Two-agent single-machine scheduling with a rate-modifying activity

We study single-machine scheduling problems involving a rate-modifying activity and two competing agents with due-date-related functions. Classical scheduling models assume that job processing times remain constant over time; however, in real-world settings, processing times may change due to factors such as technological upgrades or machine maintenance. We complement this with the notion of multiple independent agents competing over the use of a shared resource, each with their own motives. These considerations allow us to model the upcoming trend of the sharing economy, where resources are shared amongst independent competitors in the market. We aim to model these scenarios by considering a variety of scheduling criteria for each agent, including the makespan, the number of late jobs, and the total late work. To account for the change in processing times, we consider an optional rate-modifying activity that once completed, results in a reduction in subsequent job processing times. We show that problems involving the total late work are binary NP-hard and propose efficient pseudo-polynomial dynamic programming algorithms for solving these problems. We also show that the remaining problems are solvable in polynomial time.