An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty
This study investigates a green intermodal routing problem considering carbon tax regulation and a mixed (combined soft and hard) time window to improve cost- and time-effectiveness and promote carbon emission reduction in intermodal transportation. To enhance the feasibility of problem optimization...
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MDPI AG
2025-05-01
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| Series: | Applied System Innovation |
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| author | Yanli Guo Yan Sun Chen Zhang |
| author_facet | Yanli Guo Yan Sun Chen Zhang |
| author_sort | Yanli Guo |
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| description | This study investigates a green intermodal routing problem considering carbon tax regulation and a mixed (combined soft and hard) time window to improve cost- and time-effectiveness and promote carbon emission reduction in intermodal transportation. To enhance the feasibility of problem optimization, we model the uncertainty of both the carbon tax rate and the intermodal network capacity in the routing problem. By using interval fuzzy numbers to formulate the twofold uncertainty, an interval fuzzy linear optimization model is established to address the problem optimization, in which the optimization objective of the model is to minimize the total costs (consisting of transportation, time, and carbon emission costs). Furthermore, we conduct crisp processing of the proposed model to make the problem solvable, in which the optimization level, a parameter whose value is determined by the receiver before solving the problem, is introduced to represent the receiver’s attitude towards the reliability of transportation. We present a numerical experiment to verify the feasibility of the optimization model. The sensitivity analysis shows that the economics and environmental sustainability of the intermodal routing optimization conflict with its reliability. Improving the reliability of transportation increases both the total costs and the carbon emissions of the intermodal route. Furthermore, through comparison with deterministic modeling, the numerical experiment shows that modeling the twofold uncertainty can cover the different decision-making attitudes of the receiver, provide intermodal routes that are sensitive to the optimization level, enable flexible route decision-making, and avoid unreliable transportation. Through comparison with hard and soft time windows, the numerical experiment proves that the mixed time window is more applicable for problem optimization, since it can obtain the intermodal route that yields improved economics and environmental sustainability and simultaneously satisfies the receiver’s requirement for timeliness. Through comparison with the green intermodal route aiming at minimum carbon emissions, the numerical experiment indicates that carbon tax regulation under an interval fuzzy carbon tax rate is not feasible in all decision-making scenarios where the receivers have different attitudes regarding the reliability of transportation. When carbon tax regulation is infeasible, bi-objective optimization can provide Pareto solutions to balance the objectives of reduced costs and lowered carbon emissions. Finally, the numerical experiment reveals the influence of the release time of the transportation order at the origin and the stability of the interval fuzzy capacity on the routing optimization in the scenario in which the receiver prefers highly reliable transportation. |
| format | Article |
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| institution | OA Journals |
| issn | 2571-5577 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied System Innovation |
| spelling | doaj-art-7d3a6b399c674f0ca85da9843b40e8832025-08-20T02:24:18ZengMDPI AGApplied System Innovation2571-55772025-05-01836810.3390/asi8030068An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate UncertaintyYanli Guo0Yan Sun1Chen Zhang2School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Media and Design, Beijing Technology and Business University, Beijing 102488, ChinaThis study investigates a green intermodal routing problem considering carbon tax regulation and a mixed (combined soft and hard) time window to improve cost- and time-effectiveness and promote carbon emission reduction in intermodal transportation. To enhance the feasibility of problem optimization, we model the uncertainty of both the carbon tax rate and the intermodal network capacity in the routing problem. By using interval fuzzy numbers to formulate the twofold uncertainty, an interval fuzzy linear optimization model is established to address the problem optimization, in which the optimization objective of the model is to minimize the total costs (consisting of transportation, time, and carbon emission costs). Furthermore, we conduct crisp processing of the proposed model to make the problem solvable, in which the optimization level, a parameter whose value is determined by the receiver before solving the problem, is introduced to represent the receiver’s attitude towards the reliability of transportation. We present a numerical experiment to verify the feasibility of the optimization model. The sensitivity analysis shows that the economics and environmental sustainability of the intermodal routing optimization conflict with its reliability. Improving the reliability of transportation increases both the total costs and the carbon emissions of the intermodal route. Furthermore, through comparison with deterministic modeling, the numerical experiment shows that modeling the twofold uncertainty can cover the different decision-making attitudes of the receiver, provide intermodal routes that are sensitive to the optimization level, enable flexible route decision-making, and avoid unreliable transportation. Through comparison with hard and soft time windows, the numerical experiment proves that the mixed time window is more applicable for problem optimization, since it can obtain the intermodal route that yields improved economics and environmental sustainability and simultaneously satisfies the receiver’s requirement for timeliness. Through comparison with the green intermodal route aiming at minimum carbon emissions, the numerical experiment indicates that carbon tax regulation under an interval fuzzy carbon tax rate is not feasible in all decision-making scenarios where the receivers have different attitudes regarding the reliability of transportation. When carbon tax regulation is infeasible, bi-objective optimization can provide Pareto solutions to balance the objectives of reduced costs and lowered carbon emissions. Finally, the numerical experiment reveals the influence of the release time of the transportation order at the origin and the stability of the interval fuzzy capacity on the routing optimization in the scenario in which the receiver prefers highly reliable transportation.https://www.mdpi.com/2571-5577/8/3/68intermodal transportationgreen routinguncertain capacityuncertain carbon tax ratemixed time windowinterval fuzzy linear optimization model |
| spellingShingle | Yanli Guo Yan Sun Chen Zhang An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty Applied System Innovation intermodal transportation green routing uncertain capacity uncertain carbon tax rate mixed time window interval fuzzy linear optimization model |
| title | An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty |
| title_full | An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty |
| title_fullStr | An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty |
| title_full_unstemmed | An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty |
| title_short | An Interval Fuzzy Linear Optimization Approach to Address a Green Intermodal Routing Problem with Mixed Time Window Under Capacity and Carbon Tax Rate Uncertainty |
| title_sort | interval fuzzy linear optimization approach to address a green intermodal routing problem with mixed time window under capacity and carbon tax rate uncertainty |
| topic | intermodal transportation green routing uncertain capacity uncertain carbon tax rate mixed time window interval fuzzy linear optimization model |
| url | https://www.mdpi.com/2571-5577/8/3/68 |
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