Integrated Production and Transportation Scheduling in a Distributed Hybrid Flow Shop Considering Dynamic Orders Under an E-Commerce Environment

Abstract

Real-time order arrivals and stringent timeliness demands in e-commerce pose significant challenges to production-distribution coordinated scheduling in distributed manufacturing systems. This paper tackles the integrated production and distribution scheduling problem within a dynamic distributed hybrid flow shop. We formulate a mixed-integer linear programming model aimed at minimizing average order tardiness and total operational cost. To address dynamic uncertainties, we propose an improved decomposition-based multi-objective evolutionary algorithm (I-MOEA/D) operating within a rolling horizon framework. The algorithm integrates three critical components: an urgency-based emergency window management strategy that caps computational complexity, a 2-opt local search operator that boosts vehicle routing efficiency, and acceleration techniques—including order dictionary indexing, lightweight object replication, and distance caching—that guarantee real-time responsiveness. The window size is determined as Wmax = 50 through sensitivity analysis. Extensive experiments conducted on 100, 200, and 300-order scenarios with 30 independent random seeds demonstrate that I-MOEA/D markedly outperforms NSGA-II, MOALNS, and a reinforcement learning-driven hyper-heuristic (RL-HH). For 200 orders, I-MOEA/D reduces average tardiness by 18.5%, 41.0%, and 58.7% compared to NSGA-II, MOALNS, and RL-HH, respectively, while maintaining competitive cost performance (a cost gap of 16.99% relative to the static lower bound). The IGD metric achieves 0.0031, confirming good convergence and diversity. Acceleration techniques cut computation time by 56% without sacrificing solution quality. The algorithm scales efficiently with problem size. These results validate that I-MOEA/D delivers effective real-time decision support for dynamic distributed production-distribution systems.