Two-Stage Modeling Approach for Solving Large-Scale Production Planning MILPs with Hexaly
Context
Bridgestone operates a large and complex industrial production planning network, manufacturing multiple tire families across several plants. Production planning decisions must balance manufacturing efficiency, service levels, capacity constraints, and inventory targets over a rolling horizon of 4 to 5 months. At this scale, industrial production planning is formulated as a very large Mixed Integer Linear Programming model. Mixed-Integer Linear Programming (MILP) provides a natural mathematical framework for production planning and supply planning. However, when applied to large-scale production planning, computational complexity becomes a critical challenge.
A benchmark was conducted to explore potential improvements in solution quality by modeling the Bridgestone production planning problem using Hexaly. The objective was to assess whether a hybrid, two-stage modeling approach could improve large-scale MILP optimization for production planning under the same runtime constraints.
The Challenge of Large-Scale MILP in Production Planning
The production planning and inventory optimization model integrates:
- Bill of materials and production costs
- Known and forecast demand
- Minimum and maximum inventory targets
- Capacity constraints across multiple production plants
- Changeover times between tire families
- Limits on simultaneous weekly production campaigns
- Machines & Resource availability constraints
The full production planning model comprises approximately 500,000 variables and 500,000 constraints.
In large-scale production planning, aggregation and decomposition techniques are commonly used to make MILP resolution computationally tractable. The global production planning model is split into smaller submodels that are solved sequentially.
While decomposition enables scalability in industrial production planning, it often introduces a limitation. Decisions optimized locally may limit the ability to achieve a globally optimal production plan across the entire planning horizon.
The benchmark, therefore, focused on improving the way large-scale MILP optimization is structured and executed in a production planning environment.
A Two-Stage Optimization Strategy for Production Planning
Hexaly implemented a multistage production planning optimization workflow designed to improve MILP solution quality while enabling scalability.
Stage 1: Decomposed Production Planning Optimization
The full production planning model was divided into approximately a dozen submodels, each containing around 50 thousand variables and constraints.
- Each submodel was solved for about 10 minutes
- The overall runtime was approximately 2 hours
- A high-quality, feasible production plan was generated
This stage ensured computational tractability for large-scale production planning.
Stage 2: Full Horizon Reoptimization
In the second stage, the complete non-decomposed production planning model was initialized using the Stage 1 solution as a starting point and reoptimized globally.
This holistic production planning optimization phase made it possible to:
- Reconsider all production and inventory decisions simultaneously
- Capture cross-plant and cross-period interactions
- Rebalance supply planning decisions over the entire 4 to 5-month horizon
- Improve overall MILP solution quality
With the same computational budget as the reference decomposition-based approach, this comparative modeling strategy produced measurable improvements in production planning performance.
Results: Improved Production Planning KPIs and Reduced Shortages
The benchmark results demonstrated meaningful improvements in KPIs for large-scale production planning. Using the same runtime for MILP optimization:
- Key supply planning indicators improved
- Production plans were better balanced across the full planning horizon
By reoptimizing the full production planning model rather than relying solely on sequential decomposition, the solver captured long-term interactions across plants and periods. This led to more robust supply planning decisions and improved service level performance.
These results show that solving large-scale production planning MILPs is not only a matter of pure solver performance. It also depends on modeling formalism, optimization workflow design, and the ability to combine decomposition with global reoptimization.
Conclusion
Large-scale production planning requires scalable and high-performance MILP optimization strategies. Decomposition remains essential for handling industrial-scale models, but pure decomposition can limit global optimality in complex production planning environments.
This benchmark demonstrates that the Hexaly modeling formalism and algorithmic capabilities provide a powerful framework for solving large-scale production planning MILPs. By combining structured decomposition with full-horizon reoptimization, Hexaly enables industrial production planning models to maintain scalability while unlocking higher solution quality.
For organizations facing the limitations of traditional large-scale MILP approaches for production planning, Hexaly offers a robust, effective alternative to improve solution quality, reduce shortages, and strengthen end-to-end supply planning performance.