WagnerWhitin

Wagner-Whitin refers to the Wagner-Whitin algorithm, a dynamic programming method for solving the deterministic single-item lot-sizing problem over a finite planning horizon. Developed by Wagner and Whitin in 1958, the algorithm finds an optimal production schedule that minimizes total costs, typically consisting of fixed setup costs for each production run and linear holding costs for inventory carried between periods.

The problem setting assumes known, period-by-period demand and no backlogging. Each production run incurs a fixed cost, while holding inventory incurs a cost per unit per period. The goal is to determine which periods to produce in and how much to produce so that all demands are met at minimum total cost over the planning horizon. Production costs per unit are usually treated as constant or are otherwise offset in the formulation, so the optimization focuses on setup and holding costs.

The Wagner-Whitin algorithm uses dynamic programming. It computes the minimum cost from every starting period to the end of the horizon by considering all feasible horizons for a first production: if production in period t covers demands up to period j, the algorithm adds the fixed setup cost plus the appropriate holding costs for inventory carried to each period and then adds the optimal cost from period j+1 onward. This recursive structure yields an optimal schedule with a time complexity on the order of O(n^2) and linear memory in the standard form.

Variants extend the basic model to include backlogging, varying holding or setup costs, multiple items, and capacity constraints. The Wagner-WhitIN algorithm remains a foundational reference in inventory theory and is widely taught in operations research and production planning.