Wagner-Whitin Algorithm

The Wagner-Whitin algorithm was published by Harvey Wagner and Thomson Whitin in 1958 in *Management Science* and is the foundational paper of the lot-sizing literature. It solves the single-product, uncapacitated, time-varying deterministic-demand variant to optimality in O(T²) (later improvements reach O(T log T)) using dynamic programming. The core idea: the state variable is 'in which period was the last production', and DP evaluates all options backward. The paper also introduces the planning-horizon theorem, allowing the horizon to be truncated safely. Single-product application is straightforward; for capacitated and multi-product variants it is also used as a warm-start heuristic. Modern APS software incorporates Wagner-Whitin as a core module.