A Comparative Modelling Approach to Improve Large Scale MILP Optimization in Production Planning
Context
Bridgestone operates a large and complex industrial production planning network, manufacturing multiple tyre families across several plants. Production planning decisions must balance manufacturing efficiency, service levels, capacity constraints, and inventory targets over a rolling horizon of four to five months.
At this scale, industrial production planning is formulated as a very large Mixed Integer Linear Programming model. MILP optimization provides a rigorous mathematical framework for production planning and supply planning. However, when applied to large-scale production planning, computational complexity becomes a critical challenge.
A benchmarking Proof of Concept was conducted with Hexaly to explore potential improvements in solution quality by modeling the Bridgestone production planning problem using the Hexaly modelling formalism and solving engine. The objective was to assess whether a comparative modelling approach could improve large-scale MILP optimization in 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 tyre 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 optimization computationally feasible. 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 benchmarking PoC, 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
Under the same computational budget as the reference decomposed exact algorithm approach, this comparative modelling strategy produced measurable improvements in production planning performance.
Results: Improved Production Planning KPIs and Reduced Shortages
The benchmarking 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 improving large-scale MILP optimization in production planning is not only a matter of solver performance. It also depends on modelling 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 case study demonstrates that Hexaly’s modelling formalism and optimization engine provide a powerful framework to improve large-scale MILP optimization in production planning. By combining structured decomposition with full horizon reoptimization, Hexaly enables industrial production planning models to preserve scalability while unlocking higher solution quality.
For organizations facing the limitations of traditional large-scale MILP approaches in production planning, Hexaly offers a robust, effective alternative to improve solution quality, reduce shortages, and strengthen end-to-end supply planning performance.