Lot Sizing

Lot sizing is a core OR production-planning problem. Over a planning horizon (typically 4-12 weeks), the production quantity for each period must meet demand; each batch incurs setup cost, and inventory held between periods incurs holding cost. The objective is to minimize total (setup + holding + production) cost. The single-product, deterministic, uncapacitated variant is solved by the Wagner-Whitin algorithm (1958) via dynamic programming in polynomial time. The capacitated (CLSP), multi-product, and multi-level variants are NP-hard and use MIP, Lagrangean decomposition, and heuristics (Silver-Meal, Part-Period Balancing). MRP systems in practice apply lot-for-lot, EOQ, or POQ rules; true LSP optima live in APS software.