A polynomial algorithm for the production/ordering planning problem with limited storage

This paper concerns the dynamic lot size problem where the storage capacity is limited and shortages are allowed. The planning horizon is divided into TT periods and, for each period, concave functions to define the holding/stockout and production costs are considered. It is proved that the results derived in a previous work for the dynamic lot size problem assuming time-varying storage capacities remain valid for the case with backlogging.