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arXiv · 1208.4824

Numerical schemes for the optimal input flow of a supply-chain

Ciro D'Apice·Rosanna Manzo·Benedetto Piccoli
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Abstract

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.

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Ciro D'Apice, Rosanna Manzo, Benedetto Piccoli. 2012-08-23. Numerical schemes for the optimal input flow of a supply-chain. https://arxiv.org/abs/1208.4824

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