I have a problem that’s as follows:

Single machine, n jobs, and *initial* processing times P_i. We’re also given a directed weighted graph with weights w_{ij}. The difference in this problem is that after scheduling job k, we reduce the processing times for all neighbors of k by the corresponding edge weight (e.g. if l is a neighbor of k, then processing time of l decreases by w_{kl}).

Goal is to minimize makespan. There are no release dates or preemption.

Is there any work done on this problem? In particular, I’m wondering about the computational complexity. There is some related literature I found on position-dependent processing times (e.g. this) but I haven’t found anything with a general graph structure that I described.