Human-Understandable Explanations of Infeasibility for Resource-Constrained Scheduling Problems

Significant work has been dedicated to developing methods for communicating reasons for decision-making within automated scheduling and planning systems to human users. However, much less focus has been placed on communicating reasons for why scheduling systems are unable to arrive at a feasible solution when over-constrained. We investigate this problem in the context of task scheduling. We introduce the agent resource-constrained project scheduling problem (ARCPSP), an extension of the resource-constrained project scheduling problem which includes a conception of agents that execute tasks in parallel. We outline a generic framework, based on efficiently enumerating minimal unsatisfiable sets (MUS) and maximal satisfiable sets (MSS), to produce small descriptions of the source of infeasibility. These descriptions are supplemented with potential relaxations that would fix the infeasibility found within the problem instance. We illustrate how this method may be applied to the ARCPSP and demonstrate how to generate different types of explanations for an over-constrained instance of the ARCPSP.