This study investigates the integrated scheduling of production and distribution within a time-sensitive supply chain at the operational level. In addition, the study specifically focuses on parallel machine scheduling and vehicle routing problem with time windows (VRP-TW) while considering flexible departure times. A hybrid multi-level optimization (HMLO) framework is developed, decomposing the problem into two primary phases: parallel machine scheduling and distribution scheduling. The initial phase entails the establishment of a comprehensive production schedule, whereas the subsequent phase focuses on segmenting the orders into batches and developing a complete distribution schedule. The framework incorporates the ant colony system (ACS) within the HMLO structure to optimize distribution costs. This is accomplished with both metaheuristics and heuristics to determine the optimal values for the decision variables. Extensive numerical experiments demonstrate that the proposed framework demonstrate that the suggested framework can yield optimal solutions for small-scale instances. Furthermore, it outperforms existing methods, including those utilized in LINGO software, for medium and large-scale instances regarding both convergence and solution quality. For large-scale instances, the proposed method achieves an average improvement of 5 to 30% when compared to LINGO solutions.
Keywords: Ant colony system; Hybrid multi-level optimization; Parallel machines; Production and distribution scheduling; Vehicle routing problem.
© 2025. The Author(s).