Numerical schemes for the optimal input flow of a supply-chain
This work addresses optimal control of supply chains modeled by PDE-ODE systems, offering a novel numerical method with theoretical guarantees for practitioners in logistics and operations research.
The paper presents a numerical technique for optimizing input flow in a supply chain to achieve desired outflow and reduce inventory costs, using generalized tangent vectors for piecewise constant control, with convergence results and error estimates demonstrated via simulations.
An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation law for the density of processed parts coupled to an ODE for the queue buffer occupancy. The control problem is stated as the minimization of a cost functional J measuring the queue size and the quadratic difference between the outflow and the expected one. The main novelty is the extensive use of generalized tangent vectors to a piecewise constant control, which represent time shifts of discontinuity points. Such method allows convergence results and error estimates for an Upwind- Euler steepest descent algorithm, which is also tested by numerical simulations.