Resource constrained scheduling problems with general truncated sum-of-processing time dependent effect under single machine and unrelated parallel machines

This paper studies some scheduling problems with general truncated sum-of-processing time dependent effect under single machine and unrelated parallel machines. Under the single machine, we consider that the actual processing time of a job is bivariate, continuous and non-increasing convex function of the total processing time of the processed jobs, its position, the amount of resource allocation and control parameter. SLK due date assignment models are involved, in which the length of due window is the same. We present the polynomial time algorithms to find the optimal job sequence, the due date and resource allocations that minimizing including the slack due date, earliness cost, tardiness cost, resource consumption costs and makespan. Under the unrelated machines, we only consider no resource locations scheduling problems. Minimizing the total the machine load and minimizing the total completion time can also be solved in a polynomial time when the number of machines is fixed, respectively.