Maximum Flexibility and Optimal Decoupling in Task Scheduling Problems

In multi-agent task scheduling one tries to find a joint schedule for a set of time-constrained tasks, where each agent is responsible for scheduling a disjoint subset of tasks. Two important problems occurring here are (i) to find a joint schedule providing maximum flexibility, i.e., a schedule that maximizes the freedom agents have in choosing the exact time they would like to start their tasks without violating scheduling constraints, (ii) to find an optimal decoupling of the original problem such that each of the agents is able to solve its own part of the task scheduling problem independently of the other agents and with maximum total flexibility. In this paper we show that both problems are closely related. We use a running example derived from a real maintenance scheduling problem occurring at Ned Train, the national Dutch railway maintenance company.