Incremental Scheduling with Upper and Lowerbound Temporospatial Constraints

Abstract

Responding quickly and efficiently to dynamic disturbances is a crucial challenge in domains such as manufacturing, aerial and underwater vehicle tasking, and health care. In many cases, accurately capturing the complicated dependencies between tasks in these environments requires the use of upper and lowerbound temporal constraints (i.e, deadlines and wait constraints). However, optimally scheduling tasks related by upper and lowerbound temporal constraints is known to be NP-Hard.3 While exact solution techniques exist to efficiently schedule resources, these techniques are computationally intractable for problems of interest with fifty or more tasks and five agents. Furthermore, techniques that seek to improve scalability often attempt to distribute the scheduling problem amongst the agents, where each agent generates its own schedule.5 However, when agents must share unary-access resources (e.g., a spatial location that can be occupied by only one agent at a time), these techniques lose their advantage because the problems do not naturally lend themselves to decomposition. As a result, many techniques work by first finding an initial, though possibly infeasible, schedule through solving a relaxed version of the problem, and then repairing the schedule to resolve any constraint violations.