On Exploitation of Supply Chain Properties by Sequential Distributed MPC

Abstract

In this work, we propose a sequential distributed MPC algorithm for control of a linear supply chain. The algorithm is developed by closely taking into account supply chain specifics and requirements from practice, e.g., orders and leavings are both treated as decision variables at each stage and communication between stages is kept low. We present the rather surprising result that terminal equality constraints employed in the local MPC formulations are inherently satisfied for the overall system, despite the presence of bilateral dynamic couplings and solving the local MPC problems sequentially. This is due to the stock and flow nature of the problem. The proposed algorithm is shown to be recursively feasible, to asymptotically satisfy a constant customer demand and to achieve asymptotic convergence of the local stock and backlog to the desired levels. This is illustrated by numerical simulations.