In version 2.0, IBM ILOG CP Optimizer has been extended by the introduction of scheduling support based on the concept of optional interval variables. This paper formally describes the new modeling language features available to the users of CP Optimizer for resource-based scheduling. We show that the new language is flexible enough to model problems never before addressed by CP scheduling engines, as well as naturally describing classical scheduling problems found in the literature. This modeling power is based on a small number of general concepts such as intervals, sequences and functions. This makes the modeling language simple, clear and easy to learn, while maintaining the high-level structural aspects of the scheduling model.
We focus specifically on the task of scheduling. Though there is commonality in scheduling system requirements and design at several levels across application domains, different scheduling environments invariably present different challenges (e.g., different dominating constraints, different objectives, different domain structure, different sources of uncertainty, etc.), and hence we can expect high-performance application systems to require customized solutions. Unfortunately, the time and cost associated with such domain-specific system development at present is typically quite large. Our work toward overcoming this application construction bottleneck has led to the development of OZONE, a toolkit for configuring constraint-based scheduling systems. A central component of OZONE is its scheduling ontology, which defines a reusable and extensible base of concepts for describing and representing scheduling problems, domains and constraints.
In this paper we present a reusable time ontology for largescale knowledge system applications that provides an easily understandable, flexible, formally defined, and effective means of representing knowledge about time. Our underlying time theory treats both time points and time intervals as primitive elements on a time line, and the ontology contains a class hierarchy, relations, axioms and instances built on those primitives. The ontology distinguishes between closed and open intervals, as opposed to many previous time ontologies. However, we provide flexibility of usage by providing two sets of relations on intervals: one that assumes that distinction and one that does not. Time granularity is implemented in the ontology to facilitate representing time in varying granularity in a layered model and switching from or relating one granularity to a coarser or finer one. The ontology also includes a representation of periodic intervals and of the standard components and properties of calendars such as calendar months, calendar days, and weekdays.
It is a challenging task to reason about a dynamically evolving system with events triggering state transitions and uncertainty about the ordering of events. In previous research, uncertainty of the event ordering is mainly modelled by partial orders over the events. In this paper, we investigate uncertainty of the event ordering modelled by time intervals in which the events may occur. Each event will occur at exactly one point of time, but it could be any point within the time interval associated with the event. We present both positive and negative results that provide insight into the complexity of temporal reasoning about events with time-interval information.