Two-Echelon Location-Routing under Uncertainty Considering Reliability

Document Type : Original Article

Authors

1 Ph. D. Student, Department of Operation Management and Information Technology, Management and Accounting Faculty, Allameh Tabataba’i University, Tehran, Iran.

2 Professor, Department of Operation Management and Information Technology, Management and Accounting Faculty, Allameh Tabataba’i University, Tehran, Iran.

3 Associate Professor, Department of Industrial Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran.

Abstract

Introduction and objectives: Urban development and the increase in intercity and intracity transportation have led to a significant rise in transportation costs. This rise in cost increases the final product price and consequently the product's market price. Additionally, the economic aspect is not the only concern; increased transportation results in higher CO2 emissions. These issues have driven the design of various transportation and vehicle routing models, including the vehicle location-routing problem. Facility location is a strategic decision due to the high costs associated with constructing and locating facilities. On the other hand, routing decisions depend on location decisions and are considered mid-term and short-term decisions.
In this study, a mathematical model for vehicle location-routing under uncertainty conditions and considering reliability is developed to simultaneously optimize sustainability objective functions while maintaining minimum reliability levels. The sustainability objectives in this study include minimizing total costs, minimizing CO2 emissions, and maximizing job opportunities based on integrated strategic and tactical decisions. The primary focus of this paper is decision-making for optimal transportation routing, considering time windows and the reliability of facility location based on their failure rates.
Methods: Given the uncertainty of the mathematical model parameters, various fuzzy and robust possibilistic programming methods were employed to formulate the model. Four different models were used to manage the uncertainty of demand parameters and transportation costs, and the results were compared. Additionally, two methods—an exact solution approach and a meta-heuristic algorithm—were employed to solve the multi-objective mathematical model. The enhanced epsilon constraint method was used to analyze small-scale mathematical models and conduct sensitivity analyses, while the NSGA-II algorithm was applied to solve larger-scale numerical examples. Furthermore, an initial solution based on prioritization was utilized for the meta-heuristic algorithm.
Results and discussion: The results indicate that although an increase in uncertainty rates leads to more job opportunities, it also raises total costs and greenhouse gas emissions. Additionally, the analysis reveals that the RPP-III method achieves the highest model robustness cost with the lowest standard deviation. In the reliability analysis, it was observed that higher facility failure rates result in an increased number of located production and distribution centers. This, in turn, leads to higher total costs, increased CO2 emissions, and more job opportunities. By analyzing 15 numerical examples, it was also found that NSGA-II is highly efficient in solving the mathematical model compared to the enhanced epsilon constraint method.
Conclusion: The findings of this research assist managers in making strategic decisions such as facility location and tactical decisions such as vehicle routing in the context of market uncertainty. Given that the model incorporates various realistic decisions and assumptions, the mathematical model can be effectively applied in distribution industries, particularly for pharmaceutical and electronic goods.

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References

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Journal of Industrial Management Perspective
Volume 14, Issue 4 - Serial Number 56
Issue in Progress
2024
Pages 165-200

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