We study the classical capacitated multi–item lot–sizing problem with hard capacities. There are N items, each of which has a specified sequence of demands over a finite planning horizon of T discrete periods; the demands are known in advance but can vary from period to period. All demands must be satisfied on time. Each order incurs a time–dependent fixed ordering cost regardless of the combination of items or the number of units ordered, but the total number of units ordered cannot exceed a given capacity C. On the other hand, carrying inventory from period to period incurs holding costs. The goal is to find a feasible solution with minimum overall ordering and holding costs.
