Research on scheduling with job-dependent learning effect and convex resource-dependent processing times

We study resource allocation scheduling with job-dependent learning effect on a single machine with or without due date assignment considerations. For a convex resource processing time function, we provide a polynomial time algorithm to find the optimal job sequence, and resource allocations that minimise the schedule criterion (the total compression cost) subject to the constraint that the total compression cost (the schedule criterion) is less than or equal to a fixed amount.