Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing

Abstract

Effective supply and demand matching for construction materials is a crucial challenge in large-scale railway projects, particularly in complex and hazardous environments. We propose a two-stage stochastic programing model that incorporates environmental uncertainties, such as natural disasters, into the supply chain optimization process. The first stage determines optimal locations and capacities for material supply points, while the second stage addresses material distribution under uncertain demand. We further enhance the model’s efficiency with Benders decomposition algorithm. The performance of our model is rigorously compared with existing optimization approaches, demonstrating its superior capability in handling environmental uncertainties and complex logistical scenarios. This study provides a novel framework for optimizing supply chains in challenging environments, offering significant improvements over traditional models in both adaptability and robustness.

1. Introduction

In recent years, the expansion of China’s railway network, particularly in the central and western regions, has become a strategic priority for national development. This expansion is crucial not only for improving connectivity and economic integration across these regions but also for promoting sustainable development in remote and underserved areas. However, the construction of railway infrastructure in these regions presents significant logistical challenges, particularly in the effective matching of supply and demand for construction materials. The success of these projects is highly dependent on the ability to manage complex supply chains in the face of unpredictable material demand and environmental disruptions such as landslides, earthquakes, and extreme weather events. Therefore, optimizing material supply chains in such environments is not just a logistical necessity but a critical factor in ensuring the timely and cost-effective completion of these large-scale projects.

Traditionally, the material supply-demand matching problem in construction projects is treated as a location-routing problem, taking into account transportation costs, construction costs, and material transport times. The original location routing problem was studied starting from pure facility location [1] and multi-warehouse vehicle routing problems [2,3,4,5,6,7,8,9], began to consider the two types of decision problems jointly, but although the location and routing problem at this time was joint, the relevant data were deterministic, and the location and routing planning was static planning. Each customer only considered the delivery of one vehicle or one model, and did not consider the inventory problem. For material supply and demand matching in uncertain scenarios [10]. Considered using expected value to transform fuzzy random variables into deterministic variables in an uncertain environment to solve the material transportation problem of large construction projects [11], developed a two-stage stochastic programming model for demand uncertainty [12], proposed a two-stage stochastic mixed integer programming to provide a prepositioning strategy in emergency response scenarios [13], constructs a two-stage distributionally robust programming based on worst-case mean-CVaR criterion to make its effect more stable [14], proposed a two-stage stochastic multiperiod model for the dynamic network design problem.

In the rugged and hazardous mountainous regions, it is crucial to consider additional environmental impacts [15,16]. These regions are characterized by difficult geological conditions, susceptibility to extreme weather events such as landslides and debris flows, and remote locations that complicate logistics and supply chain management. For mountain logistics in complex environment, emergency logistics is mainly studied at present [17], built a bi-level model under a random fuzzy environment to provide decision-making reference for emergency logistics in mountainous areas after earthquakes [18]. Considering the supply of emergency supplies and the impact of natural disasters on road damage, made the decision on site selection and distribution scheme [19]. Developed a two-layer emergency logistics system for fire emergency logistics [20]. Established a two-stage chance constrained stochastic programming model and proposed the method of multimodal transport for post-disaster response transportation. Different from the emergency logistics in mountainous areas, the time requirement of construction logistics is not so high, but the transportation volume of materials is large, which is several or even dozens of times of the transportation volume of emergency materials. However, there is a lack of relevant research on the specific problem of matching the supply and demand of construction materials in complex and difficult mountainous areas [21], studies combining drone cruise to improve the efficiency of material supply for railway construction in mountainous areas (

Table 1. Literature review.

Author of the Paper and Year of Publication of the Paper	Research Topic or Method	Field of Application
Daskin M. 1997 [1]	Facility location issues	Construction logistics field
Cordeau JF, Gendreau M, Laporte G. 1997 [2]	Multi-warehouse vehicle routing problem	Construction logistics field
Albareda-Sambola M, Rodríguez-Pereira J. 2019 [9]	Location routing problem	Construction logistics field
Yan F, Xu J, Han BT. 2015 [10]	Transportation of large engineering materials under uncertain environment	Construction logistics field
Barbarosoglu G, Arda Y. 2004 [11]	Two-stage stochastic programing with uncertain demand	Optimization modeling domain
Rawls CG, Turnquist MA. 2010 [12]	Two-stage stochastic mixed integer programing	Emergency logistics location field
Wang WQ, Yang K, Yang LX, Gao ZY. 2021 [13]	Two-stage distributionally robust programing	Optimization modeling domain
Liu K, Yang L, Zhao Y, Zhang Z-H. 2023 [14]	A two-stage stochastic multiperiod model	Optimization modeling domain
Cui P, He M, Tapponnier P, et al., 2023 [15]	Consider the impact of engineering construction in the mountainous environment	Actual engineering project
Qin Y, Zheng B. 2010 [16]	Consider the impact of engineering construction in the mountainous environment	Actual engineering project
Xu J, Wang Z, Zhang M, Tu Y. 2016 [17]	A bi-level model under a random fuzzy environment	Emergency logistics in mountainous areas
Jin Z, Hong-xing Z, Hao S, Guo-qi L. 2023 [18]	Site selection and distribution scheme	Optimization modeling domain
Yang Z, Guo L, Yang Z. 2019 [19]	Two-layer emergency logistics system	Emergency logistics in mountainous areas
Meng L, Wang X, He J, et al., 2023 [20]	Two-stage chance constrained stochastic programing model	Emergency logistics in mountainous areas
Liu-jiang K, Hao L, Hui-jun S, Jian-jun W. 2023 [21]	Combining drone cruise to improve the efficiency of material supply	Construction logistics in mountainous areas

).

Traditional approaches to material supply–demand matching in construction projects have largely focused on deterministic location-routing models, which optimize transportation costs, construction costs, and material transport times based on fixed and predictable variables. However, these models fail to account for the dynamic and stochastic nature of material demand, especially in complex and uncertain environments like mountainous regions. As a result, there is a significant gap in the existing literature regarding the development of models that integrate environmental uncertainties into the supply chain optimization process. To address this gap, the primary objective of this research is to develop a novel two-stage stochastic programing model that effectively incorporates environmental uncertainties and dynamic demand scenarios into the material supply chain planning for large-scale railway projects. This model aims to provide a more resilient and adaptive framework, capable of optimizing material flows under unpredictable and challenging conditions. This research makes several important contributions to the field of construction logistics and supply chain management:

i.

Innovative modeling framework: We introduce a two-stage stochastic programing model that uniquely integrates environmental factors such as terrain difficulty, weather variability, and potential disruptions into the supply chain optimization process, which are often overlooked in traditional models.

ii.

Algorithmic development: The study develops a Benders decomposition algorithm that significantly enhances the computational efficiency of solving large-scale stochastic programing problems, making the model applicable to real-world scenarios in complex environments.

iii.

Practical application and validation: Through a detailed case study of a large-scale railway project in a mountainous region, we demonstrate the model’s ability to reduce logistics costs and improve project efficiency. This empirical validation underscores the model’s practical relevance and effectiveness in managing supply chains under uncertainty.

iv.

Theoretical advancement: By extending existing stochastic programing approaches to include complex environmental variables, this research provides new insights and a robust framework that can be adapted for various types of infrastructure projects beyond railway construction.

The insights gained from this study have significant implications for both theory and practice, offering a powerful tool for decision-makers in the planning and execution of large-scale infrastructure projects in challenging environments.

2. Problem Formulation and Model Establishment

2.1. Characteristics Analysis of a Complex and Difficult Environment

Super large railway engineering construction logistics is a large-scale and complex system. There are significant seasonal fluctuations in the supply and demand of engineering construction materials, and the uncertainty of material supply and transportation is also very high. Different from the mega-projects such as the Three Gorges Project and the Hong Kong-Zhuhai-Macao Bridge, railway construction faces a complex and precipitous environment, which is characterized by the following:

(1)

The mountainous region of central and western China has complex geology: harsh natural conditions, prone to extreme weather, such as landslides, debris flows, etc.; these extreme environments will seriously affect the already fragile transportation network, resulting in difficulties in material transportation.

(2)

The remote location of the construction section: The construction area along the railway is often located in the uninhabited area or the area with extreme lack of resources, and the material supply cannot be completed nearby. It is usually necessary to plan and build the material supply base in advance.

(3)

Lack of storage facilities: There are usually no social storage facilities along the railway in complex and difficult mountainous areas, and the land in mountainous areas is limited and easily affected by the environment. Therefore, it is necessary to consider not only the cost but also the environmental impact when building a material supply base.

(4)

Underdeveloped logistics network: it is difficult to adopt the “net-to-line” or “net-to-point” material supply mode, but not the “point-to-line” material supply mode, which leads to a large imbalance in logistics supply.

2.2. Description of Material Supply–Demand Matching Problem in Complex and Difficult Environments

In the matching of supply and demand of engineering materials, there are two types of main bodies involved in the construction site, namely the material demand point and the material supply place. Usually, the selection of the material supply place takes into account the construction cost and the transportation cost between the supply point and the demand point. Railway construction is mostly in the mountains region and requires tunneling, and the demand for materials is large. Once natural disasters and other environmental impacts occur, if the material supply and demand matching planning is not made in advance, the project construction is likely to be interrupted and the personal and property safety of construction workers will be damaged.

The above problems are as follows: In the complex and difficult mountainous environment, in the face of a large number of complex material demands of multiple sections, how to reduce costs through the location and capacity of material supply places to improve the efficiency of project construction, and ensure that the project is carried out on schedule. For example, the location of the material supply site in the first stage affects the transportation and distribution of the materials in the second stage, and the transportation of the materials in the second stage is also a consideration in the location of the material supply site in the first stage.

2.3. Complex Environment Two-Stage Stochastic Programing Model (CE-TSSP)

Model assumptions include: (1) material demand occurs in different scenarios of multiple road segments; (2) the transportation unit cost of each material supply place to the demand node is fixed; (3) the material supply is transported according to the shortest path from the material supply place to the demand node; (4) the weight of the material transportation efficiency affected by the environment and other factors is fixed; (5) the transportation loss during the material transportation is fixed.

Definition 1.

The uncertainty in demand for each road segment is modeled by discretizing the sample space. The first stage is the problem of material supply location and capacity determination before project construction.

The total cost of material supply for construction $F$ is expressed as:

$$F={\displaystyle \sum _{i\in I}{f}_i{x}_i+{\displaystyle \sum _{k\in K}{P}^k}}({\displaystyle \sum _{i\in I}{\displaystyle \sum _{j\in J}{\displaystyle \sum _{m\in M}{c}_{ijm}^k}}}{y}_{ijm}^k+{\displaystyle \sum _{i\in I}{s}_i}{z}_i)$$

(1)

where $I=\left\{1,2,\cdots ,i\right\}$ denotes the optional material supply point; $J=\left\{1,2,\cdots ,j\right\}$ represents the set of demand nodes; $M=\left\{1,2,\cdots ,\mathrm{m}\right\}$ represents the collection of transport vehicles; $P^k$ denotes the probability of scenario $k$ occurring; $x_i$ means material supply place $i$; $y_{ijm}^k$ represents the material transportation volume from material supply place $i$ to material demand place $j$ with vehicle type $m$ under scenario $k$; $f_i$ represents the material storage capacity of each material supply location $i$; $c_{ijm}^k$ represents the amount of material transportation from the material supply place $i$ to the demand point $j$ using the vehicle type $m$ in the scenario $k$; In the scenario $k$, the amount of material transportation from the material supply place $i$ to the demand point $j$ using the vehicle type $m$; $s_i$ represents the unit material storage cost of the material supply place; and $z_i$ represents the actual material inventory at the material supply place.

Definition 2.

Because demand is randomly unknown, refer to Delage E [22] and Zeng B’s C&CG [23] algorithm to express the uncertainty of demand as:

$$\delta =\left\{\delta :{\delta }_j=\underset{¯}{{\delta }_j}+k_j\stackrel{⏜}{{\delta }_j},k_j\in [0,1],{\displaystyle {\sum }_j{k}_j}\le \Gamma ,j\in J\right\}$$

(2)

where the basic demand is $\underset{¯}{{\delta }_j}$ and the maximum deviation is $\stackrel{⏜}{{\delta }_j}$, ${\zeta }_m$ represents the volume of transport vehicle type $m$, $q_i$ represents the maximum storage cost at supply location $i$, and a predefined integer value is introduced to define the limit of the budget uncertainty $\Gamma$, the model is as follows:

$$\min F=\min \left\{{\displaystyle \sum _{i\in I}{f}_i{x}_i+{\displaystyle \sum _{k\in K}{P}^k({\displaystyle \sum _{i\in I}{\displaystyle \sum _{j\in J}{\displaystyle \sum _{m\in M}{c}_{ijm}^k{y}_{ijm}^k}}}}}+{\displaystyle \sum _{i\in I}{s}_i{z}_i})\right\}$$

(3)

$${\displaystyle \sum _{i\in I}{\displaystyle \sum _{m\in M}{y}_{ijm}^k}}\ge {\delta }_j^k,\forall j\in J,\forall k\in K$$

(4)

$$y_{ijm}^k\le M{x}_i,\forall i\in I,\forall j\in J,\forall m\in M,\forall k\in K$$

(5)

$${\displaystyle \sum _{j\in J}{y}_{ijm}^k}\le {\zeta }_m,\forall i\in I,\forall m\in M,\forall k\in K$$

(6)

$$s_i{z}_i\le q_i{x}_i,\forall i\in I$$

(7)

$$y_{ijm}^k\ge 0,z_i\ge 0,\forall i\in I,\forall j\in J,\forall m\in M,\forall k\in K$$

(8)

In the model (CE-TSSP) of this paper, we set four scenarios. In view of the particularity of the mountain environment, we set the occurrence probability of the four scenarios to the same probability (25%). In Scenario 1, the impact of the mountain environment is ignored, and the construction materials are transported normally; Scenario 2 is affected by the change in mountain environment, but the transportation scheme remains unchanged, and the impact is reflected in the increase in transportation cost; in Scenario 3, due to the impact of environmental changes in mountainous areas, some transportation schemes are changed and transportation costs are also changed. In Scenario 4, due to the impact of environmental changes in mountainous areas, some material supply places stop supplying, which not only changes the transportation scheme and transportation cost, but also changes the transportation network. The above scene changes and effects will be shown in detail in Section 4.2 of this paper combined with sample examples.

3. Algorithm Design—Benders Algorithm

The Benders decomposition method is one of the most common methods for solving two-stage stochastic problems with multiple cases. The main idea is to solve the final master problem by replacing the values of the second-stage subproblems with a single variable ${\theta }_k$ and inserting a dynamic constraint (Benders cut) to gradually force these variables to reach the optimal solution of the subproblems. In the above model, the problem of Equation (1) can be divided into a master problem and a subproblem, and the specific model is as follows:

$$\min {\displaystyle \sum _{i\in I}{f}_i}{x}_i+{\displaystyle \sum _{k\in K}{\theta }_k}$$

(9)

$$x_i\in \left\{0,1\right\},\forall i\in I$$

(10)

The initial feasible solution $\overline{x_i}$ can be obtained by solving Equation (9), and the subproblem is constructed as follows:

$$\min {\displaystyle \sum _{i\in I}{\displaystyle \sum _{j\in J}{\displaystyle \sum _{m\in M}{c}_{ijm}^k}}}{y}_{ijm}^k+{\displaystyle \sum _{i\in I}{s}_i}{z}_i$$

(11)

$${\displaystyle \sum _{i\in I}{\displaystyle \sum _{m\in M}{y}_{ijm}^k}}\ge {\delta }_j^k,\forall j\in J$$

(12)

$${\displaystyle \sum _{j\in J}{\displaystyle \sum _{m\in M}{y}_{ijm}^k}}\le q_i{x}_i,\forall i\in I$$

(13)

$${\displaystyle \sum _{j\in J}{y}_{ijm}^k}\le {\zeta }_m,\forall i\in I,\forall m\in M,\forall k\in K$$

(14)

$$y_{ijm}^k\ge 0,\forall i\in I,\forall j\in J,\forall m\in M$$

(15)

Equation (11) introduces dual variables ${\mathbb{Q}}_j^k$ for the demand satisfaction constraint, dual variables ${ℝ}_i^k$ for the supply point capacity constraint, and dual variables ${\mathbb{N}}_{im}^k$ for the vehicle load constraint. Benders cuts are generated from the dual solutions of the subproblems and used to update the master problem. The generated Benders cuts are of the form:

$${\theta }_k\ge {\displaystyle \sum _{j\in J}{\mathbb{Q}}_j^k}{d}_j^k+{\displaystyle \sum _{i\in I}{ℝ}_i^k}{q}_i{x}_i+{\displaystyle \sum _{i\in I}{\displaystyle \sum _{m\in M}{\mathbb{N}}_{im}^k}}{\zeta }_m$$

(16)

We refer to [24] and show the pseudocode of the algorithm as follows:

After the construction cost and unit transportation cost of each material supply alternative point are determined, the material capacity limit is determined, and the demand node is added and the fluctuation range is determined; with the continuous increase in the number of iterations of the algorithm, the Benders cut generated by the algorithm will also increase, and the location of the alternative point and the material scheduling scheme will continue to approach the optimal solution until the algorithm converges. At this time, the optimal location plan and transportation plan output in Algorithm 1 $(x^{*},y^{*},{\theta }^{*})$ is the optimal scheme.

Algorithm 1. Benders Decomposition Algorithm
Step 1:	Make $LB=-\infty , UB=+\infty , k=1, R=\Phi$
Step 2:	solve the master problem (9) to obtain the optimal solution $({\widehat{x}}_{k+1},{\widehat{\phi }}_{k+1},{\widehat{y}}^1,\cdots ,{\widehat{y}}^k)$, and update the lower bound $L{B}^k$
Step 3:	The optimal solution is obtained by bringing it into the subproblem and updating the upper bound $({\widehat{x}}_{k+1},{\widehat{\phi }}_{k+1},{\widehat{y}}^1,\cdots ,{\widehat{y}}^k)R^k$ $U{B}^k=\min \left\{U{B}^{k-1}\right.,\left.L{B}^k\right\}$
Step 4:	If, then go back and perform step five; $UB-LB\le \epsilon {\widehat{x}}_{k+1}$. Otherwise, update, and go to step two $k=k+1$
Step 5:	Output the optimal location plan and transportation plan: $(x^{*},y^{*},{\theta }^{*})$

4. Numerical Experiments

4.1. Data Description

Taking a super large railway construction project in the mountainous area as an example, in the complex and difficult mountain scene, the construction of engineering projects is extremely vulnerable to the natural environment, such as landslides, debris flows, sudden temperature drops, and other natural disasters. On the one hand, when the construction project is affected by disasters, it will randomly generate material demand. On the other hand, due to natural disasters and other reasons, the storage of materials will also decline or even lead to being unable to transport construction materials out. Considering the complex and difficult mountain environment, the unit transportation cost is weighted by the distance between each point and the mountain environment around the road. Suppose there are five alternative points for material supply, and add capacity restrictions to the alternative points for material supply. The capacity of each material supply location is different, covering thirteen demand points, and the demand of the thirteen demand points is random. The weight of the environmental impact of each material supply point is added to the construction cost. Due to the uncertainty of the mountainous environment, the transportation cost of the partially random transportation network will change with the change in the scenario. In order to simplify the processing, the loss in the transportation process was uniformly calculated in the unit transportation cost of transporting construction materials from the material supply point to the demand point. (The relevant data are from a mountain city in the west of China).

4.2. Analysis of Results

Note: In the actual situation, the material demand at each demand point is uncertain, so each demand point in the model sets a certain range of demand fluctuations to represent the uncertainty of demand.

Under the conditions of Scenario 1, construction materials are transported in all five material supply sites, as shown in Figure 1, and the blue solid line in (a) indicates the normal supply of materials. As shown in (b), material supply location 1 supplies materials to demand points 1 and 2; supply location 2 supplies to demand points 3 and 4; supply site 3 to demand points 5 and 6; supply site 4 to demand points 7, 8, 9, and 10; supply site 5 supplies to demand points 11, 12, and 13.

Under the conditions of Scenario 2, the material transportation scheme and transportation network do not change, as shown in Figure 2.

Under the conditions of Scenario 3, the transportation method is changed due to the impact of environmental changes in mountainous areas, as shown in Figure 3. In (a), the blue solid line is the original normal transportation route, the blue dashed line is the new transportation route added compared with the previous one, and the red solid line is the transportation route interrupted due to anomalies. (b) The material supply point of No. 1 is changed to the demand point of No. 1, No. 2, and No. 3; No. 2 material supply point is changed to only transport to No. 4 demand point; No. 3 material supply place is changed to only transport to No. 5 demand point; No. 4 supplies will be transported to No. 6, No. 7, No. 8, No. 9, and No. 10 demand points; there has been no change in the transportation plan for supply site 5.

Under the conditions of Scenario 4, the original transportation scheme and transportation network are further changed, as shown in Figure 4. In (b), the supply location of material No. 1 is changed to supply demand points No. 1, No. 2, No. 3, and No. 4; No. 2 material supply stops transporting materials to the outside; No. 3 material supply place has not changed; No. 4 material supply place is changed to transport materials to No. 6, 7, 8, and 9 demand points; material supply location 5 is changed to transport materials to demand points 10, 11, 12, and 13.

4.3. Sensitivity Analysis

This section examines the impact of changes in the capacity of the material supply site and demand at the demand point on transportation costs. Under the condition that other parameters remain unchanged, the influence of the capacity of the material supply place on the transportation cost is shown in Figure 5. This section examines the impact of capacity changes at material supply locations and demand at demand points on transportation costs. The effect of the change in the capacity of No. 4 material supply location on the transportation cost is shown in Figure 5 when other parameters remain unchanged. When the capacity is lower than 850, the transportation cost decreases with the increase in capacity, which is mainly because under this condition, No. 4 material supply place is always operating at full capacity. Each increase in capacity will lead to an increase in the transportation volume of No. 4 supply place and a decrease in the transportation volume of other material supply places, thus resulting in an overall decrease in transportation cost. Under this condition, the demand of the demand point has been met, the transportation volume of the material supply place No. 4 will not change, and the other material supply places will not be affected, so that the transportation cost tends to be stable and does not change.

Figure 6 shows the relationship between transportation cost and demand change in different scenarios. It can be easily seen from the figure that the two show a typical linear correlation. With the increase in environmental change, transportation cost also increases, and the obvious growth trend of Scenario 3 and 4 can be better explained in the actual background. Hailstorms, rainstorms, and other severe weather even cause landslides, mudslides, and other disasters, and the supply capacity of material supply points is damaged or even unable to supply, resulting in a significant acceleration in the growth of transportation costs.

4.4. Model Performance Analysis

To illustrate the applicability of the proposed complex environment two-stage stochastic programing model (CE-TSSP), it is compared with the robust optimization programing model (RO) [25], mixed-integer linear programing (MILP) [26], and dynamic stochastic programing (DSP) [27]. When other parameters are unchanged, the solution results and solving time of the model are as follows:

As shown in Figure 7, the results obtained by the complex environment two-stage stochastic programing model (CE-TSSP) model are better, because the solutions obtained by the other models are too conservative compared with the processing of random demand ${\delta }_j$. In Figure 8, the solution time of the CE-TSSP model constructed in this paper is slightly longer than that of the RO and MILP models, but in general, the CE-TSSP model still has good performance and applicability.

5. Discussions and Conclusions

This study addresses the critical challenge of matching supply and demand for construction materials in large-scale engineering projects under complex and challenging environments. By constructing a two-stage linear stochastic programing model that integrates environmental factors and accounts for limited capacity and random demand, we provide a robust framework for optimizing material supply chains in such conditions. The Benders decomposition algorithm was employed to enhance the computational efficiency of solving this complex model, and its effectiveness was validated through a detailed case study.

The findings from this study offer several practical insights:

• In complex and difficult environments where engineering construction is significantly affected by environmental factors, it is more effective to add new material supply points rather than merely expanding existing ones. This conclusion is particularly evident in Scenario 4, where the material supply capacity of site 2 is completely lost, and the capacity of site 3 is significantly reduced. In such scenarios, expanding the capacity of existing supply points proves far less effective than establishing new ones, despite the additional costs. This strategy mitigates the risks associated with supply chain disruptions and is an innovative aspect of our model, as it addresses the high probability of such conditions occurring in real-world applications.
• The construction capacity of material supply points should be carefully controlled and set within reasonable limits. Our study, particularly the analysis of the No. 4 material supply site, shows that when storage capacity is below 850 tons, transportation costs decrease with increased capacity. However, beyond 850 tons, the transportation costs stabilize with minimal change. This finding underscores the importance of strategic capacity planning, as it can effectively reduce costs while maintaining or improving transportation efficiency.
• Across various scenarios, an increase in demand inevitably leads to a substantial rise in transportation costs, as demonstrated in our analysis. This highlights the crucial need for decision-makers to accurately predict material demand and make informed decisions regarding the type and quantity of material supplies. Proactive planning and precise demand forecasting are essential to avoid cost overruns and logistical inefficiencies, ensuring that the supply chain can meet the dynamic needs of large-scale engineering projects.

When comparing our findings with the existing literature, our model offers a more comprehensive approach by incorporating environmental uncertainties into the material supply chain optimization process. While traditional models often assume deterministic conditions, our approach acknowledges and addresses the variability and unpredictability inherent in large-scale construction projects, particularly in challenging terrains. This study advances existing knowledge by demonstrating the value of stochastic programing in construction logistics, providing a framework that is adaptable to different environmental scenarios and better equipped to handle the complexities of real-world applications.

However, this research is not without limitations. One significant limitation is that the current model does not account for the variability in the types of construction materials, which may require different logistical considerations. Additionally, the effectiveness of the model heavily depends on the accuracy of the input data, particularly regarding environmental conditions and material demand forecasts. Inaccurate data can lead to suboptimal decisions, reducing the model’s practical utility. Furthermore, the model has been validated in the context of a specific case study, and its generalizability to other types of infrastructure projects or geographic regions remains to be fully explored.

Future research should focus on addressing these limitations by developing models that consider the uncertainty and variability in material types and expanding the application of the model to different infrastructure projects and regions. Moreover, exploring hybrid optimization techniques could further enhance the model’s scalability and computational efficiency, particularly in handling larger and more complex scenarios.

In conclusion, this study contributes to the field of construction logistics by offering a novel approach that integrates environmental factors into the optimization of material supply chains in challenging environments. Our findings not only align with existing research but also extend it by addressing key gaps in the literature, particularly regarding the incorporation of uncertainty in supply chain management. Despite its limitations, this research provides a solid foundation for future studies aimed at improving the resilience and efficiency of supply chains in large-scale engineering projects.