Abstract
This paper shows how to compute optimal control policies for a certain class of supply networks via a combination of stochastic dynamic programming and parametric programming.We consider supply networks where the dynamics of the material and information flows within the entire network can be expressed by a system of first-order difference equations and where some inputs to the system act as external disturbances. Assuming piecewise linear costs on state and control inputs, optimal control policies are computed for a risk-neutral objective function using the expected cost and for a risk-averse objective function using the worst-case cost. The obtained closed-loop control policies are piecewise-affine and continuous functions of the state variables, representing as a generalization of the common order-up-to policies. The optimal value functions are piecewise affine and convex, which is the essential structural property to allow for the solution via a sequence of parametric linear programs. Some numerical results are given on an example network with two suppliers with different costs and lead times.
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Laumanns, M. (2008). Determining Optimal Control Policies for Supply Networks Under Uncertainty. In: Kreowski, HJ., Scholz-Reiter, B., Haasis, HD. (eds) Dynamics in Logistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76862-3_12
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DOI: https://doi.org/10.1007/978-3-540-76862-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76861-6
Online ISBN: 978-3-540-76862-3
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