The paper deals with resource allocation scheduling problems in which the processing time of a job is defined by a function of its starting times and its position in a sequence. We also assume that the resource-dependent ready times of jobs are continuous functions of their consumed resource. Our objective is to minimize the resource consumption (the makespan) subject to the makespan constraint (limited resource availability). We prove that these two single-machine scheduling problems can be solved in polynomial time.

Jian Jin and Ping Ji. Scheduling jobs with resource-dependent ready times and processing times depending on their starting times and positions. The Computer Journal, 2017.