On LQ optimal control of uncapacitated goods distribution systems with non-negligible transport delay

The paper examines the potential of linear-quadratic (LQ) optimal controllers in the application to goods distribution systems with multiple, interconnected nodes. The goods, exchanged among the nodes with non-negligible time delay, are used to answer external, uncertain demand. A model of the considered class of systems with delay is constructed and used to solve a dynamic optimization problem. In order to alleviate the computational complexity a suboptimal solution is proposed. In addition to a smaller problem dimension, the suboptimal controller brings the benefits of lower costs and better dynamical properties with respect to the optimal solution when analyzed in the context of logistic networks.