Single-machine scheduling with an external resource

This paper studies the complexity of single-machine scheduling with an external resource, which is rented for a non-interrupted period. Jobs that need this resource are executed only when available. There cost associated jobs and duration renting period resource. We look at four classes problems resource: class where budgeted needs to be minimized, two-objective both, cost, linear combination minimized. provide thorough analysis (NP-hardness proofs (pseudo-)polynomial algorithms) different members these classes.