Single item lot sizing problems

A state-of-the-art of a particular planning problem, the Single Item Lot Sizing Problem, is given for its uncapacitated and capacitated versions. First classes of lot sizing problems are briefly surveyed. Various solution methods for the Uncapacitated Single Item Lot Sizing Problem are reviewed. Four different mathematical programming formulations of the classical problem are presented. Different extensions for real-world applications of this problem are discussed. Complexity results of the Capacitated Single Item Lot Sizing Problem are given together with its different formulations and solution techniques.