Toward Cyclic Scheduling of Concurrent Multimodal Processes

The problem of cyclic scheduling of multimodal cyclic processes (MCPs) is considered. The issue follows the production engineering and supply chains environment, where the imposition of the integer domain results (due to inherent process features such as discrete slot sizes, etc.) in the Diophantine character of a scheduling problem. Consequently, some classes of MCPs scheduling problems can be regarded as non-decidable ones. Since system constraints its behavior, both system structure configuration and desired schedule have to be considered simultaneously. Therefore, MCP scheduling problem solution requires that the system structure configuration must be determined for the purpose of processes scheduling, yet scheduling must be done to devise the system configuration. The approach proposed in this paper provides the framework allowing one to take into account both direct and reverse formulation of the cyclic scheduling problem. It permits to determine the model for the assessment of the impact of the structure of local cyclic processes on the parameters of global MCP. Discussion of some solubility issues concerning multimodal cyclic process dispatching problems is provided.