Aggregate planning optimization models solve the problem of determining production levels and workforce sizing to minimize total cost under demand constraints. The field encompasses multiple mathematical approaches—tabular evaluation, linear programming, transportation models, and dynamic programming—each handling different cost structures (regular time, overtime, inventory, shortages, hiring/layoff, outsourcing) and constraints. A key distinction in dynamic programming models is the introduction of setup costs: fixed charges incurred whenever production occurs, making cost functions piecewise and requiring different optimization techniques than purely linear cost models. Table of Contents: - Aggregate planning problem definition: workforce and production level optimization - Cost structure: eight cost categories arranged in pairs (regular/overtime labor, inventory/shortage, hiring/layoff, outsourcing/underutilization) - Tabular method: evaluative approach with manual parameter adjustment for local optimization - Linear programming formulation: systematic treatment of all cost categories and constraints - Transportation model: restricted LP variant excluding workforce variables, handling six cost types - Dynamic programming approach: forward-scanning optimization with setup cost inclusion - Setup costs as fixed charges: fundamental distinction triggering variable cost structure - Cost linearity assumption: proportional relationship between quantity and cost in basic models - Constraint types: demand satisfaction, capacity, workforce continuity, non-negativity conditions - Relationship to higher-level and detailed planning: aggregate planning as mid-range decision bridge
Aggregate planning optimization models solve the problem of determining production levels and workforce sizing to minimize total cost under demand constraints. The field encompasses multiple mathemat…