An FPTAS for the single-item capacitated economic lot-sizing problem with supply and demand

We present a fully polynomial time approximation scheme (FPTAS) for the single-item capacitated economic lot-sizing problem with an objective function of a general form. The demand values may be negative, i.e., they may represent supply. For nn time periods, the FPTAS runs in O(n4ε2+⋯) arithmetic operations and calls to an oracle computing the cost functions.