Scheduling Deteriorating Jobs Dependent on Resources for the Makespan Minimization

The paper deals with a single machine scheduling problem for the maximum completion time (makespan) minimization subject to the constraint on the total amount of available resources. The job processing times are given by non-decreasing linear functions simultaneously dependent on the starting moment of their execution and on the amount of allocated resources. We prove the ordinary NP-completeness of the considered problem by reducing to it the ordinary NP-complete Partition Problem. We give also some properties of the optimal resource allocation. The optimal solutions for some special cases of the latter problem are also presented.