On optimization of a highly re-entrant production system

Ciro D'Apice; Peter I. Kogut; Rosanna  Manzo; Ciro D'Apice; Peter I. Kogut; Rosanna  Manzo

doi:10.3934/nhm.2016003

Networks and Heterogeneous Media

2016, Volume 11, Issue 3: 415-445. doi: 10.3934/nhm.2016003

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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: 01 March 2015 Revised: 01 July 2015
35L65, 90B30, 49J20, 76N25.

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.
- Conservation laws,
- optimal control,
- existence result,
- re-entrant systems
Citation: Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On optimization of a highly re-entrant production system[J]. Networks and Heterogeneous Media, 2016, 11(3): 415-445. doi: 10.3934/nhm.2016003

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Abstract

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.

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