This paper presents a multiobjective, mixed-integer linear programming (MILP) model that integrates production scheduling, inventory management, and vessel assignment for a global supply chain. Given that such large-scale problems are NP-hard and usually suffer from symmetry, we conduct an exploratory analysis to identify complexity sources. Following this, we design a novel variant of the large neighborhood search metaheuristic to tackle the problem efficiently. While symmetry is considered an issue in the literature, the implemented algorithm provides a practical way of profiting from instead of breaking it. Computationally, we reach near-optimal solutions in real-world instances. Compared to the default CPLEX and a reference algorithm that mimics real life, we gain significantly in terms of time, quality, and the number of feasible integer solutions found during the solving process. In addition to efficiency, integrated optimization enhances operations management capabilities and supply chain resilience.