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We discuss the optimal control problem (OCP) stated as the minimization of the queues\udand the difference between the effective outflow and a desired one for the continuous model of supply chains,\udconsisting of a PDE for the density of processed parts and an ODE for the queue buffer occupancy. The\udmain goal is to consider this problem with pointwise control and state constraints. Using the so-called Henig\uddelation, we propose the relaxation approach to characterize the solvability and regularity of the original\udproblem by analyzing the corresponding relaxed OCP

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