Time-varying demand lot-sizing problem requires determining order quantities for each period when demand is known but non-uniform across periods. The Wagner-Whitin theorem establishes that optimal solutions exhibit specific structure: order quantities should be integer combinations of consecutive periods' demands, and orders should occur only when inventory reaches zero. Integer programming formulations or dynamic programming methods solve this finite-horizon problem, with sensitivity analysis for average vs. ending inventory accounting. Table of Contents: • Time-varying demand assumption: demand differs across finite planning periods • Wagner-Whitin optimality conditions: order quantity spans consecutive periods, zero-inventory ordering • Integer programming formulation: binary variables Y (order/no-order), continuous X (quantity) • Constraint structure: inventory balance equations ensuring all demand is met with zero backorder • Cost computation: ending inventory vs. average inventory cost calculations • Objective function transformation: substituting inventory variables to reduce dimensionality • Numerical solution approach: finding months with orders (months 1,3,5,6,8,9,11 in 12-month example) • Comparison with Economic Order Quantity (EOQ): EOQ inapplicable when demand varies significantly • Advantages of lot-sizing: fewer orders (7 vs. 12 for equal-order heuristic) and lower costs • Practical issue: rolling forecasts with expanding horizons requiring heuristic approaches
Time-varying demand lot-sizing problem requires determining order quantities for each period when demand is known but non-uniform across periods. The Wagner-Whitin theorem establishes that optimal so…