# American Institute of Mathematical Sciences

September  2014, 9(3): 501-518. doi: 10.3934/nhm.2014.9.501

## On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains

 1 Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano (SA), Italy 2 Department of Differential Equations, Dnipropetrovsk National University, Gagarin av., 72, 49010 Dnipropetrovsk, Ukraine 3 Dept. of Information Eng., Electrical Eng. and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, I 84084 Fisciano (SA), Italy

Received  April 2014 Revised  July 2014 Published  October 2014

We discuss the optimal control problem (OCP) stated as the minimization of the queues and the difference between the effective outflow and a desired one for the continuous model of supply chains, consisting of a PDE for the density of processed parts and an ODE for the queue buffer occupancy. The main goal is to consider this problem with pointwise control and state constraints. Using the so-called Henig delation, we propose the relaxation approach to characterize the solvability and regularity of the original problem by analyzing the corresponding relaxed OCP.
Citation: Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains. Networks & Heterogeneous Media, 2014, 9 (3) : 501-518. doi: 10.3934/nhm.2014.9.501
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