The disaggregation problem bridges aggregate planning outputs (total production time available) to individual product-level decisions by determining sequence and timing of product production runs. Using inventory ratios (time units of inventory per unit demand), products are sequenced to delay stockout; cycle length is maximized subject to demand meeting constraints. Redistribution of initial inventories across products can further extend cycle times while maintaining feasibility, addressing practical concerns of Just-In-Time manufacturing without violating deterministic demand assumptions. Table of Contents: • Aggregate planning context: production time PT available for multiple products • Inventory ratio Rj: time buffers before stockouts, determines production sequence • Sequencing rule: ascending order of R values minimizes unmet demand risk • Cycle time T: common production cycle for all products, maximization objective • Production timing constraints: production must start before inventory exhaustion • Demand satisfaction constraints: production during period must ≥ cycle demand • Initial inventory effect: total inventory determines achievable cycle length • Inventory reallocation models: first-cycle vs. steady-state optimization • Zero-inventory ordering: steady-state solution with inventory reaching zero before each production • Cycle length extension: dynamic redistribution of fixed total inventory pool • Practical interpretation: longer cycles achievable through better inventory positioning, not additional stock
The disaggregation problem bridges aggregate planning outputs (total production time available) to individual product-level decisions by determining sequence and timing of product production runs. Us…