Continuous-time models for production scheduling in constrained subcontracting conditions

This paper focuses on an optimal control approach to continuous-time multi-item scheduling of parallel flexible machines in typical subcontracting conditions. The conditions comprise subcontracting of: constant in-time amount of items along the planning horizon; arbitrary changing in-time amounts; and limited-change in-time amounts of items. Mathematical formulations are presented to model the three typical subcontracting conditions and are studied with the aid of the maximum principle. Based on the properties of the optimal solutions derived, efficient time-decomposition methods are suggested for solving the corresponding problems.