Document Type : Research Paper

Authors

• Maryam Tajik Khaveh ¹
• Maryam Daneshvar ²
• Seyed Hossein Razavi Hajiagha ³

¹ .Master of industrial management, Management Dept, Faculty of Management and Finance, Khatam University, Tehran, Iran.

² Assistant Professor, Management Dept, Faculty of Management and Finance, Khatam University, Tehran, Iran.

³ Associate Professor, Management Dept, Faculty of Management and Finance, Khatam University, Tehran, Iran.

Abstract

Route selection in multimodal transport networks is a key issue in transport management and planning that requires advanced modeling and optimization approaches due to the multimodal nature and complexities arising from uncertainty. This study aims to develop a multi-objective mathematical model for optimal route selection in multimodal transportation networks, simultaneously minimizing transportation costs, carbon emissions, and delivery time deviations while preserving cargo value. This model, by considering time windows and uncertainty management, seeks to provide sustainable solutions to improve the transport system’s performance. In this model, transport capacity and demand are assumed to be fixed in each period, and costs and time are uncertain. The output of the model determines optimal routes and transport modes to achieve the defined objectives. Also, a robust optimization approach is used to manage uncertainty and provide a model that maintains its reliability even under uncertain conditions. In order to validate the model, a numerical example of a multimodal transportation network is solved using the goal programming approach. The results show that the proposed model, using robust optimization, has the necessary flexibility to adapt to changes and can help improve the quality of service and reduce operating costs. Also, using the robust optimization approach in a multimodal transportation network leads to increased resilience and network efficiency.
Introduction
The advancement of economic globalization and information technology has significantly facilitated global communication. A singular mode of transportation is insufficient to satisfy the demands of the transportation market, leading to the emergence of multimodal transportation (Peng et al., 2023). The route selection strategy of a multimodal transportation network is a complex multi-objective decision-making problem that has become a key aspect of multimodal transportation systems (Elbert et al., 2020).
In this research, the multimodal transportation structure is a network structure with nodes (terminals) and edges (transportation) representing multiple modes of transportation. Also, in the research conducted, the objectives related to reducing travel time have been considered, while in the real world, arriving on time is preferable to arriving early. Hence, adding a time window to the objective functions is one of the innovations of this study.
Considering uncertainty factors in the decision-making process is essential for designing optimal routes. Robust optimization, as one of the approaches in the field of uncertainty management, has the ability to provide models that enable better decision-making by maintaining stability and efficiency in uncertain conditions. In this study, a multi-objective robust optimization model is developed to minimize the total transportation cost, delivery delays, and carbon emissions while maintaining the value of perishable goods, considering the time window for timely arrival of goods.
According to the above, the innovations of this paper are as follows:

Adding time windows to objective functions.
Defining the value function of perishable goods.
Combining uncertainty in time and cost with the perishability factor.
Considering uncertainty with a robust optimization approach.

 
Research background
Multimodal freight transport means the transport of goods by at least two different modes of transport (UNECE, 2009). This type of transport ensures the efficiency of transport in terms of the timely availability of products and raw materials. This method usually involves a combination of land (truck, train), sea (ship), and air transport. The main feature of multimodal transport is that even if several modes of transport are used, the transport process is managed under a single contract or general responsibility, which helps to reduce delays, improve efficiency, and reduce transport risks. Other advantages of this transport method include cost reduction through the optimal use of different modes of transport, the possibility of using the fastest transport methods in specific conditions, and increased transparency and damage reduction through integrated management. The combination of methods can also help reduce energy consumption and greenhouse gas emissions. For a transport system to be efficient, it must be multimodal to meet different needs. Hence, the importance of multimodal transport lies in its ability to improve efficiency, reduce costs, and enhance delivery speed by strategically combining different modes of transport (Udomwannakhet et al., 2018).
Methodology
The main objective of this research is to develop a mathematical model for route selection in a multimodal transportation network. Therefore, this research is applied research conducted within the positivist paradigm. In order to collect research data, information related to multimodal transportation networks has been extracted from reports, databases, and scientific articles. Since the routing problem formulated in this paper is a multi-objective problem, weighted goal programming (GP) is used to solve it. To account for the uncertainty in the parameters of transportation cost and time, the Bertsimas and Sim robust optimization approach is applied, and a robust goal programming model has also been formulated.
 
Discussion and Results
To verify the validity of the model, real data and numerical scenarios have been used. The results of solving the model show that the proposed model is able to provide optimal paths considering uncertainty and multiple objectives (cost reduction, carbon emission reduction, and product value preservation). Solving the model and specifying the values of the decision variables indicate the structural coherence and feasibility of the model. One of the main validation criteria in mathematical modeling is the ability of the model to provide a justified and optimal solution. In addition, the model results are consistent with the logic of the problem and the defined constraints. Also, the proposed model has been solved using the goal programming method, which is one of the valid methods for solving multi-objective optimization problems. Furthermore, the sensitivity analysis of key parameters shows that the model behaves stably in response to changes in input parameters and that its outputs are reasonable and reliable.
 
Conclusion
The findings indicate that integrating multiple transportation modes and optimizing routing decisions can significantly reduce total costs. Furthermore, the incorporation of time windows and the reduction of delivery time deviation enhance customer satisfaction compared to conventional models. The study confirms that the robust optimization model can recommend routes that maintain high levels of stability and efficiency, even in the presence of uncertainty. The model also accounts for the perishability of goods, thereby contributing to waste reduction. Overall, the proposed model improves the performance of transportation systems under uncertain conditions, lowers costs, improves productivity, and offers a practical solution applicable across various industries.

Keywords

• Routing
• Multimodal Transportation network
• Robust Optimization
• Uncertainty
• Time Window

Main Subjects

• uncertainty