Abstract
Determining the production rate of a factory as a function of current and previous states is at the heart of the production planning problem. Different approaches to this problem presented in this book are reviewed and their relationship is discussed. Necessary conditions for the success of a clearing function as a quasi steady approximation are presented and more sophisticated approaches allowing the prediction of outflow in transient situations are discussed. Open loop solutions to the deterministic production problem are introduced and promising new research directions are outlined.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aouam T, Uzsoy R, An exploratory analysis of production planning in the face of stochastic demand and workload-dependent lead times, this volume
Armbruster D, Marthaler D, Ringhofer C (2004) Kinetic and fluid model hierarchies for supply chains. SIAM Multiscale Model Simul 2(1):43–61
Armbruster D, Marthaler D, Ringhofer C, Kempf K, T-C Jo (2006) A continuum model for a re-entrant factory. Oper Res 54(5):933–950
Armbruster D, Göttlich S, Herty M (2011) A scalar conservation law with discontinuous flux for supply chains with finite buffers. SIAM J App Math 71(4):1070–1087
Asmundsson JM, Rardin RL et al (2009) Production planning models with resources subject to congestion. Naval Res Logist 56:142–157
Bramson M (2008) Stability of queueing networks. Lecture notes in mathematics, 1950. Springer, Berlin
Braun MW, Schwartz JD, A control theoretic evaluation of schedule nervousness suppression techniques for Master Production Scheduling, this volume
Daganzo CA (2003) Theory of supply chains. Springer, New York
Fonteijn J (2009) Analysis of clearing functions and transient PDE models.Technical report TU Eindhoven, SE 420613
Goossens P (2007) Modeling of manufacturing systems with finite buffer sizes using PDEs. Masters thesis, TU Eindhoven, Department of Mechanical Engineering, SE 420523
Göttlich S, Herty M, Ringhofer C, Optimal order and distribution strategies in production networks, this volume
Hackman T, Leachman RC (1989) A General framework for modeling production. Manag Sci 35(4):478–495
Hopp WJ, Spearman ML (2000) Factory physics, 2nd edn. Irwin/McGraw-Hill, New York
Karmarkar US (1989) Capacity loading and release planning with work-in-progress (wip) and lead-times. J Manuf Oper Manag 2:105–123
Lefeber E, Modeling and control of manufacturing systems, this volume
LeVeque RJ (2002) Finite volume methods for hyperbolic problems. Cambridge University Press, Cambridge
Lighthill MJ, Whitham GB (1955) On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc Royal Soc Lond A(229):317–345
La Marca. M, Armbruster D, Herty M, Ringhofer C (2010) Control of continuum models of production systems. IEEE Trans Autom Control 55(11):2511–2526
Missbauer H (2010) Order release planning with clearing functions. A queueing-theoretical analysis of the clearing function concept. Int J Prod Econ. doi:10.1016/j.ijpe.2009.09.003
Perdaen D, Armbruster D, Kempf K, Lefeber E, Controlling a re-entrant manufacturing line via the pushpull point, this volume
Ringhofer C, Traffic flow models and service rules for complex production systems, this volume
Acknowledgements
This research was supported in parts by a grant from the Stiftung Volkswagenwerk, by NSF grant DMS 1023101 and by the INTEL Research Council.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London
About this chapter
Cite this chapter
Armbruster, D. (2012). The Production Planning Problem: Clearing Functions, Variable Lead Times, Delay Equations and Partial Differential Equations. In: Armbruster, D., Kempf, K. (eds) Decision Policies for Production Networks. Springer, London. https://doi.org/10.1007/978-0-85729-644-3_12
Download citation
DOI: https://doi.org/10.1007/978-0-85729-644-3_12
Published:
Publisher Name: Springer, London
Print ISBN: 978-0-85729-643-6
Online ISBN: 978-0-85729-644-3
eBook Packages: Business and EconomicsBusiness and Management (R0)