A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi‐item capacitated lot‐sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fill rate constraint is in effect. It is assumed that, according to the static‐uncertainty strategy of Bookbinder and Tan , all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed ${\mathit{ABC}}_{\mathrm{\&Bgr;}}$ heuristic is proposed.