Purpose: This study presents a tri-objective model for the integrated planning of production and distribution within a multi-level supply chain network that encompasses multiple product types and time periods. Research methodology: The supply chain network includes manufacturer plants (MPs), distribution centers (DCs), retailers, and final customers. The proposed model aims to minimize total supply chain costs, ensure timely delivery of products to customers, and reduce the lost demand rate. Classified as a linear integer programming problem, which is NP-Hard, the model’s complexity is addressed using two multi-objective meta-heuristic approaches based on the Pareto method: the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Non-Dominated Ranking Genetic Algorithm (NRGA). The Taguchi method is employed to optimize the input parameters of these algorithms. Results: The performance of the proposed solution methods is evaluated through various test problems of different dimensions. Statistical analyses confirm the effectiveness and reliability of both algorithms in achieving the defined objectives. Conclusions: The findings highlight that multi-objective meta-heuristic approaches, when parameter-tuned appropriately, provide efficient and practical solutions for integrated supply chain planning, offering a balance among cost, service level, and demand fulfillment. Limitations: The study acknowledges the inherent complexity of the problem and the dependency of meta-heuristic outputs on parameter settings, which may influence solution robustness. Contribution: This research contributes to the literature by providing a robust framework for optimizing production and distribution in complex supply chain networks, delivering insights into the application of advanced algorithmic strategies in operational planning.
Bazyar et al. (Thu,) studied this question.