Simple temporal problems represent a powerful class of models capable of describing the temporal relations between events that arise in many real-world applications such as logistics, robot planning and management systems. The classic simple temporal problem permits each event to have only a single release and due date. In this paper, we focus on the case where events may have an arbitrarily large number of release and due dates. This type of problem, however, has been referred to by various names. In order to simplify and standardize nomenclatures, we introduce the name Simple Disjunctive Temporal Problem. We provide three mathematical models to describe this problem using constraint programming and linear programming. To efficiently solve simple disjunctive temporal problems, we design two new algorithms inspired by previous research, both of which exploit the problem's structure to significantly reduce their space complexity. Additionally, we implement algorithms from the literature and provide the first in-depth empirical study comparing methods to solve simple disjunctive temporal problems across a wide range of experiments. Our analysis and conclusions offer guidance for future researchers and practitioners when tackling similar temporal constraint problems in new applications. All results, source code and instances are made publicly available to further assist future research.

翻译：简单时间问题是一类强大的模型，能够描述诸多实际应用（如物流、机器人规划与管理系统）中事件间的时间关系。经典简单时间问题允许每个事件仅具有唯一的释放日期与截止日期。本文聚焦于事件可能具有任意多个释放日期与截止日期的情况。此类问题先前已有多种不同命名，为简化并统一术语，我们提出"简单析取时间问题"这一名称。我们利用约束规划与线性规划构建了三种数学描述模型。为高效求解简单析取时间问题，受既有研究启发，我们设计了两种新算法，两者均利用问题结构显著降低了空间复杂度。此外，我们实现了文献中的算法，并通过大量实验首次对解决简单析取时间问题的各类方法进行了深入实证比较。分析结论为未来研究人员及从业者在新型应用中处理类似时间约束问题提供了指导。所有结果、源代码及实例均已公开，以进一步促进后续研究。