Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty
This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an un...
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MDPI AG
2024-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/3/200 |
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| author | Xinya Li Yan Sun Jinfeng Qi Danzhu Wang |
| author_facet | Xinya Li Yan Sun Jinfeng Qi Danzhu Wang |
| author_sort | Xinya Li |
| collection | DOAJ |
| description | This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model. |
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| language | English |
| last_indexed | 2024-04-24T18:33:02Z |
| publishDate | 2024-03-01 |
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| series | Axioms |
| spelling | doaj.art-1d12a4467f62492496e6ef8c495036b52024-03-27T13:21:06ZengMDPI AGAxioms2075-16802024-03-0113320010.3390/axioms13030200Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold UncertaintyXinya Li0Yan Sun1Jinfeng Qi2Danzhu Wang3Institute of Technology, Shandong Open University, Jinan 250010, ChinaSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaInstitute of Technology, Shandong Open University, Jinan 250010, ChinaTransportation & Economics Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, ChinaThis study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.https://www.mdpi.com/2075-1680/13/3/200green multimodal transportationroutingsoft time windowtwofold uncertaintytriangular fuzzy numbersfuzzy chance-constrained programming |
| spellingShingle | Xinya Li Yan Sun Jinfeng Qi Danzhu Wang Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty Axioms green multimodal transportation routing soft time window twofold uncertainty triangular fuzzy numbers fuzzy chance-constrained programming |
| title | Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty |
| title_full | Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty |
| title_fullStr | Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty |
| title_full_unstemmed | Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty |
| title_short | Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty |
| title_sort | chance constrained optimization for a green multimodal routing problem with soft time window under twofold uncertainty |
| topic | green multimodal transportation routing soft time window twofold uncertainty triangular fuzzy numbers fuzzy chance-constrained programming |
| url | https://www.mdpi.com/2075-1680/13/3/200 |
| work_keys_str_mv | AT xinyali chanceconstrainedoptimizationforagreenmultimodalroutingproblemwithsofttimewindowundertwofolduncertainty AT yansun chanceconstrainedoptimizationforagreenmultimodalroutingproblemwithsofttimewindowundertwofolduncertainty AT jinfengqi chanceconstrainedoptimizationforagreenmultimodalroutingproblemwithsofttimewindowundertwofolduncertainty AT danzhuwang chanceconstrainedoptimizationforagreenmultimodalroutingproblemwithsofttimewindowundertwofolduncertainty |