Abstract
The idea of using clearing functions in Linear Programming models for production planning to represent the nonlinear dependence between workload and lead times in productive systems may result in a large nonlinear convex model. Nevertheless, this convex programming model is not considered directly, but approximated by using linear programming models which sometimes results in a large linear programming problem, requiring mathematical decomposition for efficient solution. The classic method of decomposition, however, does not function properly in the presence of the restriction of capacity provided by the clearing function, frustrating the efforts to introduce lead times into the models. In this chapter we provide a strategy to modify the classical decomposition approach using a penalty function for the subproblems, which circumvents the pointed drawbacks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kefeli, A., Uzsoy, R., Fathi, Y., Kay, M.: Using a mathematical programming model to examine the marginal price of capacity resources. Int. J. Prod. Econ. 131, 383–391 (2011)
Chu, S.C.K.: Optimal master production scheduling in a flexible manufacturing system: the case of totral aggregation. In: Proceedings of the First Conference on the Operational Research Society of Hong Kong, pp. 103–108 (1991)
Srinivassan, A., Carey, M., Morton, T.E.: Resource Pricing and Aggregate Scheduling in Manufacturing Systems. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh (1988)
Asmundsson, J.M., Rardin, R.L., Turkseven, C.H., Uzsoy, R.: Production Planning with Resources Subject to Congestion. Published in Wiley Interscience (www.interscience.wiley.com), doi:10.1002/nav.20335 (2009). Accessed 20 Jan 2009
Kempf, K.G., Keskinocak, P., Uzsoy, R.: Planing Production and Inventories in the Extended Enterprise. A State of Art Handbook, vol. 1. Springer, New York (2011)
Irdem, D.F., Kacar, N.B., Uzsoy, R.: An exploratory analysis of two iterative linear programming-simulation approaches for production planning. IEEE Trans. Semicond. Manuf. 23(3) (2010)
Rockafellar, R.T.: Convex Analysis. Academic Press, New York (1970)
Missbauer, H., Uzsoy, R.: Optimization models for production planning. In: Kempf, K.G., Keskinocak, P., Uzsoy, R. (eds.) Planning Production and Inventories in the Extended Enterprise, vol. 1. Springer, New York (2010)
Uzsoy R., de Sampaio, R.J.B.: Unifying Inner and Outer Approachs of Clearing Function to Deal with Pricing Capacity of Resources at Lows Levels of Utilization (in preparation)
de Sampaio R.J.B., Vieira, G.E., Favaretto, F.: An Approach of Mathematical Programming to the Master Production Scheduling Problem, Technical Report 2009, PUCPR-PPGEPS, Brazil (2009)
Hopp, W.J., Spearman, M.L.: Factory Physics: Foundations of Manufacturing Management. Irwin/McGraw-Hill, Boston (2001)
Karmarkar, U.S.: Capacity loading and release planning with work-in-process and lead times. J. Manuf. Oper. Manage. 2, 105–123 (1989)
Graves, S.C.: A tactical planning model for a job shop. Oper. Res. 34, 522–533 (1986)
de Sampaio, R.J.B., Uzsoy, R., Wollmann, R.R.G.: Using a clearing function approach with decomposition for roduction planning problem, XVII. In: ICIEOM: The International Conference on Industrial Engineering and Operations Management, Belo Horizonte, Brazil (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Sampaio, R.J.B., Wollmann, R.R.G., Yuan, J.Y., Favaretto, F. (2014). Using Penalty in Mathematical Decomposition for Production-Planning to Accommodate Clearing Function Constraints of Capacity. In: Xu, H., Teo, K., Zhang, Y. (eds) Optimization and Control Techniques and Applications. Springer Proceedings in Mathematics & Statistics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43404-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-43404-8_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43403-1
Online ISBN: 978-3-662-43404-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)