Modelling Operations Dynamics, Planning and Scheduling

Abstract

In this chapter, we present mathematical models and algorithms for operations dynamics planning and scheduling. The basics of the research approach are discussed. A complex of dynamic models for integrated planning and scheduling is presented. This complex is composed of dynamic models for collaborative operations control, resource control and flow control. Subsequently, we consider algorithms for optimal SC operations control and develop our own one. The proposed approach is based on the fundamental scientific results of modern control theory and systems analysis in combination with the optimization methods of OR. We formulate the planning and scheduling as optimal control problems, taking into account the discreteness of decision-making and the continuity of flows with the use of special techniques, e.g., by transferring the non-linearity from the dynamic models into the left part of the differential equations in constraints. The modelling procedure is based on an essential reduction of a problem dimensionality that is under solution at each instant of time due to connectivity decreases. For the computations, the dynamic Lagrange relaxation, transformation of the optimal control problem to the boundary problem and maximization of Hamiltonians with the use of Pontryagin’s maximum principle are used.