Single-machine past-sequence-dependent setup times scheduling with resource allocation and learning effect

This paper addresses single-machine scheduling problem with resource allocation and learning effect in the background of past-sequence-dependent (p-s-d) setup times. In the proposed model of this paper, the actual job processing times are dependent on learning effect and the amount of resource allocated, and the setup times are proportional to the length of the already processed jobs. The resource function used here is a general convex one. The optimal job sequence and the optimal amount of resource allocated to each job are determined jointly for the objective function yielded by a combination of the total completion time, total absolute differences in completion times, and the total resource consumption. Besides, we also discuss some extension and special cases of this problem. It is shown that all the problems under study are polynomially solvable while the complexity results are different