What question did this study set out to answer?

The research aims to optimize supply chain processes by minimizing costs and environmental impacts while ensuring timely deliveries.

January 14, 2026Open Access

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

Key Points

The research aims to optimize supply chain processes by minimizing costs and environmental impacts while ensuring timely deliveries.
Developed a bi-objective mixed-integer nonlinear programming (MINLP) model.
Optimized single-machine production scheduling and heterogeneous-fleet vehicle routing.
Used numerical experiments and the epsilon-constraint method for validation.
Implemented two multi-objective metaheuristics: NSGA-II and MOPSO.
Evaluated performance using metrics like convergence and distribution quality.
NSGA-II reduced average distribution costs from 126.2 to 69.3 million LCU (45% reduction).
Tardiness was decreased from 23,950 to 858 hours (96% reduction) using NSGA-II.
MOPSO achieved a 32% cost reduction, reducing costs from 108.4 to 68.1 million LCU.
MOPSO showed a 96% tardiness reduction but less diversity in solutions.
NSGA-II consistently demonstrated superior solution quality and convergence over MOPSO.

Abstract

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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