Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing
Abstract
:1. Introduction
- 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.
2. Problem Formulation and Model Establishment
2.1. Characteristics Analysis of a Complex and Difficult Environment
- (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
2.3. Complex Environment Two-Stage Stochastic Programing Model (CE-TSSP)
3. Algorithm Design—Benders Algorithm
Algorithm 1. Benders Decomposition Algorithm | |
Step 1: | Make |
Step 2: | solve the master problem (9) to obtain the optimal solution , and update the lower bound |
Step 3: | The optimal solution is obtained by bringing it into the subproblem and updating the upper bound |
Step 4: | If, then go back and perform step five; . Otherwise, update, and go to step two |
Step 5: | Output the optimal location plan and transportation plan: |
4. Numerical Experiments
4.1. Data Description
4.2. Analysis of Results
4.3. Sensitivity Analysis
4.4. Model Performance Analysis
5. Discussions and Conclusions
- 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.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Material Supply Place | Area (sqm) | Capacity (tonnes) |
---|---|---|
1 | 8000 | 1200 |
2 | 5000 | 700 |
3 | 3880 | 400 |
4 | 7000 | 900 |
5 | 3200 | 360 |
Demand Point | Demand Range (tonnes) |
---|---|
1 | [100, 500] |
2 | [200, 600] |
3 | [150, 450] |
4 | [100, 400] |
5 | [200, 500] |
6 | [300 ,700] |
7 | [100, 400] |
8 | [200, 600] |
9 | [150, 450] |
10 | [100, 500] |
11 | [100, 300] |
12 | [150, 400] |
13 | [200, 500] |
Demand Point\Material Supply Place | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
1 | 33.75 | 36.87 | 41.21 | 51.00 | 61.04 |
2 | 32.33 | 36.21 | 38.57 | 47.43 | 59.27 |
3 | 36.25 | 35.25 | 36.22 | 45.78 | 57.55 |
4 | 37.41 | 35.67 | 34.43 | 41.55 | 54.04 |
5 | 43.22 | 37.24 | 31.20 | 37.65 | 51.33 |
6 | 42.11 | 37.68 | 31.55 | 34.51 | 48.25 |
7 | 51.23 | 41.68 | 33.67 | 32.25 | 43.93 |
8 | 52.33 | 43.78 | 34.44 | 33.12 | 41.35 |
9 | 57.24 | 45.31 | 35.89 | 34.75 | 37.60 |
10 | 57.45 | 50.43 | 42.72 | 36.43 | 34.69 |
11 | 60.45 | 54.81 | 45.64 | 38.09 | 33.74 |
12 | 64.35 | 57.43 | 48.25 | 41.05 | 32.44 |
13 | 64.27 | 57.66 | 52.96 | 43.55 | 33.10 |
References
- Daskin, M. Network and discrete location: Models, algorithms and applications. J. Oper. Res. Soc. 1997, 48, 763–764. [Google Scholar] [CrossRef]
- Cordeau, J.F.; Gendreau, M.; Laporte, G. A tabu search heuristic for periodic and multi-depot vehicle routing problems. Netw. Int. J. 1997, 30, 105–119. [Google Scholar] [CrossRef]
- Balakrishnan, A.; Ward, J.E.; Wong, R.T. Integrated facility location and vehicle routing models: Recent work and future prospects. Am. J. Math. Manag. Sci. 1987, 7, 35–61. [Google Scholar] [CrossRef]
- Min, H.; Jayaraman, V.; Srivastava, R. Combined location-routing problems: A synthesis and future research directions. Eur. J. Oper. Res. 1998, 108, 1–15. [Google Scholar] [CrossRef]
- Nagy, G.; Salhi, S. Location-routing: Issues, models and methods. Eur. J. Oper. Res. 2007, 177, 649–672. [Google Scholar] [CrossRef]
- Lopes, R.B.; Ferreira, C.; Santos, B.S.; Barreto, S. A taxonomical analysis, current methods and objectives on location-routing problems. Int. Trans. Oper. Res. 2013, 20, 795–822. [Google Scholar] [CrossRef]
- Drexl, M.; Schneider, M. A survey of variants and extensions of the location-routing problem. Eur. J. Oper. Res. 2015, 241, 283–308. [Google Scholar]
- Cuda, R.; Guastaroba, G.; Speranza, M.G. A survey on two-echelon routing problem. Comput. Oper. Res. 2015, 55, 185–199. [Google Scholar] [CrossRef]
- Albareda-Sambola, M.; Rodríguez-Pereira, J. Location-routing and location-arc routing. In Location Science; Springer: Cham, Switzerland, 2019; pp. 431–451. [Google Scholar]
- Yan, F.; Xu, J.; Han, B.T. Material transportation problems in construction projects under an uncertain environment. KSCE J. Civ. Eng. 2015, 19, 2240–2251. [Google Scholar] [CrossRef]
- Barbarosoglu, G.; Arda, Y. A two-stage stochastic programming framework for transportation planning in disaster response. J. Oper. Res. Soc. 2004, 55, 43–53. [Google Scholar] [CrossRef]
- Rawls, C.G.; Turnquist, M.A. Pre-positioning of emergency supplies for disaster response. Transp. Res. Part B Methodol. 2010, 44, 521–534. [Google Scholar] [CrossRef]
- Wang, W.Q.; Yang, K.; Yang, L.X.; Gao, Z.Y. Two-stage distributionally robust programming based on worst-case mean-CVaR criterion and application to disaster relief management. Transp. Res. Part E Logist. Transp. Rev. 2021, 149, 102332. [Google Scholar] [CrossRef]
- Liu, K.; Yang, L.; Zhao, Y.; Zhang, Z.-H. Multi-period stochastic programming for relief delivery considering evolving transportation network and temporary facility relocation/closure. Transp. Res. Part E Logist. Transp. Rev. 2023, 180, 103357. [Google Scholar] [CrossRef]
- Cui, P.; He, M.; Tapponnier, P.; Zhang, L.; Li, Z.; Gong, W.; Zhou, G.G.; Guo, J. Preface for “Geohazards and mitigation along the Sichuan-Tibet Railway”. Eng. Geol. 2023, 317, 107095. [Google Scholar] [CrossRef]
- Qin, Y.; Zheng, B. The Qinghai–Tibet Railway: A landmark project and its subsequent environmental challenges. Environ. Dev. Sustain. 2010, 12, 859–873. [Google Scholar] [CrossRef]
- Xu, J.; Wang, Z.; Zhang, M.; Tu, Y. A new model for a 72-h post-earthquake emergency logistics location-routing problem under a random fuzzy environment. Transp. Lett. 2016, 8, 270–285. [Google Scholar] [CrossRef]
- Zhang, J.; Zhu, H.; Shen, H.; Li, G. Location-routing Problem of Emergency Logistics for Engineering Construction Projects Under Complex Environments. J. Transp. Syst. Eng. Inf. Technol. 2023, 23, 280. [Google Scholar]
- Yang, Z.; Guo, L.; Yang, Z. Emergency logistics for wildfire suppression based on forecasted disaster evolution. Ann. Oper. Res. 2019, 283, 917–937. [Google Scholar] [CrossRef]
- Meng, L.; Wang, X.; He, J.; Han, C.; Hu, S. A two-stage chance constrained stochastic programming model for emergency supply distribution considering dynamic uncertainty. Transp. Res. Part E Logist. Transp. Rev. 2023, 179, 103296. [Google Scholar] [CrossRef]
- Kang, L.; Li, H.; Sun, H.; Wu, J. UAV Cruising for Material Transportation Under Engineering Construction in Complex Mountainous Areas: Modeling and Case Study. J. Transp. Syst. Eng. Inf. Technol. 2023, 23, 290. [Google Scholar]
- Delage, E.; Ye, Y.Y. Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems. Oper. Res. 2010, 58, 595–612. [Google Scholar] [CrossRef]
- Zeng, B.; Zhao, L. Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 2013, 41, 457–461. [Google Scholar] [CrossRef]
- Hooker, J.N.; Ottosson, G. Logic-based Benders decomposition. Math. Program. 2003, 96, 33–60. [Google Scholar] [CrossRef]
- Ben-Tal, A.; Nemirovski, A. Robust optimization–methodology and applications. Math. Program. 2002, 92, 453–480. [Google Scholar] [CrossRef]
- Vielma, J.P. Mixed integer linear programming formulation techniques. Siam Rev. 2015, 57, 3–57. [Google Scholar] [CrossRef]
- Bar-Shalom, Y. Stochastic dynamic programming: Caution and probing. IEEE Trans. Autom. Control 1981, 26, 1184–1195. [Google Scholar] [CrossRef]
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 |
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Bao, L.; Zhang, P.; Guo, Z.; Wang, W.; Zhu, Q.; Ding, Y. Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing. Mathematics 2024, 12, 2683. https://doi.org/10.3390/math12172683
Bao L, Zhang P, Guo Z, Wang W, Zhu Q, Ding Y. Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing. Mathematics. 2024; 12(17):2683. https://doi.org/10.3390/math12172683
Chicago/Turabian StyleBao, Liu, Peigen Zhang, Ze Guo, Wanqi Wang, Qing Zhu, and Yulin Ding. 2024. "Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing" Mathematics 12, no. 17: 2683. https://doi.org/10.3390/math12172683