A unified MILP framework for integrated serial-parallel production batching and inter-factory delivery in multi-factory environments

Abstract This study addresses the integrated serial–parallel production batching and inter-factory delivery scheduling problem in multi-factory environments – an operational configuration that has been largely overlooked in existing research. The challenge arises because upstream serial batching, downstream parallel batching, and inter-factory delivery batching are strongly interdependent, yet prior studies model them separately. To fill this gap, a unified mixed-integer linear programming (MILP) formulation is developed to jointly determine batch formation, batch sequencing, and inter-factory release timing. The model internalizes production–delivery trade-offs and captures all major cost components, including tardiness, holding, transportation, and production. Using Gurobi, 27 OFAT-designed instances are solved to proven optimality, with solution times ranging from 427 seconds (median) to 30.8 hours for the largest cases. Sensitivity analysis reveals that unit production cost is the primary driver of total cost, while tardiness penalties have the strongest impact on batch allocation behaviour. Delivery fees moderately affect outsourcing decisions, while holding costs have a negligible impact on operations. The results provide actionable managerial insights by identifying when inter-factory delivery batching becomes economically advantageous and how batch-formation rules shape downstream workload synchronization. Overall, this study provides a unified analytical framework that explicitly links batch-based production decisions across stages with inter-factory delivery timing and shipment frequency in a multi-factory environment.