# American Institute of Mathematical Sciences

September  2016, 11(3): 415-445. doi: 10.3934/nhm.2016003

## On optimization of a highly re-entrant production system

 1 Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano (SA) 2 Department of Differential Equations, Dnipropetrovsk National University, Gagarin av., 72, 49010 Dnipropetrovsk 3 Università degli Studi di Salerno, Dipartimento di Ingegneria dell'Informazione, Ingegneria Elettrica e Matematica Applicata, Via Giovanni Paolo II, 132, 84084 Fisciano (SA)

Received  March 2015 Revised  July 2015 Published  August 2016

We discuss the optimal control problem stated as the minimization in the $L^2$-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law 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 switch dispatch point (SDP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a quasi-pull policy. The main question we discuss in this paper is about the optimal choice of the input in-flux, push and quasi-pull constituents, and the position of SDP.
Citation: Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On optimization of a highly re-entrant production system. Networks & Heterogeneous Media, 2016, 11 (3) : 415-445. doi: 10.3934/nhm.2016003
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