General Mathematical Model of Optimal Planning, Scheduling and Control and a Hypercube of Its Special Cases
Petr Shlepakov · 2024
A single general model of optimal control of objects in space and time is considered. From this model, subtasks for a variety of industries, objects and processes are built as special cases. The model is based on abstract "resources" and "actions" with resources, in relation to which discrete-continuous nonlinear constraints and criteria are formulated. The architecture of the Aleph-cube solver, unified for all mixed subtasks, is described, it’s implemented as a cloud service for reuse. The relationship between tasks, processes and regulations is formalized in the form of a hypercube of special cases. This will simplify the ROLAP analysis of subtasks, and most importantly, it will allow to automate the mechanisms of integration, iterative aggregation and detailing, composition and decomposition of submodels. Dozens of applied problems have been solved as special cases of the single model: strategic, investment, financial, production planning and scheduling, balancing, dispatching, operational control, design, project management, etc. in various industries, as well as classical optimization problems and typical tasks for primary school.