We discuss the existence of weak solutions to the Cauchy problem for one class of hyperbolic conservation laws that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the so-called push-pull point (PPP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a pull policy. The main question we discuss in this paper is about the optimal choice of the input in-ux, push and pull constituents, and the position of PPP.