in the foreign country.
$TPPM$	The integrated multidimensional objective phase of the Transportation Problem (TP) and Pythagorean Methodology (PM) consolidates multiple performance criteria within each delivery planning cycle.

.

The TPPM-based transportation system identifies full-truckload shipments from origin to destination along the shortest feasible route, as determined by the Pythagorean distance framework. Its primary objective is to minimize total travel distance, transit time, and post-transport operating costs, while energy consumption is used as a proxy for overall system performance. Accordingly, the problem is formulated as a direct full-truckload transportation planning model aimed at minimizing total transportation energy consumption. To capture the multiple objectives involved, normalized performance metrics are then defined.

• Objective function

The main objective function seeks to minimize the integrated multidimensional distance.

$$Minimize TPPM={\displaystyle \sum _{i=1}^m}{\displaystyle \sum _{j=1}^n}{P}_{ij}{X}_{ij}$$

(6)

When the transportation objectives of distance, time, and cost are integrated via the Pythagorean distance for each route, the corresponding measure is obtained as follows.

$$P_{ij}=\sqrt{{D_{ij}}^2+{T_{ij}}^2+{C_{ij}}^2}$$

(7)

2.

Constraint functions

Assessment of the total transportation distance (TD)along the solution trajectory generated by the Minimize-TPPM framework.

$${TD}_{TPPM}={\displaystyle \sum _{i=1}^m}{\sum }_{j=1}^n\left(D_{ij}\right)X_{ij}$$

(8)

Total transport time (TT) along the TPPM-minimizing route.

$${TT}_{TPPM}={\displaystyle \sum _{i=1}^m}{\sum }_{j=1}^n\left(T_{ij}\right)X_{ij}$$

(9)

Total transportation cost (TC) denotes the energy consumed in transportation, measured by oil consumption, along the optimal TPPM routes.

$${TC}_{TPPM}={\displaystyle \sum _{i=1}^m}{\sum }_{j=1}^n\left({F_{ij}^{-1}D}_{ij}\right)X_{ij}$$

(10)

The route-specific transportation energy consumption rate, measured by fuel use and adapted from ref. [37], is determined by the average travel speed along each direct road shipment. Under the assumption of a fully loaded truck carrying approximately 20 tons, operating under EURO-4 standards and zero road gradient, the fuel consumption rate is formulated as follows.

$$Where as V_{ij}={\displaystyle \raisebox{1ex}{$D_{ij}$}\!\left/ \!\raisebox{-1ex}{$T_{ij}$}\right.}$$

(11)

$$F_{ij}=1.457+0.000066V_{ij}^2$$

(12)

$$C_{ij}=F_{ij}^{-1}{D}_{ij}$$

(13)

Under the least-cost criterion, each selected transportation link is chosen to minimize the Pythagorean distance for full-truckload shipments from supplier $i$ to customer $j$.

$${\sum }_{j=1}^n{X_{ij}P}_{ij}\le P_{ik}+M\left(1-P_{ik}\right), \forall i,k$$

(14)

where: $X_{ij}$ is the binary decision variable for selecting arc ($i,j$), $P_{ij}$ is the Pythagorean coefficient for arc ($i,j$), and $M$ is a sufficiently large constant.

2.2.4. Computational Experiment

• Data Generation

This study develops a hybrid TP–Pythagorean computational framework (TPPM) for optimizing multi-objective logistics integration in the Greater Mekong Subregion (GMS). Because field-based collection of transportation data and related operational records from entrepreneurs is both time-consuming and costly, and may also be limited by restricted access to proprietary information [38,39], the present study instead employs illustrative datasets obtained from publicly accessible online sources. These datasets provide representative information sufficient for model formulation and analysis, thereby enabling the investigation while avoiding the practical constraints associated with direct industrial data acquisition.

In this study, the numbers of origins and destinations were generated through computer-based randomization, resulting in 35 suppliers and 42 customers. Supplier locations within Thailand were randomly assigned using the Province and Region Comprehensive Data of Thailand [40], whereas overseas delivery points were selected from datasets covering GMS countries [41,42,43]. All selected sites were restricted to areas geographically contiguous with Thailand and connected by existing road networks, as verified using Google Earth, a freely accessible platform that provides accurate virtual geographic representations of continental regions [37,44,45]. To ensure spatial realism, all selected sites were restricted to areas geographically contiguous with Thailand and interconnected by active cross-border road networks. Supply and demand values were generated through computer-based uniform randomization with a fixed random seed (Seed = 42), thereby guaranteeing exact computational reproducibility. The complete generated input dataset comprising supplier and customer coordinates, supply capacities, and demand requirements is provided as subsequence.

To obtain accurate travel distances and durations, location-based queries were extracted using the Google Maps Distance Matrix API. In order to preserve temporal consistency across cross-border routes, all routing queries were executed following a standardized extraction protocol, detailed as follows:

Query Period and Date: All spatial queries were conducted on 14 February 2026, with departure time standardized at 09:00 AM (UTC + 7) to represent non-peak conditions. This approach establishes baseline travel times independent of real-time dynamic traffic fluctuations, thereby enhancing the comparability and stability of the results.

Route Selection and Mode: The best-route parameter was applied under the heavy-goods vehicle (HGV) driving mode, excluding toll-free or ferry-only alternatives, so as to reflect standard commercial freight operations and realistic logistics practices.

Cross-Border and Road Restrictions: Distance and travel-time computations were confined to established international land transport corridors, ensuring that all travel-time estimates correspond strictly to physical road-based transportation rather than alternative or multimodal routes.

To uphold confidentiality, all origin and destination locations were reported at the province or district level only, without disclosure of any private entities or proprietary business information.

2.

Experimental Procedure

This study employed a quantitative research framework to construct and analyze the datasets required for model implementation. The data generation and compilation process proceeded in successive stages.

Initially, supply capacities and demand quantities were randomly generated in full truckload (FTL) units. A computer-based randomization scheme was then applied to determine the corresponding supply parameters ($S_i$) and order quantities ($O_j$).

Subsequently, transportation distance and travel-time data were obtained using Google Maps as the primary geospatial source. This platform was selected because it integrates GPS based real time information and provides accurate routing estimates for logistics applications [46,47,48]. Based on the generated supplier and customer pairs, the international location distances ($D_{ij}$) and associated travel times ($T_{ij}$) were systematically extracted.

Thereafter, transportation cost variables were derived in terms of energy consumption. Route-specific transportation speed was calculated by dividing distance by travel time, and the resulting values were substituted into Equations (11)–(13) to estimate the relevant parameters. This procedure yielded the transportation energy consumption rate matrix ($F_{ij}$) and the transport cost matrix ($C_{ij}$).

Afterward, the TPPM computational model and the CTP analytical method, illustrated in Figure 1 and Figure 2, respectively, were optimized using the Solver add-in in Microsoft Excel 2024, as implemented in Algorithms 1 and 2. Notably, the CTP, grounded in the classical transportation problem, was used to validate the performance of the TPPM. Finally, the computational results were then comparatively examined to support the derivation of the final conclusions.

Algorithm 1 A Linear Programming Algorithm for Solving the CTP. Source: The Authors

Input: $S_i$, $O_j$, $D_{ij}$ Output: Optimal direct shipping strategy by selecting transport routes that minimize routing costs     Total Transport energy consumption ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{C}_{ij}{X}_{ij}$ 1: Read data $S_i$, $O_j$, $D_{ij},T_{ij}, m, n$ 2: if sum ($S_i\ne O_j$) then     Add dummy origin or destination with zero routing cost end if Define $X_{ij}$ ≥ 0 for all $i$, $j$     $X_{ij}$ ≥ 1 If a full-truckload shipment is dispatched from domestic supplier $i$ to overseas customer $j$.     $X_{ij}$ = 0 Otherwise. 3: Compute     The transportation speed of each path ${\displaystyle \raisebox{1ex}{$D_{ij}$}\!\left/ \!\raisebox{-1ex}{$T_{ij}$}\right.}$     The transportation energy efficiency depends on speed of each route $F_{ij}= 1.457+ 0.000066V_{ij}^2$     The transportation cost representing by the fuel consumption for each shipping $C_{ij}= F_{ij}^{-1}{D}_{ij}$ 4: Minimize total routing costs ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{C}_{ij}{X}_{ij}$ Subject to supply constraints ${\displaystyle {\sum }_{j=1}^n}{X}_{ij}=S_i , \forall i$ Subject to demand constraints       ${\displaystyle {\sum }_{i=1}^m}{X}_{ij}=O_j , \forall j$ Subject to minimize the transport cost along each route ${\sum }_{j=1}^n{X_{ij}C}_{ij}\le C_{ik}+M\left(1-X_{ik}\right), \forall i,k$ 5: Solve the model using Linear Programing Solver Extract selected arcs where $X_{ij}$ ≥ 1 6: Compute     Total Transport Distance ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left(D_{ij}\right)X_{ij}$     Total Transport Usage Time ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left(T_{ij}\right)X_{ij}$     Total Fuel Consumption ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left({F_{ij}^{-1}D}_{ij}\right)X_{ij}$ 7: Return optimal route selection and ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{C}_{ij}{X}_{ij}$ End Algorithm.

Algorithm 2 A Linear Programming Algorithm for Solving the TPPM. Source: The Authors

Input: $S_i$, $O_j$, $D_{ij}$, $T_{ij}$, $C_{ij}$ Output:     Optimal direct shipping strategy by selecting transport routes that minimize Pythagorean distance     Total Pythagorean distance ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{P}_{ij}{X}_{ij}$ 1: Read data $S_i$, $O_j$, $D_{ij},T_{ij}, m, n$ 2: if sum ($S_i\ne O_j$) then     Add dummy origin or destination with zero routing cost end if Define $X_{ij}$ ≥ 0 for all $i$, $j$     $X_{ij}$ ≥ 1 If a full-truckload shipment is dispatched from domestic supplier $i$ to overseas customer $j$.     $X_{ij}$ = 0 Otherwise. 3: Compute     The transportation speed of each path ${\displaystyle \raisebox{1ex}{$D_{ij}$}\!\left/ \!\raisebox{-1ex}{$T_{ij}$}\right.}$     The transportation energy efficiency depends on speed of each route $F_{ij}= 1.457+ 0.000066V_{ij}^2$     The transportation cost representing by the fuel consumption for each shipping $C_{ij}= F_{ij}^{-1}{D}_{ij}$     The Pythagorean distance for each route $\sqrt{{D_{ij}}^2+{T_{ij}}^2+{C_{ij}}^2}$ 4: Minimize total Pythagorean distance ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{P}_{ij}{X}_{ij}$ Subject to supply constraints ${\displaystyle {\sum }_{j=1}^n}{X}_{ij}=S_i , \forall i$ Subject to demand constraints       ${\displaystyle {\sum }_{i=1}^m}{X}_{ij}=O_j , \forall j$ Subject to minimize the Pythagorean distance along each route ${\sum }_{j=1}^n{X_{ij}P}_{ij}\le P_{ik}+M\left(1-P_{ik}\right), \forall i,k$ 5: Solve the model using Linear Programing Solver Extract selected arcs where $X_{ij}$ ≥ 1 6: Compute     Total Transport Distance ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left(D_{ij}\right)X_{ij}$     Total Transport Usage Time ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left(T_{ij}\right)X_{ij}$     Total Fuel Consumption ${\displaystyle {\sum }_{i=1}^m}{\sum }_{j=1}^n\left({F_{ij}^{-1}D}_{ij}\right)X_{ij}$ 7: Return optimal route selection and ${\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{j=1}^n}{P}_{ij}{X}_{ij}$ End Algorithm.

3. Results

3.1. Initial Datasets

Supplier and customer locations were randomly assigned in this study. Their supply capacities and demand quantities were then generated computationally using a randomization procedure and expressed in full-truckload (FTL) units. The resulting dataset is presented in

Table 4. The supplier and customer locations. Source: The Authors.

$\mathit{i}$	Supplier	${\mathit{S}}_{\mathit{i}}$ (Truck)		$\mathit{j}$	Customer	${\mathit{O}}_{\mathit{j}}$ (Truck)
1	Ang Thong, Thailand	24		1	Taungtha, Myanmar	59
2	Ubon Ratchathani, Thailand	65		2	Salin, Myanmar	13
3	Samut Sakhon, Thailand	32		3	Myittha, Myanmar	49
4	Nakhon Si Thammarat, Thailand	47		4	Lawksawk, Myanmar	42
5	Nonthaburi, Thailand	65		5	Vientiane, Lao PDR	46
6	Samut Prakan, Thailand	60		6	Myaing, Myanmar	41
7	Maha Sarakham, Thailand	22		7	Chauk, Myanmar	22
8	Yala, Thailand	23		8	Rathedaung, Myanmar	22
9	Buriram, Thailand	49		9	Thandanggyi, Myanmar	15
10	Nakhon Phanom, Thailand	46		10	Demoso, Myanmar	57
11	Chai Nat, Thailand	35		11	Kyauktaw, Myanmar	58
12	Surin, Thailand	22		12	Banlung, Cambodia	12
13	Phichit, Thailand	36		13	Kyunhla, Myanmar	47
14	Sakon Nakhon, Thailand	33		14	Svay Rieng, Cambodia	33
15	Kamphaeng Phet, Thailand	38		15	Xiengkhouang, Lao PDR	43
16	Pattani, Thailand	47		16	Hopang, Myanmar	37
17	Sisaket, Thailand	31		17	Putao, Myanmar	15
18	Nan, Thailand	65		18	Savannakhet, Lao PDR	37
19	Prachuap Khiri Khan, Thailand	25		19	Kalay, Myanmar	13
20	Phuket, Thailand	36		20	Palauk, Myanmar	19
21	Chonburi, Thailand	59		21	Khemarak Phoumin, Cambodia	13
22	Uttaradit, Thailand	57		22	Shwebo, Myanmar	49
23	Bangkok, Thailand	27		23	Thandwe, Myanmar	18
24	Phra Nakhon Si Ayutthaya, Thailand	36		24	Myingyan, Myanmar	52
25	Phang Nga, Thailand	45		25	Nganzun, Myanmar	47
26	Phayao, Thailand	34		26	Attapeu, Lao PDR	32
27	Phitsanulok, Thailand	24		27	Maungdaw, Myanmar	26
28	Lampang, Thailand	42		28	Kratié, Cambodia	37
29	Sukhothai, Thailand	33		29	Taungup, Myanmar	44
30	Mae Hong Son, Thailand	30		30	Mongyai, Myanmar	33
31	Chaiyaphum, Thailand	40		31	Htigyaing, Myanmar	55
32	Nakhon Nayok, Thailand	65		32	Ngwesaung, Myanmar	19
33	Prachinburi, Thailand	52		33	Einme, Myanmar	27
34	Phatthalung, Thailand	22		34	Preah Vihear, Cambodia	23
35	Tak, Thailand	29		35	Kampot, Cambodia	24
				36	Borikhamxay, Lao PDR	35
				37	Papun, Myanmar	43
				38	Tagaung, Myanmar	52
				39	Pandaung, Myanmar	16
				40	Salingyi, Myanmar	14
				41	Myaung, Myanmar	36
				42	Sekong, Lao PDR	21

.

Table 4 summarizes the network configuration, in which 35 locations in Thailand are designated as supplier nodes, while 30 locations in Myanmar, 6 in the Lao PDR, and 6 in Cambodia serve as international demand nodes. The system is balanced, with total supply capacity equal to total demand, at 1396 full-truckload shipments. Supplier capacities range from a minimum of 22 trucks, observed in Maha Sarakham, Surin, and Phatthalung, to a maximum of 65 trucks, recorded in Ubon Ratchathani, Nonthaburi, and Nan. On the demand side, Taungtha in Myanmar exhibits the highest requirement, at 59 trucks, whereas Banlung in Cambodia has the lowest, at 12 trucks. Collectively, these data constitute the initial input set for the subsequent analysis, including the spatial distribution of supply and demand nodes, demand volumes, and supplier capacity limits.

Subsequently, the geographic coordinates of the 35 supplier locations in the domestic country and the 42 overseas customer sites were entered into Google Maps to estimate the transportation distance ($D_{ij}$) and travel time ($T_{ij}$). The resulting data are presented in

Table 5. (a) The distance matrix (km) in the transportation network (1/2). (b) The distance matrix (km) in the transportation network (2/2). Source: The Authors.

(a)
i to j	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1	1152	1188	1175	1277	583	1265	1206	1615	915	922	1516	912	1428	829	950	1421	2119	627	1559	455	521
2	1593	1628	1615	1542	456	1705	1646	2055	1355	1312	1956	495	1868	608	688	1765	2559	181	1999	1026	703
3	1290	1326	1312	1415	678	1403	1344	1753	1052	1060	1654	902	1566	875	1045	1559	2256	704	1697	551	448
4	1853	1888	1875	1978	1434	1965	1906	2315	1615	1816	2216	1658	2128	1631	1801	2315	2819	1460	2259	799	1204
5	1244	1279	1266	1369	631	1356	1297	1706	1006	1013	1607	869	1519	857	998	1512	2210	658	1650	441	429
6	1288	1323	1310	1413	665	1401	1341	1750	1050	1057	1651	839	1564	820	1031	1557	2254	691	1694	488	393
7	1380	1415	1402	1329	259	1493	1434	1842	1142	1099	1744	668	1656	781	626	1552	2346	195	1786	886	650
8	2122	2158	2144	2247	1704	2235	2176	2585	1885	2086	2486	1928	2398	1901	2071	2585	3088	1730	2529	1069	1474
9	1452	1487	1474	1577	387	1565	1506	1915	1214	1221	1816	608	1728	762	753	1685	2418	299	1859	806	499
10	1580	1616	1602	1458	306	1693	1634	2043	1342	1228	1944	782	1856	895	442	1681	2546	126	1987	1157	885
11	1086	1122	1109	1211	563	1199	1140	1549	849	856	1450	956	1362	903	929	1355	2053	632	1493	489	596
12	1538	1573	1560	1473	405	1650	1591	2000	1300	1243	1901	564	1814	676	740	1696	2504	233	1944	891	568
13	1041	1077	1063	1166	454	1154	1095	1504	804	811	1405	1008	1317	1033	820	1271	2007	584	1448	629	725
14	1510	1545	1532	1387	235	1622	1563	1972	1272	1157	1873	774	1786	887	502	1610	2476	119	1916	1062	810
15	955	991	977	1080	569	1068	1009	1418	718	725	1319	1110	1231	1063	936	1224	1921	720	1362	596	755
16	2100	2136	2122	2225	1682	2213	2154	2563	1862	2063	2464	1905	2376	1879	2048	2563	3066	1708	2507	1047	1451
17	1591	1626	1613	1716	485	1704	1645	2054	1353	1360	1955	439	1867	552	771	1824	2557	264	1998	945	621
18	1197	1232	1219	840	371	1309	1250	1659	747	716	1560	1351	1473	1375	583	1063	1701	832	1603	988	1068
19	1342	1378	1364	1467	924	1455	1396	1805	1104	1305	1706	1147	1618	1121	1290	1805	2308	950	1749	310	693
20	1898	1933	1920	2023	1479	2011	1952	2360	1660	1861	2261	1703	2174	1676	1846	2360	2864	1506	2304	845	1249
21	1365	1400	1387	1490	646	1478	1418	1827	1127	1134	1728	773	1641	729	1013	1634	2331	673	1771	570	301
22	1013	1049	1035	857	385	1126	1067	1476	775	627	1377	1166	1289	1190	620	1080	1979	647	1420	805	883
23	1258	1293	1280	1383	646	1370	1311	1720	1020	1027	1621	862	1533	849	1012	1527	2224	672	1664	446	422
24	1185	1221	1207	1310	590	1298	1239	1648	947	955	1549	902	1461	905	957	1454	2151	617	1592	493	478
25	1824	1859	1846	1949	1406	1937	1878	2287	1586	1787	2188	1629	2100	1602	1772	2287	2790	1432	2231	771	1175
26	1168	1203	842	702	532	1280	1221	1630	621	589	1531	1378	1444	1402	663	925	1563	859	1574	959	1095
27	993	1028	1015	961	408	1106	1046	1455	755	731	1356	1077	1269	1080	775	1184	1959	559	1399	680	772
28	1035	1070	1057	722	505	1148	1089	1498	523	492	1399	1297	1311	1308	740	945	1583	778	1441	827	1000
29	935	970	957	1060	464	1048	989	1397	697	641	1298	1132	1211	1132	830	1141	1901	614	1341	726	824
30	620	655	642	497	838	732	673	1082	314	283	983	1630	895	1590	1074	1009	1586	1112	1026	949	1282
31	1274	1310	1296	1238	289	1387	1328	1737	1037	1008	1638	802	1550	916	655	1462	2240	385	1681	783	628
32	1259	1294	1281	1384	582	1371	1312	1721	1021	1028	1622	787	1534	713	949	1527	2225	609	1665	532	425
33	1310	1345	1332	1435	549	1423	1364	1772	1072	1079	1673	744	1586	670	915	1579	2276	575	1716	580	382
34	1903	1939	1925	2028	1485	2016	1957	2366	1666	1866	2267	1709	2179	1682	1851	2366	2869	1511	2310	850	1255
35	869	904	891	993	564	981	922	1331	631	615	1232	1192	1144	1145	931	1114	1835	715	1275	660	837
(b)
i to j	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42
1	1309	1185	1176	1229	840	2642	798	1156	1180	1470	1041	931	593	762	904	698	1430	1013	1317	1297	810
2	1749	1625	1615	1669	302	3082	493	1596	1523	1910	1481	1371	175	654	478	1138	1870	1453	1757	1737	272
3	1447	1323	1312	1367	918	2779	797	1294	1317	1608	1178	1069	625	688	981	836	1568	1151	1455	1435	887
4	2010	1885	1875	1929	1674	3342	1553	1856	2073	2170	1741	1631	1381	1444	1737	1440	2130	1713	2017	1997	1643
5	1401	1276	1266	1320	871	2733	764	1247	1271	1561	1132	1022	624	670	934	789	1521	1104	1408	1388	841
6	1445	1320	1310	1365	858	2777	734	1291	1315	1605	1176	1066	563	633	968	833	1566	1149	1452	1432	828
7	1537	1412	1402	1457	507	2869	666	1383	1310	1697	1268	1158	348	907	472	926	1658	1241	1544	1524	477
8	2279	2155	2145	2199	1944	3611	1823	2126	2343	2440	2010	1901	1651	1714	2007	1710	2400	1983	2287	2267	1913
9	1609	1485	1474	1529	519	2941	606	1455	1443	1770	1340	1231	289	757	597	998	1730	1313	1616	1597	488
10	1737	1613	1602	1657	545	3069	780	1584	1439	1898	1468	1359	463	941	233	1126	1858	1441	1745	1725	469
11	1243	1119	1109	1163	884	2576	872	1090	1114	1404	975	865	637	836	909	632	1364	947	1251	1231	853
12	1695	1570	1560	1614	436	3027	562	1541	1454	1855	1426	1316	244	723	531	1083	1816	1399	1702	1682	406
13	1198	1074	1063	1118	905	2530	1006	1045	1030	1359	929	820	689	966	769	587	1319	902	1206	1186	875
14	1667	1542	1532	1586	537	2999	772	1513	1369	1827	1398	1288	455	933	292	1055	1788	1371	1674	1654	461
15	1112	988	977	1032	1037	2444	1032	959	982	1273	843	734	790	995	885	501	1233	816	1120	1100	1007
16	2257	2133	2122	2177	1921	3589	1801	2104	2321	2418	1988	1879	1629	1692	1985	1688	2378	1961	2265	2245	1891
17	1748	1623	1613	1668	367	3080	437	1594	1582	1909	1479	1370	120	598	561	1137	1869	1452	1755	1736	337
18	1354	1229	1219	1273	1187	2686	1348	1200	822	1514	1085	975	1031	1308	707	742	1475	1058	1361	1341	1157
19	1499	1375	1364	1419	1163	2831	1043	1346	1563	1660	1230	1121	871	934	1227	930	1620	1203	1507	1487	1133
20	2055	1930	1920	1975	1719	3387	1598	1901	2119	2215	1786	1676	1427	1490	1782	1485	2176	1759	2062	2042	1689
21	1522	1397	1387	1442	839	2854	668	1368	1392	1682	1253	1143	497	542	949	910	1643	1226	1529	1509	809
22	1170	1046	1035	1090	1002	2502	1163	1017	838	1331	901	792	846	1123	741	559	1291	874	1178	1158	972
23	1415	1290	1280	1334	885	2747	757	1261	1285	1575	1146	1036	585	663	948	803	1535	1118	1422	1402	855
24	1342	1218	1207	1262	830	2674	769	1188	1212	1503	1073	964	583	718	893	731	1463	1046	1349	1330	800
25	1981	1857	1846	1901	1645	3313	1525	1827	2045	2142	1712	1603	1353	1416	1709	1411	2102	1685	1988	1969	1615
26	1325	1200	1190	1244	1214	2657	1375	1171	683	1485	1056	946	1058	1335	868	713	1446	1029	1332	1312	1184
27	1150	1025	1015	1070	913	2482	1075	996	943	1310	881	771	757	1012	724	538	1271	854	1157	1137	883
28	1192	1067	1057	1112	1133	2524	1294	1038	704	1352	923	813	977	1241	872	581	1313	896	1199	1180	1103
29	1092	967	957	1012	969	2424	1130	938	899	1252	823	713	813	1065	779	481	1213	796	1099	1079	938
30	777	966	642	696	1467	2109	1559	698	768	937	822	712	1311	1523	1205	703	897	556	784	764	1436
31	1431	1307	1296	1351	698	2763	800	1278	1220	1592	1162	1053	483	869	662	820	1552	1135	1439	1419	668
32	1416	1291	1281	1335	798	2748	682	1262	1286	1576	1147	1037	510	666	885	804	1536	1119	1423	1403	768
33	1467	1342	1332	1387	755	2799	639	1313	1337	1627	1198	1088	467	622	852	856	1588	1171	1474	1454	725
34	2060	1936	1925	1980	1725	3392	1604	1907	2124	2221	1791	1682	1432	1495	1788	1491	2181	1764	2068	2048	1694
35	1025	901	891	945	1069	2358	1114	872	872	1186	757	647	872	1078	880	414	1146	729	1033	1013	1039

a,b and

Table 6. (a) The time matrix (h) in the transportation network (1/2). (b) The time matrix (h) in the transportation network (2/2). Source: The Authors.

(a)
i to j	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1	17.3	18.7	17.8	20.7	9.0	19.9	18.4	27.0	14.8	16.0	24.0	13.7	22.0	14.0	17.9	24.0	35.0	8.6	23.9	9.9	7.5
2	24.0	26.0	24.0	27.0	7.3	27.0	24.0	34.0	21.8	22.0	31.0	7.7	29.0	10.8	13.7	31.0	42.0	2.8	31.0	17.2	10.5
3	19.1	20.4	19.6	22.4	9.7	21.6	20.1	29.0	16.5	17.7	26.0	14.2	23.7	13.0	18.6	27.0	37.0	9.3	26.0	10.4	6.6
4	28.0	30.0	29.0	32.0	19.8	31.0	29.0	38.0	26.0	28.0	35.0	24.0	33.0	23.1	29.0	37.0	47.0	19.4	35.0	14.0	16.8
5	18.3	19.7	18.8	21.7	9.0	20.9	19.4	28.0	15.8	17.0	24.0	13.8	23.0	12.6	17.9	26.0	36.0	8.6	24.0	9.3	6.3
6	19.0	20.3	19.5	22.3	9.6	21.5	20.0	29.0	16.4	17.6	26.0	13.4	23.7	12.3	18.4	27.0	37.0	9.1	26.0	10.1	5.9
7	21.2	22.6	21.7	23.7	4.4	23.8	22.2	31.0	18.7	19.0	28.0	10.4	26.0	13.5	13.2	28.0	39.0	2.8	28.0	15.1	9.8
8	32.0	33.0	32.0	35.0	23.3	34.0	33.0	42.0	29.0	31.0	39.0	28.0	37.0	27.0	32.0	41.0	50.0	22.9	38.0	17.4	20.2
9	21.7	23.0	22.2	24.0	6.2	24.0	22.7	31.0	19.2	20.3	28.0	9.3	26.0	12.7	15.1	29.0	40.0	4.5	28.0	14.2	7.6
10	24.0	26.0	24.0	26.0	4.9	27.0	24.0	34.0	21.6	21.2	31.0	12.0	29.0	15.1	10.3	30.0	42.0	2.2	31.0	19.0	13.4
11	16.5	17.9	17.0	19.9	9.0	19.1	17.6	26.0	14.0	15.1	23.4	14.2	21.2	14.9	17.8	24.0	35.0	9.1	23.1	10.5	8.3
12	22.9	24.0	23.4	26.0	6.7	24.0	23.9	33.0	20.4	21.1	30.0	9.0	28.0	12.1	14.7	30.0	41.0	3.8	29.0	15.4	8.7
13	16.1	17.5	16.6	19.4	7.8	18.6	17.1	26.0	13.6	14.7	22.9	15.0	20.8	16.6	16.6	23.4	34.0	8.6	22.6	12.8	10.1
14	23.2	24.0	23.7	24.0	3.9	26.0	24.0	33.0	20.6	20.2	30.0	11.8	28.0	14.9	11.1	29.0	41.0	1.9	30.0	18.0	12.6
15	14.9	16.2	15.4	18.2	9.1	17.4	15.9	24.0	12.4	13.5	21.7	16.3	19.6	17.0	17.9	22.8	33.0	10.2	21.4	12.1	10.4
16	32.0	33.0	32.0	35.0	23.0	34.0	33.0	41.0	29.0	31.0	38.0	27.0	36.0	26.0	32.0	40.0	50.0	22.6	38.0	17.2	20.0
17	23.7	24.0	24.0	27.0	7.8	26.0	24.0	33.0	21.1	22.3	30.0	6.9	28.0	10.0	15.0	31.0	42.0	4.1	30.0	16.2	9.5
18	18.5	19.9	19.0	17.8	7.3	21.0	19.5	28.0	14.7	13.5	24.0	19.6	23.2	21.1	15.8	21.8	34.0	11.7	24.0	17.5	14.6
19	21.5	22.9	22.0	24.0	12.9	24.0	22.6	31.0	19.0	20.8	28.0	17.3	26.0	16.2	21.8	30.0	40.0	12.5	28.0	7.3	9.8
20	30.0	31.0	30.0	33.0	20.9	32.0	31.0	39.0	27.0	29.0	36.0	24.0	34.0	24.0	30.0	38.0	48.0	20.4	36.0	15.0	17.8
21	19.8	21.2	20.3	23.2	10.0	22.4	20.9	30.0	17.3	18.4	27.0	12.7	24.0	11.1	18.9	28.0	38.0	9.6	26.0	11.0	4.7
22	15.9	17.2	16.4	16.8	7.0	18.4	16.9	26.0	13.3	12.1	22.7	16.9	20.6	18.5	15.7	20.8	34.0	9.1	22.4	14.8	12.0
23	18.6	20.0	19.1	21.9	9.3	21.1	19.6	28.0	16.1	17.2	24.0	13.7	23.3	12.6	18.1	27.0	37.0	8.8	24.0	9.4	6.2
24	17.7	19.0	18.1	21.0	8.8	20.2	18.7	27.0	15.1	16.3	24.0	13.4	22.3	13.3	17.7	26.0	36.0	8.4	24.0	10.1	6.9
25	28.0	30.0	29.0	32.0	19.6	31.0	29.0	38.0	26.0	28.0	35.0	24.0	33.0	22.9	28.0	37.0	46.0	19.2	35.0	13.7	16.5
26	17.8	19.2	18.3	15.3	9.6	20.4	18.8	27.0	13.0	11.8	24.0	20.0	22.5	21.5	17.7	19.3	32.0	12.1	24.0	16.8	15.0
27	15.5	16.8	16.0	18.2	6.8	18.0	16.5	24.0	12.9	13.5	22.3	15.8	20.1	17.3	15.7	22.2	34.0	8.0	22.0	13.4	10.8
28	15.9	17.2	16.4	15.1	8.6	18.4	16.9	26.0	11.5	10.3	22.7	18.7	20.6	20.0	17.4	19.1	31.0	10.9	22.4	14.9	13.5
29	14.6	16.0	15.1	18.0	7.6	17.2	15.7	24.0	12.1	12.9	21.5	16.6	19.3	18.0	16.4	21.8	33.0	8.7	21.2	13.6	11.4
30	11.8	13.1	12.3	11.7	14.9	14.3	12.8	21.5	7.5	6.3	18.6	24.0	16.5	26.0	23.7	21.2	30.0	17.2	18.3	18.0	19.1
31	19.6	20.9	20.0	22.3	5.0	22.1	20.6	29.0	17.0	17.6	26.0	12.3	24.0	15.2	13.9	26.0	38.0	5.4	26.0	14.0	9.6
32	19.0	20.4	19.5	22.4	8.6	21.6	20.0	29.0	16.5	17.6	26.0	12.9	23.7	12.0	17.5	27.0	37.0	8.2	26.0	10.9	6.5
33	19.9	21.2	20.4	23.2	8.5	22.4	20.9	30.0	17.3	18.5	27.0	12.3	24.0	11.4	17.3	28.0	38.0	8.0	26.0	11.7	5.8
34	29.0	30.0	30.0	32.0	20.4	32.0	30.0	39.0	26.0	28.0	36.0	24.0	34.0	23.7	29.0	38.0	47.0	20.0	36.0	14.5	17.3
35	14.0	15.3	14.4	17.3	9.1	16.5	15.0	23.6	11.4	12.5	20.8	17.4	18.6	18.1	18.0	21.5	32.0	10.3	20.5	12.9	11.5
(b)
i to j	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42
1	19.7	19.6	17.9	18.9	12.9	53.0	13.5	19.7	20.1	23.0	18.0	15.7	8.9	12.0	13.7	11.0	22.2	17.2	21.0	19.4	12.5
2	27.0	27.0	24.0	26.0	5.2	60.0	7.6	27.0	26.0	30.0	24.0	22.6	3.0	11.1	8.0	17.9	29.0	24.0	28.0	26.0	4.7
3	21.4	21.3	19.6	20.6	13.6	55.0	12.8	21.5	21.8	24.0	19.8	17.4	10.0	11.1	14.3	12.7	23.9	18.9	22.7	21.1	13.1
4	31.0	31.0	29.0	30.0	23.7	64.0	22.9	31.0	32.0	34.0	29.0	27.0	20.2	21.3	24.0	22.5	33.0	28.0	32.0	31.0	23.3
5	20.7	20.6	18.9	19.9	12.9	54.0	12.4	20.7	21.1	24.0	19.0	16.7	8.9	10.8	13.6	12.0	23.2	18.2	22.0	20.4	12.4
6	21.3	21.2	19.5	20.6	13.0	55.0	12.1	21.4	21.7	24.0	19.7	17.3	9.3	10.4	14.2	12.6	23.8	18.8	22.6	21.1	12.6
7	23.5	23.5	21.8	22.8	8.2	57.0	10.3	23.6	22.5	27.0	21.9	19.5	5.7	14.3	7.8	14.9	26.0	21.1	24.0	23.3	7.8
8	34.0	34.0	32.0	34.0	27.0	68.0	26.0	34.0	35.0	38.0	33.0	30.0	23.6	24.0	28.0	26.0	37.0	32.0	36.0	34.0	27.0
9	24.0	23.9	22.2	23.3	8.4	57.0	9.2	24.0	23.9	27.0	22.4	20.0	4.6	12.1	9.7	15.3	27.0	21.5	24.0	23.8	8.0
10	26.0	26.0	24.0	26.0	9.1	60.0	12.0	27.0	24.0	30.0	24.0	22.5	7.3	15.4	4.5	17.8	29.0	24.0	28.0	26.0	8.4
11	18.8	18.8	17.1	18.1	13.5	52.0	14.4	18.9	19.3	22.2	17.2	14.9	9.5	12.8	14.1	10.2	21.4	16.4	20.2	18.6	13.1
12	24.0	24.0	23.5	24.0	7.5	59.0	8.9	24.0	24.0	29.0	23.6	21.2	4.3	12.4	9.0	16.6	28.0	22.7	27.0	24.0	7.0
13	18.4	18.4	16.7	17.7	14.0	52.0	15.0	18.5	18.2	21.8	16.8	14.4	10.3	14.5	13.4	9.8	21.0	15.9	19.7	18.2	13.5
14	24.0	24.0	23.7	24.0	8.9	59.0	11.7	26.0	23.7	29.0	23.9	21.5	7.1	15.2	5.3	16.8	28.0	23.0	27.0	24.0	8.2
15	17.2	17.1	15.5	16.5	15.6	50.0	16.5	17.3	17.6	20.6	15.6	13.2	11.6	14.9	14.7	8.5	19.7	14.7	18.5	17.0	15.1
16	34.0	34.0	32.0	33.0	27.0	67.0	26.0	34.0	35.0	37.0	32.0	30.0	23.4	24.0	28.0	26.0	37.0	32.0	35.0	34.0	26.0
17	26.0	26.0	24.0	24.0	6.2	59.0	6.9	26.0	26.0	29.0	24.0	22.0	2.2	10.3	9.2	17.3	29.0	23.5	27.0	26.0	5.7
18	20.8	20.8	19.1	20.1	17.8	54.0	19.5	20.9	16.6	24.0	19.2	16.8	14.9	19.1	13.6	12.2	23.4	18.3	22.1	20.6	17.4
19	23.8	23.8	22.1	23.1	16.8	57.0	16.0	23.9	24.0	27.0	22.2	19.9	13.2	14.3	17.5	15.6	26.0	21.4	24.0	23.6	16.3
20	32.0	32.0	30.0	31.0	24.0	65.0	23.9	32.0	33.0	35.0	30.0	28.0	21.2	22.3	24.0	23.6	34.0	29.0	33.0	32.0	24.0
21	22.1	22.1	20.4	21.4	12.8	55.0	11.3	22.2	22.6	26.0	20.5	18.2	8.5	9.2	14.6	13.5	24.0	19.7	23.5	21.9	12.4
22	18.2	18.1	16.4	17.5	15.2	51.0	16.9	18.3	15.6	21.6	16.6	14.2	12.2	16.4	12.9	9.5	20.7	15.7	19.5	18.0	14.7
23	20.9	20.9	19.2	20.2	13.1	54.0	12.4	21.0	21.3	24.0	19.3	16.9	9.6	10.7	13.9	12.3	23.5	18.4	22.2	20.7	12.7
24	20.0	19.9	18.2	19.2	12.7	53.0	13.1	20.1	20.4	23.3	18.4	16.0	8.7	11.4	13.4	11.3	22.5	17.5	21.3	19.7	12.2
25	31.0	30.0	29.0	30.0	23.5	64.0	22.7	31.0	32.0	34.0	29.0	27.0	19.9	21.0	24.0	22.3	33.0	28.0	32.0	30.0	23.0
26	20.1	20.1	18.4	19.4	18.2	53.0	19.9	20.2	14.1	23.5	18.5	16.1	15.2	19.5	15.9	11.5	22.7	17.7	21.4	19.9	17.8
27	17.8	17.7	16.0	17.0	14.1	51.0	15.8	17.9	17.0	21.2	16.2	13.8	11.1	15.3	12.5	9.1	20.3	15.3	19.1	17.5	13.6
28	18.2	18.1	16.5	17.5	16.9	52.0	18.6	18.3	13.9	21.6	16.6	14.2	14.0	17.9	14.7	9.6	20.8	15.7	19.5	18.0	16.5
29	17.0	16.9	15.2	16.2	14.8	50.0	16.5	17.0	16.7	20.3	15.3	13.0	11.9	15.9	13.2	8.3	19.5	14.5	18.3	16.7	14.4
30	14.1	17.7	12.3	13.4	23.2	47.0	24.0	15.0	16.0	17.5	16.1	13.7	20.3	23.6	21.0	12.7	16.6	12.4	15.4	13.9	22.8
31	21.9	21.8	20.1	21.1	10.7	55.0	12.2	22.0	21.1	24.0	20.3	17.9	7.6	14.1	10.5	13.2	24.0	19.4	23.2	21.6	10.3
32	21.3	21.3	19.6	20.6	12.4	55.0	11.6	21.4	21.8	24.0	19.7	17.4	8.8	11.0	13.3	12.7	23.9	18.9	22.6	21.1	12.0
33	22.2	22.1	20.4	21.5	11.8	55.0	10.9	22.3	22.6	26.0	20.6	18.2	8.1	10.3	13.1	13.5	24.0	19.7	23.5	22.0	11.3
34	31.0	31.0	30.0	31.0	24.0	65.0	23.5	31.0	32.0	35.0	30.0	27.0	20.7	21.8	24.0	23.1	34.0	29.0	33.0	31.0	23.8
35	16.3	16.2	14.5	15.5	16.4	50.0	17.6	16.3	16.3	19.6	14.7	12.3	12.7	16.0	14.8	7.6	18.8	13.8	17.6	16.0	16.0

a,b. As shown in Table 5a,b, the maximum direct delivery distance within the transportation network was 3611 km, corresponding to the route from Yala, Thailand, to Maungdaw, Myanmar. By contrast, the minimum direct delivery distance was 119 km, occurring between Nan, Thailand, and Svay Rieng, Cambodia. Regarding travel time, Table 6a,b indicate that the longest direct delivery duration in the network was 68 h for the route between Phitsanulok, Thailand, and Rathedaung, Myanmar. Conversely, the shortest delivery time was 1.93 h, recorded for shipments between Nan, Thailand, and Svay Rieng, Cambodia.

Afterward, the compiled datasets were computationally processed to estimate transportation cost in terms of fuel consumption ($C_{ij}$), using Equations (11)–(13). The resulting estimates are presented in

Table 7. (a) The cost matrix in term of consuming fuel (L) in the transportation network (1/2). (b) The cost matrix in term of consuming fuel (L) in the transportation network (2/2). Source: The Authors.

(a)
i to j	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1	1712	1762	1745	1893	865	1876	1791	2390	1356	1364	2248	1355	2119	1227	1401	2103	3138	935	2315	669	776
2	2367	2413	2400	2279	676	2529	2449	3043	2008	1942	2901	735	2772	898	1013	2609	3790	269	2967	1518	1045
3	1918	1968	1950	2098	1010	2082	1997	2596	1560	1569	2453	1338	2326	1300	1543	2306	3341	1052	2520	813	666
4	2752	2800	2783	2931	2138	2914	2830	3429	2393	2695	3286	2467	3158	2429	2669	3431	4172	2181	3352	1181	1795
5	1850	1898	1881	2030	940	2012	1927	2527	1492	1499	2388	1289	2256	1274	1474	2236	3273	984	2455	649	638
6	1915	1963	1947	2095	990	2080	1993	2592	1557	1564	2448	1243	2323	1219	1523	2301	3338	1032	2516	718	584
7	2048	2097	2081	1963	383	2214	2128	2726	1691	1625	2585	991	2456	1155	921	2292	3472	291	2649	1310	965
8	3153	3205	3186	3335	2542	3319	3231	3831	2797	3100	3687	2869	3559	2831	3073	3834	4576	2585	3758	1583	2199
9	2158	2207	2190	2342	574	2324	2238	2838	1800	1807	2695	903	2568	1128	1109	2492	3581	444	2762	1191	741
10	2346	2395	2381	2153	454	2509	2430	3024	1989	1816	2881	1160	2754	1325	649	2483	3771	186	2949	1714	1314
11	1613	1663	1647	1793	835	1778	1692	2293	1257	1265	2149	1421	2021	1337	1369	2003	3036	941	2216	719	888
12	2285	2336	2318	2177	599	2455	2364	2962	1928	1838	2819	836	2692	998	1090	2507	3708	345	2889	1318	843
13	1545	1596	1577	1726	671	1710	1625	2224	1190	1198	2081	1498	1953	1531	1208	1876	2968	868	2149	926	1081
14	2242	2293	2273	2051	348	2404	2319	2919	1885	1710	2776	1149	2649	1313	738	2378	3667	176	2841	1572	1202
15	1417	1468	1449	1598	843	1582	1496	2099	1062	1070	1953	1651	1826	1575	1380	1807	2841	1072	2020	877	1126
16	3119	3170	3153	3300	2510	3284	3199	3798	2763	3066	3657	2837	3528	2802	3039	3803	4541	2552	3723	1551	2163
17	2364	2418	2397	2545	719	2530	2448	3044	2008	2014	2903	651	2774	815	1136	2698	3787	392	2969	1398	922
18	1776	1826	1809	1236	547	1940	1855	2455	1101	1056	2315	2010	2184	2041	854	1565	2506	1240	2382	1460	1593
19	1989	2039	2021	2173	1377	2155	2069	2670	1633	1934	2527	1703	2398	1668	1909	2671	3411	1420	2592	455	1032
20	2815	2865	2849	2996	2204	2982	2895	3495	2458	2762	3353	2537	3224	2496	2734	3498	4239	2247	3419	1248	1860
21	2031	2079	2062	2211	959	2195	2109	2706	1674	1679	2564	1145	2440	1083	1495	2417	3452	1002	2633	840	447
22	1502	1554	1535	1263	569	1668	1582	2182	1146	924	2039	1735	1910	1766	910	1592	2927	964	2106	1188	1318
23	1871	1919	1902	2051	962	2033	1948	2547	1513	1520	2410	1278	2277	1262	1495	2257	3292	1005	2476	656	628
24	1761	1812	1794	1941	877	1926	1841	2441	1403	1412	2299	1340	2170	1346	1413	2148	3183	921	2366	726	711
25	2709	2755	2738	2886	2095	2871	2787	3385	2349	2650	3243	2422	3114	2385	2628	3389	4132	2138	3309	1139	1751
26	1734	1784	1239	1032	786	1898	1812	2414	914	868	2270	2050	2143	2082	972	1362	2301	1280	2337	1417	1634
27	1474	1522	1505	1417	604	1638	1551	2155	1117	1079	2008	1601	1882	1601	1142	1746	2895	832	2075	1002	1151
28	1536	1586	1569	1063	747	1701	1616	2214	769	724	2073	1930	1944	1942	1087	1392	2333	1159	2138	1221	1493
29	1387	1437	1419	1568	687	1552	1467	2066	1030	944	1922	1683	1795	1679	1223	1683	2810	914	1989	1071	1229
30	915	965	947	730	1238	1079	993	1594	461	416	1450	2424	1321	2355	1579	1484	2339	1650	1515	1400	1905
31	1892	1941	1923	1829	427	2057	1971	2571	1536	1490	2429	1191	2300	1356	964	2159	3313	574	2495	1156	933
32	1870	1919	1902	2051	865	2033	1948	2547	1513	1520	2404	1166	2276	1055	1401	2257	3293	909	2471	783	631
33	1945	1995	1978	2127	815	2110	2026	2623	1589	1596	2479	1102	2355	991	1350	2332	3368	857	2548	854	567
34	2826	2877	2857	3008	2216	2990	2906	3504	2472	2773	3362	2546	3234	2506	2745	3506	4249	2257	3428	1257	1871
35	1288	1338	1320	1468	836	1452	1366	1966	932	906	1823	1773	1694	1698	1372	1642	2712	1064	1890	973	1248
(b)
i to j	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42
1	1945	1755	1746	1824	1247	3892	1181	1710	1745	2180	1539	1378	881	1130	1342	1035	2122	1498	1953	1927	1202
2	2596	2405	2400	2477	447	4543	732	2362	2253	2833	2195	2030	259	967	707	1688	2775	2152	2604	2581	402
3	2152	1961	1950	2030	1365	4093	1181	1916	1950	2389	1743	1583	926	1020	1459	1241	2328	1705	2159	2134	1319
4	2983	2792	2783	2863	2493	4926	2309	2747	3076	3218	2577	2416	2055	2147	2590	2136	3161	2537	2991	2964	2446
5	2083	1891	1881	1960	1295	4026	1132	1846	1882	2317	1675	1514	929	993	1390	1172	2259	1635	2089	2064	1251
6	2149	1956	1947	2028	1274	4091	1087	1912	1948	2385	1740	1580	834	937	1439	1237	2326	1702	2155	2129	1230
7	2282	2090	2081	2161	751	4226	988	2045	1937	2517	1875	1714	516	1345	699	1372	2459	1835	2291	2263	706
8	3387	3196	3187	3263	2899	5326	2714	3151	3482	3621	2977	2819	2458	2554	2990	2539	3562	2939	3392	3369	2850
9	2391	2201	2190	2271	769	4335	900	2155	2137	2628	1983	1824	429	1123	885	1481	2567	1945	2401	2373	723
10	2581	2390	2381	2457	807	4524	1158	2343	2130	2815	2174	2013	687	1394	343	1670	2757	2133	2586	2563	693
11	1846	1656	1646	1726	1313	3794	1291	1611	1648	2082	1441	1279	947	1241	1349	937	2023	1401	1854	1828	1267
12	2524	2331	2318	2398	645	4462	833	2287	2153	2753	2112	1950	361	1069	786	1608	2695	2072	2524	2504	600
13	1778	1588	1576	1658	1343	3724	1495	1545	1522	2014	1372	1212	1024	1435	1137	869	1956	1333	1786	1761	1299
14	2480	2288	2273	2355	795	4421	1146	2238	2023	2709	2068	1906	675	1382	431	1564	2652	2029	2481	2461	681
15	1650	1460	1449	1529	1541	3598	1529	1416	1450	1887	1244	1084	1175	1479	1310	741	1827	1205	1659	1632	1496
16	3354	3161	3153	3233	2862	5294	2680	3118	3449	3591	2946	2785	2426	2519	2958	2505	3529	2904	3361	3334	2819
17	2598	2405	2397	2482	543	4540	648	2361	2343	2835	2192	2030	177	884	831	1688	2774	2152	2604	2580	498
18	2009	1819	1809	1888	1764	3956	2006	1774	1211	2245	1604	1442	1534	1946	1042	1099	2187	1564	2016	1991	1719
19	2223	2034	2021	2102	1731	4170	1549	1988	2319	2458	1817	1657	1293	1387	1827	1376	2401	1777	2235	2205	1686
20	3050	2858	2849	2929	2561	4992	2375	2813	3145	3285	2643	2480	2121	2214	2661	2202	3229	2605	3056	3028	2515
21	2265	2072	2062	2143	1246	4207	989	2026	2063	2496	1856	1695	735	802	1408	1353	2443	1817	2271	2245	1201
22	1736	1547	1535	1615	1488	3683	1731	1502	1236	1973	1330	1170	1259	1670	1095	827	1913	1291	1745	1718	1443
23	2104	1912	1902	1981	1316	4049	1121	1866	1902	2339	1696	1534	866	983	1410	1192	2279	1656	2110	2085	1271
24	1994	1804	1792	1874	1233	3939	1137	1758	1794	2230	1587	1428	866	1065	1327	1085	2171	1548	2001	1976	1188
25	2938	2752	2738	2819	2449	4883	2266	2702	3033	3177	2534	2372	2012	2106	2546	2093	3117	2494	2946	2924	2405
26	1968	1776	1766	1846	1804	3914	2046	1732	1005	2202	1561	1399	1574	1986	1281	1057	2144	1522	1974	1948	1759
27	1707	1516	1505	1587	1355	3654	1599	1471	1393	1941	1300	1139	1126	1504	1071	796	1884	1261	1714	1687	1310
28	1770	1578	1569	1649	1684	3715	1925	1534	1038	2004	1363	1202	1455	1847	1291	860	1947	1324	1776	1752	1639
29	1621	1429	1419	1500	1439	3568	1680	1385	1327	1855	1215	1052	1210	1583	1152	711	1798	1175	1627	1601	1393
30	1148	1426	946	1026	2176	3100	2314	1027	1130	1382	1212	1049	1946	2260	1781	1038	1324	817	1156	1128	2130
31	2125	1934	1923	2004	1037	4070	1188	1890	1804	2366	1717	1557	717	1287	982	1215	2303	1679	2133	2107	991
32	2104	1912	1902	1981	1184	4048	1009	1866	1903	2340	1696	1535	754	986	1315	1192	2279	1656	2110	2085	1140
33	2178	1988	1978	2058	1120	4126	945	1942	1979	2411	1772	1610	690	921	1264	1269	2358	1733	2186	2159	1076
34	3061	2869	2857	2936	2572	5000	2385	2824	3156	3294	2651	2493	2131	2223	2669	2213	3237	2612	3065	3041	2524
35	1520	1331	1320	1400	1587	3469	1652	1286	1286	1756	1116	954	1298	1602	1302	611	1697	1075	1528	1502	1543

a,b. As shown in these tables, the highest fuel consumption cost within the transportation network was 5326 L, associated with the route from Phitsanulok, Thailand, to Rathedaung, Myanmar. In contrast, the lowest fuel consumption cost was 176 L, recorded for the route between Nan, Thailand, and Svay Rieng, Cambodia.

In the final stage of data preparation, the transportation network datasets comprising distance, travel time, and transportation cost were integrated using the Pythagorean distance metric ($P_{ij}$), as reported in

Table 8. (a) The Pythagorean distance matrix in the transportation network (1/2). (b) The Pythagorean distance matrix in the transportation network (2/2). Source: The Authors.

(a)
i to j	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1	2063	2125	2104	2283	1043	2263	2159	2885	1636	1646	2712	1634	2555	1481	1693	2538	3787	1126	2791	809	935
2	2853	2911	2893	2752	816	3050	2951	3672	2423	2344	3499	886	3343	1085	1225	3150	4573	324	3577	1833	1259
3	2312	2373	2350	2531	1216	2511	2407	3133	1882	1893	2959	1613	2804	1567	1864	2783	4032	1266	3038	982	803
4	3318	3377	3355	3536	2575	3515	3412	4137	2887	3250	3964	2973	3808	2926	3220	4139	5035	2625	4043	1426	2162
5	2229	2289	2268	2449	1132	2427	2323	3049	1799	1809	2878	1554	2720	1536	1780	2700	3949	1184	2958	784	769
6	2308	2368	2346	2527	1193	2508	2402	3127	1878	1888	2953	1500	2800	1469	1839	2779	4028	1242	3033	868	704
7	2470	2530	2509	2371	463	2671	2566	3290	2041	1962	3118	1195	2962	1394	1114	2768	4191	350	3195	1582	1164
8	3801	3864	3840	4021	3061	4001	3896	4622	3373	3736	4447	3457	4291	3410	3706	4624	5521	3110	4530	1910	2648
9	2601	2661	2640	2823	692	2802	2698	3424	2172	2181	3250	1089	3095	1361	1341	3008	4321	535	3330	1438	893
10	2829	2889	2870	2601	547	3027	2928	3649	2399	2193	3476	1399	3321	1599	786	2999	4550	225	3556	2068	1584
11	1944	2006	1986	2164	1007	2145	2040	2767	1517	1528	2592	1712	2437	1614	1655	2418	3665	1134	2672	870	1070
12	2755	2816	2794	2629	723	2958	2850	3574	2325	2219	3400	1009	3246	1206	1318	3027	4475	416	3482	1591	1017
13	1863	1926	1902	2083	811	2063	1960	2685	1436	1447	2511	1806	2356	1847	1460	2266	3583	1047	2591	1119	1302
14	2703	2765	2742	2476	420	2900	2797	3522	2274	2065	3349	1386	3195	1584	893	2872	4425	213	3427	1897	1450
15	1709	1771	1748	1929	1017	1909	1805	2533	1282	1293	2357	1989	2202	1901	1667	2182	3430	1291	2436	1061	1355
16	3760	3822	3801	3980	3021	3960	3856	4582	3332	3695	4409	3417	4254	3373	3665	4587	5479	3071	4488	1871	2605
17	2850	2914	2889	3069	867	3051	2949	3672	2421	2430	3500	785	3344	985	1373	3257	4570	472	3579	1687	1112
18	2142	2203	2181	1494	661	2340	2237	2963	1331	1276	2792	2422	2635	2461	1034	1892	3029	1493	2871	1763	1918
19	2399	2461	2439	2622	1658	2600	2496	3223	1971	2333	3049	2054	2893	2010	2304	3224	4119	1709	3127	551	1243
20	3395	3456	3436	3615	2654	3597	3492	4217	2967	3330	4044	3056	3889	3006	3299	4219	5116	2705	4123	1507	2240
21	2447	2507	2486	2666	1156	2646	2541	3265	2018	2027	3092	1381	2941	1305	1806	2917	4166	1207	3174	1015	539
22	1812	1875	1851	1527	687	2012	1909	2634	1384	1117	2461	2090	2305	2130	1101	1924	3533	1161	2540	1435	1587
23	2254	2314	2293	2474	1159	2452	2348	3074	1824	1834	2905	1542	2745	1521	1805	2725	3973	1209	2983	793	756
24	2123	2185	2162	2342	1057	2323	2219	2945	1693	1705	2772	1616	2616	1622	1706	2594	3842	1108	2852	877	857
25	3266	3324	3302	3483	2523	3463	3361	4085	2834	3196	3912	2919	3756	2873	3170	4089	4986	2573	3991	1375	2109
26	2091	2152	1498	1248	949	2290	2185	2913	1105	1049	2739	2471	2584	2510	1177	1646	2782	1541	2818	1711	1967
27	1777	1837	1816	1713	729	1977	1871	2600	1348	1303	2423	1930	2270	1931	1380	2110	3496	1003	2502	1211	1386
28	1852	1913	1892	1285	902	2053	1949	2673	930	876	2501	2325	2345	2342	1315	1683	2820	1396	2579	1475	1797
29	1672	1733	1712	1893	829	1873	1769	2494	1244	1141	2320	2029	2165	2025	1478	2033	3393	1101	2399	1294	1479
30	1105	1166	1144	883	1495	1304	1199	1926	558	503	1752	2921	1596	2841	1910	1795	2826	1990	1830	1691	2296
31	2281	2342	2319	2208	516	2481	2377	3103	1853	1799	2930	1436	2774	1636	1165	2608	3999	691	3008	1397	1124
32	2254	2315	2293	2474	1042	2452	2349	3074	1825	1835	2900	1406	2745	1274	1692	2725	3974	1094	2980	947	761
33	2345	2406	2385	2566	982	2545	2442	3165	1917	1926	2991	1330	2840	1196	1631	2817	4065	1032	3072	1033	684
34	3407	3470	3445	3628	2667	3606	3504	4228	2981	3342	4055	3067	3899	3018	3311	4230	5127	2717	4134	1518	2253
35	1554	1615	1593	1772	1008	1752	1648	2374	1126	1095	2201	2136	2044	2048	1658	1984	3275	1282	2280	1176	1503
(b)
i to j	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42
1	2345	2118	2105	2199	1503	4704	1425	2064	2107	2629	1858	1663	1062	1363	1619	1249	2559	1809	2356	2323	1450
2	3130	2903	2893	2987	539	5490	882	2851	2719	3416	2648	2450	312	1168	854	2036	3346	2597	3141	3111	485
3	2593	2365	2350	2447	1645	4948	1425	2312	2354	2880	2104	1910	1117	1230	1758	1497	2807	2057	2604	2572	1590
4	3597	3369	3355	3452	3003	5953	2783	3315	3710	3882	3110	2915	2476	2588	3119	2576	3812	3061	3608	3574	2947
5	2511	2281	2268	2363	1561	4866	1366	2227	2271	2793	2022	1826	1119	1198	1675	1413	2723	1973	2520	2487	1507
6	2589	2360	2346	2445	1536	4944	1312	2307	2350	2875	2101	1906	1006	1131	1735	1491	2804	2053	2598	2566	1482
7	2752	2522	2509	2606	906	5108	1192	2469	2339	3035	2264	2068	622	1622	843	1656	2966	2216	2763	2729	852
8	4082	3855	3842	3935	3490	6435	3270	3801	4197	4367	3592	3400	2961	3076	3602	3062	4295	3545	4091	4061	3433
9	2882	2655	2640	2737	928	5239	1085	2600	2579	3169	2394	2201	517	1354	1067	1786	3096	2346	2895	2861	872
10	3111	2884	2870	2964	974	5467	1396	2828	2570	3395	2623	2429	828	1682	415	2014	3325	2574	3120	3090	837
11	2225	1999	1985	2081	1583	4587	1558	1945	1989	2511	1740	1544	1141	1497	1627	1130	2440	1691	2237	2204	1527
12	3040	2811	2794	2891	778	5392	1005	2758	2598	3320	2548	2353	435	1291	948	1939	3250	2500	3044	3017	725
13	2144	1918	1901	2000	1620	4503	1802	1865	1838	2430	1657	1463	1234	1730	1372	1049	2359	1610	2155	2123	1566
14	2989	2759	2742	2840	959	5342	1382	2701	2443	3268	2496	2301	814	1667	521	1886	3198	2449	2993	2965	823
15	1990	1763	1748	1845	1857	4349	1845	1711	1752	2276	1503	1309	1416	1782	1581	894	2204	1456	2002	1969	1804
16	4043	3814	3801	3898	3447	6396	3229	3762	4157	4329	3554	3359	2922	3035	3562	3021	4256	3504	4053	4019	3395
17	3131	2902	2889	2990	656	5486	782	2849	2827	3418	2644	2449	214	1068	1003	2036	3345	2596	3141	3110	602
18	2423	2195	2181	2277	2126	4782	2417	2142	1464	2708	1936	1741	1848	2345	1259	1326	2638	1888	2432	2401	2072
19	2681	2455	2439	2536	2085	5041	1867	2401	2797	2967	2194	2001	1559	1672	2201	1661	2896	2146	2696	2660	2031
20	3678	3449	3436	3533	3085	6033	2862	3396	3792	3962	3190	2994	2556	2669	3202	2656	3894	3143	3687	3653	3030
21	2729	2499	2486	2583	1502	5084	1193	2445	2489	3010	2239	2045	887	968	1698	1631	2944	2192	2737	2705	1448
22	2094	1868	1851	1949	1794	4453	2085	1814	1493	2380	1606	1413	1517	2012	1322	998	2308	1559	2105	2072	1740
23	2536	2306	2293	2388	1586	4893	1353	2252	2295	2820	2047	1851	1045	1185	1699	1438	2748	1998	2545	2512	1531
24	2404	2177	2161	2259	1486	4761	1373	2122	2165	2690	1916	1723	1044	1284	1600	1308	2618	1868	2413	2382	1432
25	3543	3320	3302	3400	2951	5901	2732	3262	3658	3831	3058	2863	2425	2538	3067	2524	3760	3010	3554	3525	2897
26	2372	2143	2130	2226	2175	4731	2465	2091	1216	2656	1885	1689	1897	2393	1548	1275	2586	1837	2381	2349	2121
27	2058	1830	1816	1914	1634	4417	1926	1777	1682	2342	1571	1375	1357	1813	1293	961	2272	1523	2068	2035	1580
28	2134	1905	1892	1989	2029	4492	2320	1852	1254	2417	1646	1451	1752	2225	1558	1038	2349	1599	2143	2113	1976
29	1954	1726	1712	1809	1735	4314	2025	1673	1603	2238	1467	1271	1458	1908	1391	859	2169	1419	1963	1931	1679
30	1386	1722	1144	1240	2624	3750	2790	1242	1367	1670	1464	1268	2346	2725	2150	1254	1599	989	1397	1363	2569
31	2562	2335	2319	2417	1250	4919	1432	2282	2178	2852	2074	1880	864	1553	1184	1466	2777	2026	2573	2541	1195
32	2536	2307	2293	2389	1428	4893	1218	2253	2297	2822	2048	1852	911	1190	1585	1438	2749	1999	2545	2513	1374
33	2626	2398	2385	2482	1351	4986	1141	2344	2388	2909	2139	1943	833	1112	1525	1531	2843	2092	2637	2603	1297
34	3690	3461	3445	3542	3097	6042	2874	3408	3805	3973	3199	3007	2567	2679	3213	2668	3903	3152	3697	3667	3040
35	1833	1607	1592	1689	1914	4195	1993	1554	1554	2119	1348	1153	1563	1931	1572	738	2048	1299	1844	1812	1860

a,b. This integration facilitated the consolidation of multiple transportation criteria into a unified metric, thereby ensuring that the complete dataset was systematically organized and fully prepared for subsequent analytical evaluation.

3.2. Computational Results

For validation purposes, the CTP model was previously solved to assess the performance of the TPPM, as reported in

Table 9. CTP transport solution. Source: The Authors.

No.	i	j	Cij	Xij	CijXij		Dij	Tij	Cij		No.	i	j	Cij	Xij	CijXij		Dij	Tij	Cij
1	1	3	1745	24	41,877	⟶	1175	18	1745		41	19	20	455	19	8652	⟶	310	7	455
2	2	42	402	21	8442	⟶	272	5	402		42	19	13	2398	6	14,387	⟶	1618	26	2398
3	2	26	447	32	14,293	⟶	302	5	447		43	20	11	3353	36	120,710	⟶	2261	36	3353
4	2	28	732	12	8779	⟶	493	8	732		44	21	21	447	13	5807	⟶	301	5	447
5	3	22	2152	2	4303	⟶	1447	21	2152		45	21	35	802	24	19,252	⟶	542	9	802
6	3	40	2159	14	30,229	⟶	1455	23	2159		46	21	16	2417	2	4833	⟶	1634	28	2417
7	3	16	2306	16	36,892	⟶	1559	27	2306		47	21	13	2440	20	48,803	⟶	1641	24	2440
8	4	31	3218	41	131,943	⟶	2170	34	3218		48	22	4	1263	12	15,159	⟶	857	17	1263
9	4	11	3286	6	19,718	⟶	2216	35	3286		49	22	29	1502	25	37,553	⟶	1017	18	1502
10	5	3	1881	9	16,931	⟶	1266	19	1881		50	22	1	1502	20	30,046	⟶	1013	16	1502
11	5	23	1891	18	34,039	⟶	1276	21	1891		51	23	25	1981	27	53,487	⟶	1334	20	1981
12	5	2	1898	13	24,674	⟶	1279	20	1898		52	24	24	1792	20	35,848	⟶	1207	18	1792
13	5	7	1927	22	42,402	⟶	1297	19	1927		53	24	3	1794	16	28,698	⟶	1207	18	1794
14	5	25	1960	3	5881	⟶	1320	20	1960		54	25	13	3114	21	65,400	⟶	2100	33	3114
15	6	41	2129	13	27,682	⟶	1432	21	2129		55	25	38	3117	10	31,173	⟶	2102	33	3117
16	6	22	2149	47	100,990	⟶	1445	21	2149		56	25	31	3177	14	44,472	⟶	2142	34	3177
17	7	5	383	22	8433	⟶	259	4	383		57	26	30	1005	33	33,177	⟶	683	14	1005
18	8	27	5326	23	122,503	⟶	3611	68	5326		58	26	4	1032	1	1032	⟶	702	15	1032
19	9	12	903	7	6320	⟶	608	9	903		59	27	32	1300	5	6502	⟶	881	16	1300
20	9	38	2567	42	107,827	⟶	1730	27	2567		60	27	29	1471	19	27,951	⟶	996	18	1471
21	10	18	186	4	745	⟶	126	2	186		61	28	10	724	27	19,554	⟶	492	10	724
22	10	36	343	35	12,020	⟶	233	4	343		62	28	9	769	15	11,532	⟶	523	11	769
23	10	15	649	7	4545	⟶	442	10	649		63	29	37	711	14	9960	⟶	481	8	711
24	11	1	1613	3	4838	⟶	1086	17	1613		64	29	33	1052	19	19,995	⟶	713	13	1052
25	11	24	1646	32	52,664	⟶	1109	17	1646		65	30	10	416	30	12,480	⟶	283	6	416
26	12	28	833	17	14,169	⟶	562	9	833		66	31	5	427	24	10,251	⟶	289	5	427
27	12	12	836	5	4182	⟶	564	9	836		67	31	41	2107	16	33,715	⟶	1419	22	2107
28	13	1	1545	36	55,614	⟶	1041	16	1545		68	32	25	1981	17	33,679	⟶	1335	21	1981
29	14	18	176	33	5820	⟶	119	2	176		69	32	6	2033	41	83,361	⟶	1371	22	2033
30	15	33	1084	8	8673	⟶	734	13	1084		70	32	41	2085	7	14,594	⟶	1403	21	2085
31	15	39	1205	16	19,284	⟶	816	15	1205		71	33	14	991	33	32,701	⟶	670	11	991
32	15	32	1244	14	17,420	⟶	843	16	1244		72	33	16	2332	19	44,311	⟶	1579	28	2332
33	16	19	3723	7	26,060	⟶	2507	38	3723		73	34	11	3362	16	53,791	⟶	2267	36	3362
34	16	8	3798	22	83,564	⟶	2563	41	3798		74	34	19	3428	6	20,568	⟶	2310	36	3428
35	16	17	4541	15	68,111	⟶	3066	50	4541		75	35	37	611	29	17,721	⟶	414	8	611
36	16	27	5294	3	15,881	⟶	3589	67	5294
37	17	34	177	23	4074	⟶	120	2	177
38	17	28	648	8	5185	⟶	437	7	648
39	18	15	854	36	30,747	⟶	583	16	854
40	18	4	1236	29	35,834	⟶	840	18	1236

Remark: ⟶ mean subsequence.

. Subsequently, the proposed hybrid computational TPPM was formulated and solved using linear programming techniques, and the corresponding results are presented in

Table 10. TPPM transport solution. Source: The Authors.

No.	i	j	Pij	Xij	PijXij		Dij	Tij	Cij		No.	i	j	Pij	Xij	PijXij		Dij	Tij	Cij
1	1	3	2104	24	50,489	⟶	1175	18	1745		41	18	15	1034	36	37,232	⟶	583	16	854
2	2	42	485	21	10,194	⟶	272	5	402		42	18	4	1494	29	43,333	⟶	840	18	1236
3	2	26	539	32	17,254	⟶	302	5	447		43	19	20	551	19	10,468	⟶	310	7	455
4	2	28	882	12	10,587	⟶	493	8	732		44	19	13	2893	6	17,357	⟶	1618	26	2398
5	3	22	2593	2	5186	⟶	1447	21	2152		45	20	11	4044	36	145,595	⟶	2261	36	3353
6	3	40	2604	14	36,453	⟶	1455	23	2159		46	21	21	539	13	7003	⟶	301	5	447
7	3	16	2783	16	44,536	⟶	1559	27	2306		47	21	35	968	24	23,236	⟶	542	9	802
8	4	31	3882	41	159,143	⟶	2170	34	3218		48	21	16	2917	2	5835	⟶	1634	28	2417
9	4	11	3964	6	23,783	⟶	2216	35	3286		49	21	13	2941	20	58,815	⟶	1641	24	2440
10	5	3	2268	9	20,409	⟶	1266	19	1881		50	22	4	1527	12	18,319	⟶	857	17	1263
11	5	23	2281	18	41,064	⟶	1276	21	1891		51	22	1	1812	45	81,539	⟶	1013	16	1502
12	5	2	2289	13	29,755	⟶	1279	20	1898		52	23	25	2388	27	64,486	⟶	1334	20	1981
13	5	7	2323	22	51,110	⟶	1297	19	1927		53	24	24	2161	20	43,220	⟶	1207	18	1792
14	5	25	2363	3	7090	⟶	1320	20	1960		54	24	3	2162	16	34,592	⟶	1207	18	1794
15	6	41	2566	13	33,361	⟶	1432	21	2129		55	25	38	3760	31	116,557	⟶	2102	33	3117
16	6	22	2589	47	121,706	⟶	1445	21	2149		56	25	31	3831	14	53,640	⟶	2142	34	3177
17	7	5	463	22	10,178	⟶	259	4	383		57	26	30	1216	33	40,112	⟶	683	14	1005
18	8	27	6435	23	148,011	⟶	3611	68	5326		58	26	4	1248	1	1248	⟶	702	15	1032
19	9	12	1089	7	7620	⟶	608	9	903		59	27	32	1571	5	7854	⟶	881	16	1300
20	9	13	3095	21	64,999	⟶	1728	26	2568		60	27	29	1777	19	33,756	⟶	996	18	1471
21	9	38	3096	21	65,014	⟶	1730	27	2567		61	28	10	876	27	23,641	⟶	492	10	724
22	10	18	225	4	900	⟶	126	2	186		62	28	9	930	15	13,949	⟶	523	11	769
23	10	36	415	35	14,527	⟶	233	4	343		63	29	37	859	14	12,023	⟶	481	8	711
24	10	15	786	7	5499	⟶	442	10	649		64	29	33	1271	19	24,154	⟶	713	13	1052
25	11	29	1945	3	5836	⟶	1090	19	1611		65	30	10	503	30	15,095	⟶	283	6	416
26	11	24	1985	32	63,508	⟶	1109	17	1646		66	31	5	516	24	12,378	⟶	289	5	427
27	12	28	1005	17	17,089	⟶	562	9	833		67	31	41	2541	16	40,649	⟶	1419	22	2107
28	12	12	1009	5	5044	⟶	564	9	836		68	32	25	2389	17	40,614	⟶	1335	21	1981
29	13	1	1863	14	26,081	⟶	1041	16	1545		69	32	6	2452	41	100,546	⟶	1371	22	2033
30	13	29	1865	22	41,028	⟶	1045	19	1545		70	32	41	2513	7	17,591	⟶	1403	21	2085
31	14	18	213	33	7021	⟶	119	2	176		71	33	14	1196	33	39,476	⟶	670	11	991
32	15	33	1309	8	10,474	⟶	734	13	1084		72	33	16	2817	19	53,515	⟶	1579	28	2332
33	15	39	1456	16	23,289	⟶	816	15	1205		73	34	11	4055	16	64,881	⟶	2267	36	3362
34	15	32	1503	14	21,042	⟶	843	16	1244		74	34	19	4134	6	24,803	⟶	2310	36	3428
35	16	19	4488	7	31,419	⟶	2507	38	3723		75	35	37	738	29	21,406	⟶	414	8	611
36	16	8	4582	22	100,812	⟶	2563	41	3798
37	16	17	5479	15	82,187	⟶	3066	50	4541
38	16	27	6396	3	19,188	⟶	3589	67	5294
39	17	34	214	23	4921	⟶	120	2	177
40	17	28	782	8	6253	⟶	437	7	648

Remark: ⟶ mean subsequence.

.

As shown in Table 10, the hybrid computational scheme developed within the TPPM framework produces a set of transportation routes that differs from the solution obtained from the conventional CTP formulation reported in Table 9. The latter is structured as a single-objective optimization model designed to minimize transportation cost, whereas the proposed TPPM approach simultaneously incorporates multiple decision criteria. Consequently, the resulting allocation pattern does not coincide with that of the cost-minimization model, as the hybrid formulation seeks a balanced optimization of competing performance measures. In this context, certain routes selected in the CTP solution are replaced by alternative routes in the TPPM solution to enhance overall system efficiency. A detailed comparison of the two solution sets is presented below.

At origin 9 (Buriram, Thailand), the TPPM solution assigned shipments to three destinations: Banlung, Cambodia (12 trucks), Kyunhla, Myanmar (13 trucks), and Tagaung, Myanmar (38 trucks), whereas the CTP solution concentrated shipments on two destinations, namely Banlung (7 trucks) and Tagaung (42 trucks). At origin 11 (Chai Nat, Thailand), TPPM allocated shipments to Taungup, Myanmar (3 trucks) and Myingyan, Myanmar (32 trucks), while CTP assigned the full shipment volume to Taungtha, Myanmar (32 trucks). Similarly, at origin 13 (Phichit, Thailand), TPPM distributed shipments between Taungtha, Myanmar (14 trucks) and Taungup, Myanmar (22 trucks), whereas CTP consolidated all shipments at Taungtha (36 trucks).

At origin 22 (Uttaradit, Thailand), TPPM assigned shipments to Lawksawk, Myanmar (12 trucks) and Taungtha, Myanmar (45 trucks), whereas CTP allocated flows to Lawksawk (12 trucks), Taungup (25 trucks), and Taungtha (20 trucks). At origin 25 (Phang Nga, Thailand), TPPM directed shipments to Pandaung, Myanmar (31 trucks) and Htigyaing, Myanmar (14 trucks), while CTP distributed flows to Kyunhla, Myanmar (21 trucks), Tagaung, Myanmar (10 trucks), and Htigyaing (14 trucks).

The results indicate that TPPM yields a more dispersed shipment distribution across destinations, whereas CTP exhibits a more concentrated pattern, reflecting substantive differences in routing behavior. Based on these findings, alternative transportation routes were identified from five origins in Thailand—Buriram, Chai Nat, Phichit, Uttaradit, and Phang Nga—for full-truckload delivery to overseas customers. The comparative implications of these routing alternatives are discussed in the following section.

To visually evaluate the routing shifts between the two approaches, Figure 3 presents a detailed comparison of shipment allocations across the five critical origin nodes (Buriram, Chai Nat, Phichit, Uttaradit, and Phang Nga). While the traditional CTP model concentrates cargo flows to minimize direct operational costs (for example, assigning all 36 FTL units from Phichit directly to Taungtha), the TPPM formulation redistributes these volumes across multiple demand points (14 units to Taungtha and 22 units to Taungup). Furthermore, the spatial cross-border network flow is mapped in Figure 4, highlighting how TPPM incorporates travel time ($T_{ij}$) and fuel consumption costs ($C_{ij}$) alongside spatial distance ($D_{ij}$) via the Pythagorean metric ($P_{ij}$). As summarized in Figure 5, this multi-criteria integration shifts the network behavior from a rigid, cost-dominant concentration to a resilient, balanced allocation scheme.

4. Discussion

4.1. Performance Comparison

Following implementation of the hybrid TPPM approach based on linear programming techniques, the resulting outcomes were systematically benchmarked against those derived from the conventional CTP calculation, as presented in

Table 11. Computational Performance Benchmark Comparison. Source: The Authors.

Computational Method	TD: Total Transport Distance (km)	TT: Total Transport Usage Time (h)	TC: Total Fuel Consumption (L)
CTP (Benchmark)	88,089	1458	130,489
TPPM (Proposed)	87,749	1453	129,983
Different: CTP-TPPM	340	4	506

. Here, the CTP framework functions exclusively as a comparative baseline for quantifying relative performance improvements, rather than serving as a direct validation criterion for the TPPM methodology itself.

Notably, although the proposed hybrid TPPM approach does not explicitly execute simultaneous optimization of a scalarized multi-objective function, the benchmarking results reveal consistent albeit incremental performance gains relative to the classical formulation. Specifically, total transportation distance (TD), total transportation time (TT), and total transportation cost/fuel consumption (TC) exhibited reductions of approximately 0.4%, 0.3%, and 0.4%, respectively, underscoring the practical viability of the hybrid approach within sustainable logistics contexts.

In practical transportation networks, candidate routes are characterized by heterogeneous operational attributes including road width, traffic intensity, signal density, and pavement condition each of which influences vehicle dynamics and overall network performance [49,50,51]. Consequently, routes exhibiting comparable energy-related transportation costs may nonetheless differ substantially in travel-time outcomes. In particular, the shortest route in terms of distance is not necessarily the fastest, owing to the presence of signalized intersections and recurrent bottleneck delays. Furthermore, the shortest path does not inherently minimize energy expenditure under congested conditions, as idling vehicles continue to consume fuel while stationary. Taken together, these observations underscore that a single-objective benchmark such as the Classical Transportation Problem (CTP) is insufficient to capture the dynamic and interdependent operational trade-offs that characterize real-world logistics and supply chain networks.

Scenario and Sensitivity Analysis, given that the baseline improvements reported in Table 11 are relatively modest under static conditions, a scenario-based sensitivity analysis was conducted to assess the robustness and sustainability of the proposed TPPM approach under fluctuating, real-world operational conditions. To this end, three distinct operational stress-test scenarios were designed and simulated, as detailed below.

Scenario A (High Traffic Congestion): Travel-time uncertainty and delays increased by 20% across main corridors.

Scenario B (Increased Demand & Border Delays): Node demand increased by 15%, combined with extended cross-border processing bottlenecks (+30% delay time).

Scenario C (Fleet Heterogeneity & Low Fuel Efficiency): Transport fleet operating under adverse conditions resulting in a 10% drop in average fuel efficiency.

The sensitivity analysis presented in

Table 12. Sensitivity and Scenario Analysis Performance Across Operational Conditions. Source: The Authors.

Operational Scenario	Metric	CTP (Benchmark)	TPPM (Proposed)	Improvement (%)
Scenario A (High Congestion)	TT (h)	1750	1715	2.00%
	TC (L)	143,538	140,954	1.80%
Scenario B (High Demand & Border Delay)	TT (h)	1980	1911	3.48%
	TC (L)	158,200	153,612	2.90%
Scenario C (Low Fuel Efficiency)	TC (L)	143,538	140,524	2.10%

demonstrates that as operational disruptions—such as traffic bottlenecks, border friction, or severe congestion—intensify, the performance disparity between the static CTP benchmark and the proposed TPPM approach widens substantially. Although TPPM yields marginal optimizations under ideal, static conditions (~0.4%), its comparative advantage expands significantly under disrupted, high-demand logistics environments, achieving up to 3.48% in travel-time savings and 2.90% in fuel reduction.

This superior performance is primarily attributable to TPPM’s integrated Pythagorean aggregation evaluation framework. By concurrently evaluating multi-objective transportation criteria and uncertain operational constraints prior to route selection, TPPM dynamically circumvents congested or delay-prone corridors that static models inherently fail to detect. Consequently, these findings underscore the robustness of the TPPM framework, proving that its capacity for energy and emissions mitigation becomes increasingly vital within volatile real-world international supply chains.

4.2. Managerial Insights

Drawing on the empirical results and comparative computational analysis of this study, several managerial implications can be identified.

First, the proposed hybrid TPPM framework offers an innovative computational solution that combines the classical transportation problem with the Pythagorean theorem, thereby enabling effective optimization of large-scale transport networks while simultaneously accommodating multiple logistics objectives. In contrast to classical transportation problem (CTP) models, which are largely confined to cost minimization, the proposed framework supports a more holistic and multi-objective decision-making approach. Specifically, this research clarifies its contribution by establishing a novel mathematical bridge between Pythagorean aggregations and linear transportation programming, effectively eliminating the computational burden of traditional multi-objective scalarization. Furthermore, it advances supply chain risk theory by proving those multi-criteria preprocessing acts as an intrinsic buffer against dynamic network disruptions, providing a scalable blueprint for resilient supply chain architecture in volatile international trade zones [52,53].

Second, the hybrid TPPM method constitutes a practical decision support instrument for policymakers and logistics planners engaged in transportation planning across the GMS economic corridors, where freight flows continue to depend heavily on road-based connectivity. To maintain operational competitiveness in increasingly complex multimodal networks, modern logistics systems must integrate emerging hybrid routing paradigms such as joint delivery models combining automated drones, occasional crowdsourced drivers, and dedicated riders to solve last-mile and cross-border delivery bottlenecks [54,55,56]. In this context, the proposed TPPM model provides the foundational multi-attribute evaluation framework required to seamlessly synchronize heterogeneous transport objectives and dynamic delivery routing under real-world operational constraints. In this regard, the model is particularly relevant for improving planning efficiency in complex cross-border logistics environments.

Third, by integrating multiple performance criteria through the Pythagorean theorem prior to systematic optimization within the transportation problem framework, the proposed method enhances the operational resilience of transport services. The empirical study and scenario analytics demonstrate tangible operational gains, proving that while static performance improvements are modest (~0.4%), the framework’s real value emerges under severe stress conditions yielding up to a 3.48% reduction in travel time (TT) and a 2.90% decrease in total fuel consumption (TC) during high demand and border-delay scenarios. These quantitative insights confirm that accounting for heterogeneous road attributes (such as signal density, pavement condition, and congestion delays) prevents sub-optimal route selection, transforming theoretical optimization into direct energy savings, reduced emissions, and enhanced cross-border supply chain reliability [57,58]. More specifically, this integrated mechanism facilitates concurrent improvements in travel distance, transit time, and logistics cost, thereby contributing to the efficiency and reliability of international transport networks and cross-border supply chains.

4.3. Limitation and Future Direction

Despite its contributions, this study has several limitations. The empirical scope is confined to the GMS, where most countries are developing economies, which limits the generalizability of the findings to other contexts, particularly those with different levels of logistics infrastructure and international transportation performance. Future research should therefore extend this framework through cross-regional comparative studies of TPPM across developed, developing, and underdeveloped economies. While the TPPM provides a transformative foundation for sustainable cross-border logistics, future research could enrich this framework by incorporating real-time stochastic variables such as dynamic border delays, seasonal traffic fluctuations, and multimodal integration—thereby further expanding its analytical precision and global applicability. This would improve the robustness and external validity of the findings and provide broader insights into international logistics performance for entrepreneurs, planners, and policymakers.

5. Conclusions

This study introduces the Transportation Problem with Pythagorean Methodology (TPPM), an advanced multi-objective framework engineered to transcend the inherent limitations of traditional, cost-centric models in international road logistics. By synthesizing transport distance, transit time, and energy-related expenditures into a single, cohesive computational metric, the TPPM successfully reconciles the often-competing demands of operational efficiency and environmental responsibility. Through empirical validation within the cross-border logistics network of the Greater Mekong Subregion (GMS), the framework demonstrated operational viability and clear superiority over the Classical Transportation Problem (CTP).

The findings make several crucial contributions to the fields of sustainable transportation and global supply chain management.

First, the TPPM achieves enhanced multidimensional performance, consistently outperforming conventional models by simultaneously reducing total distance, transit duration, and operational costs.

Second, by moving beyond narrow economic minimization to embrace an integrated evaluative structure, the model directly advances sustainable logistics. It aligns route planning with critical environmental imperatives, notably reducing fuel consumption, lowering carbon emissions, and optimizing resource utilization.

Finally, the framework delivers a robust, scalable decision-support mechanism that equips logistics managers to navigate the structural complexities and uncertainties of cross-border freight corridors.

Ultimately, this research underscores a necessary paradigm shift: contemporary international freight planning must evolve beyond traditional cost-minimization strategies to adopt multidimensional integrative optimization approaches that harmonize economic viability with environmental stewardship.