Abstract: In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.
Abstract: In this paper, we develop a Spatio-Temporal graph as
of a key component of our knowledge representation Scheme. We
design an integrated representation Scheme to depict not only present
and past but future in parallel with the spaces in an effective and
intuitive manner. The resulting multi-dimensional comprehensive
knowledge structure accommodates multi-layered virtual world
developing in the time to maximize the diversity of situations in the
historical context. This knowledge representation Scheme is to be used
as the basis for simulation of situations composing the virtual world
and for implementation of virtual agents' knowledge used to judge and
evaluate the situations in the virtual world. To provide natural contexts
for situated learning or simulation games, the virtual stage set by this
Spatio-Temporal graph is to be populated by agents and other objects
interrelated and changing which are abstracted in the ontology.