Multi-objective integrated sustainable supply chain scheduling with environmentally friendly and time windows freight transportation

Maliheh Ganjia; Rahmat Rabet; Seyed Mojtaba Sajadi; Mohammad  Daneshvar Kakhki

doi:10.1007/s12351-025-01013-0

Multi-objective integrated sustainable supply chain scheduling with environmentally friendly and time windows freight transportation

Maliheh Ganjia
, Rahmat Rabet
, Seyed Mojtaba Sajadi^*
, Mohammad Daneshvar Kakhki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

Integrated sustainable supply chain scheduling (ISSCS) is essential for minimizing distribution costs, reducing environmental impacts, and improving customer service. This study develops a bi-objective mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes single-machine production scheduling, due-date assignment, batch delivery decisions, and heterogeneous-fleet vehicle routing with customer-specific time windows. The objectives are to reduce freight transportation and emission costs while minimizing delivery tardiness. Numerical experiments based on real operational data validate the model using the
-constraint method, which produces Pareto-optimal solutions with relative gaps below 0.8%. For large-scale instances, two multi-objective metaheuristics, Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO), are designed, tuned using Taguchi analysis, and evaluated using generational distance, mean ideal distance, spacing, diversity, and computational time. Experimental results show that NSGA-II delivers superior convergence and solution quality: within 50 iterations, it reduces average distribution cost from 126.2 to 69.3 million LCU (a 45% reduction) and decreases tardiness from 23,950 to 858 h (a 96% reduction). MOPSO achieves 32% cost reduction (108.4–68.1 million LCU) and 96% tardiness reduction (29,595–1047 h), but with less diversity and slower convergence. Pareto-front and convergence analyses confirm that NSGA-II consistently provides better-distributed and more stable non-dominated solutions. Overall, the proposed integrated model effectively reduces transportation, emission, and customer-dissatisfaction costs; the batch-delivery formulation ensures timely service across multiple time windows; and the metaheuristic frameworks especially NSGA-II demonstrate strong capability for solving large-scale sustainable supply-chain scheduling and environmentally friendly freight transportation problems.

Original language	English
Article number	19
Number of pages	38
Journal	Operational Research
Volume	26
Early online date	13 Jan 2026
DOIs	https://doi.org/10.1007/s12351-025-01013-0
Publication status	Published - 13 Jan 2026

Bibliographical note

Copyright © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Keywords

Batch delivery
Carbon emission
Freight transportation
Metaheuristic algorithm
Multi-objective
Scheduling
Sustainable supply chain
Time-windows

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10.1007/s12351-025-01013-0Licence: CC BY 4.0

Multi-objective integrated sustainable supply chain scheduling with environmentally friendly and time windows freight transportation
Copyright © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
Final published version, 4.87 MBLicence: CC BY 4.0

Cite this

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title = "Multi-objective integrated sustainable supply chain scheduling with environmentally friendly and time windows freight transportation",

abstract = "Integrated sustainable supply chain scheduling (ISSCS) is essential for minimizing distribution costs, reducing environmental impacts, and improving customer service. This study develops a bi-objective mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes single-machine production scheduling, due-date assignment, batch delivery decisions, and heterogeneous-fleet vehicle routing with customer-specific time windows. The objectives are to reduce freight transportation and emission costs while minimizing delivery tardiness. Numerical experiments based on real operational data validate the model using the -constraint method, which produces Pareto-optimal solutions with relative gaps below 0.8\%. For large-scale instances, two multi-objective metaheuristics, Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO), are designed, tuned using Taguchi analysis, and evaluated using generational distance, mean ideal distance, spacing, diversity, and computational time. Experimental results show that NSGA-II delivers superior convergence and solution quality: within 50 iterations, it reduces average distribution cost from 126.2 to 69.3 million LCU (a 45\% reduction) and decreases tardiness from 23,950 to 858 h (a 96\% reduction). MOPSO achieves 32\% cost reduction (108.4–68.1 million LCU) and 96\% tardiness reduction (29,595–1047 h), but with less diversity and slower convergence. Pareto-front and convergence analyses confirm that NSGA-II consistently provides better-distributed and more stable non-dominated solutions. Overall, the proposed integrated model effectively reduces transportation, emission, and customer-dissatisfaction costs; the batch-delivery formulation ensures timely service across multiple time windows; and the metaheuristic frameworks especially NSGA-II demonstrate strong capability for solving large-scale sustainable supply-chain scheduling and environmentally friendly freight transportation problems.",

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author = "Maliheh Ganjia and Rahmat Rabet and Sajadi, \{Seyed Mojtaba\} and \{Daneshvar Kakhki\}, Mohammad",

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N1 - Copyright © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

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N2 - Integrated sustainable supply chain scheduling (ISSCS) is essential for minimizing distribution costs, reducing environmental impacts, and improving customer service. This study develops a bi-objective mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes single-machine production scheduling, due-date assignment, batch delivery decisions, and heterogeneous-fleet vehicle routing with customer-specific time windows. The objectives are to reduce freight transportation and emission costs while minimizing delivery tardiness. Numerical experiments based on real operational data validate the model using the -constraint method, which produces Pareto-optimal solutions with relative gaps below 0.8%. For large-scale instances, two multi-objective metaheuristics, Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO), are designed, tuned using Taguchi analysis, and evaluated using generational distance, mean ideal distance, spacing, diversity, and computational time. Experimental results show that NSGA-II delivers superior convergence and solution quality: within 50 iterations, it reduces average distribution cost from 126.2 to 69.3 million LCU (a 45% reduction) and decreases tardiness from 23,950 to 858 h (a 96% reduction). MOPSO achieves 32% cost reduction (108.4–68.1 million LCU) and 96% tardiness reduction (29,595–1047 h), but with less diversity and slower convergence. Pareto-front and convergence analyses confirm that NSGA-II consistently provides better-distributed and more stable non-dominated solutions. Overall, the proposed integrated model effectively reduces transportation, emission, and customer-dissatisfaction costs; the batch-delivery formulation ensures timely service across multiple time windows; and the metaheuristic frameworks especially NSGA-II demonstrate strong capability for solving large-scale sustainable supply-chain scheduling and environmentally friendly freight transportation problems.

AB - Integrated sustainable supply chain scheduling (ISSCS) is essential for minimizing distribution costs, reducing environmental impacts, and improving customer service. This study develops a bi-objective mixed-integer nonlinear programming (MINLP) model that simultaneously optimizes single-machine production scheduling, due-date assignment, batch delivery decisions, and heterogeneous-fleet vehicle routing with customer-specific time windows. The objectives are to reduce freight transportation and emission costs while minimizing delivery tardiness. Numerical experiments based on real operational data validate the model using the -constraint method, which produces Pareto-optimal solutions with relative gaps below 0.8%. For large-scale instances, two multi-objective metaheuristics, Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO), are designed, tuned using Taguchi analysis, and evaluated using generational distance, mean ideal distance, spacing, diversity, and computational time. Experimental results show that NSGA-II delivers superior convergence and solution quality: within 50 iterations, it reduces average distribution cost from 126.2 to 69.3 million LCU (a 45% reduction) and decreases tardiness from 23,950 to 858 h (a 96% reduction). MOPSO achieves 32% cost reduction (108.4–68.1 million LCU) and 96% tardiness reduction (29,595–1047 h), but with less diversity and slower convergence. Pareto-front and convergence analyses confirm that NSGA-II consistently provides better-distributed and more stable non-dominated solutions. Overall, the proposed integrated model effectively reduces transportation, emission, and customer-dissatisfaction costs; the batch-delivery formulation ensures timely service across multiple time windows; and the metaheuristic frameworks especially NSGA-II demonstrate strong capability for solving large-scale sustainable supply-chain scheduling and environmentally friendly freight transportation problems.

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Multi-objective integrated sustainable supply chain scheduling with environmentally friendly and time windows freight transportation

Abstract

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Keywords

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