Regulation of the input flow of supply chains to optimize the production

The optimal control problem of adjusting the inflow, of piecewise constant type, to a supply chain in order to minimize the queue size and the quadratic difference between the outflow and the expected one is considered. The controls are represented by the duration of injections of different amounts of goods. The supply chain is modelled by a PDE-ODE: the conservation law describes the density of processed parts and the ODE the queue buffer occupancy. The numerical technique is based on the extensive use of generalized tangent vectors to a piecewise constant control, which represent time shifts of discontinuity points.