Complexity of single machine scheduling subject to nonnegative inventory constraints

This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs.