Multi-agent scheduling problems under multitasking

We consider a multitasking scheduling model with multiple agents, each of which has a set of tasks to perform on a cloud manufacturing platform on a competitive basis. Each agent wishes to minimise its desirable objective function related to the completion times of its own tasks only. However, the cloud manufacturing platform wishes to minimise the objective of one agent (being long-term critical agent), while keeping the objective of each of the other agents (being short-term one-off agents) within a given limit. The objective functions considered are the maximum of a regular function (associated with each task), the total completion time, and the weighted number of late jobs. Cloud manufacturing enables multitasking scheduling, under which the processing of a selected task may be interrupted by other tasks that are available but unfinished. We ascertain the computational complexity status of each of the problems we consider and devise solution procedures, if viable, for them. We also conduct numerical studies to generate insights into the effects of multitasking on scheduling outcomes, with which the decision maker can justify making investments to adopt or avoid multitasking.