An Algorithm for Infinite Horizon Lot Sizing with  Deterministic Demand

Milan Horniaček

doi:10.4236/am.2014.52023

Home > Journals > Physics & Mathematics > AM

Applied Mathematics > Vol.5 No.2, January 2014

An Algorithm for Infinite Horizon Lot Sizing with Deterministic Demand ()

Faculty of Social and Economic Sciences, Institute of Public Policy and Economics, Comenius University in Bratislava, Mlynske luhy 4, Bratislava, Slovakia.

DOI: 10.4236/am.2014.52023 PDF HTML XML 2,722 Downloads 4,293 Views Citations

Abstract

We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environment (demand, fixed ordering cost, variable procurement cost, holding cost) which is repeated after a finite number of periods. Future cost is discounted. In general, minimization of the sum of discounted total cost over the cycle does not give the minimum of the sum of discounted total cost over the infinite horizon. We construct an algorithm for computing of an optimal strategy over the infinite horizon. It is based on a forward in time dynamic programming recursion.

Keywords

Natural Asset; Financial Value; Neural Network

Share and Cite:

M. Horniaček, "An Algorithm for Infinite Horizon Lot Sizing with Deterministic Demand," Applied Mathematics, Vol. 5 No. 2, 2014, pp. 217-225. doi: 10.4236/am.2014.52023.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. A. Muckstadt and A. Sapra, “Principles of Inventory Management,” Springer-Verlag, Berlin, 2010. http://dx.doi.org/10.1007/978-0-387-68948-7
[2]	M. J. Osborne and A. Rubinstein, “A Course in Game Theory,” The MIT Press, Cambridge, 1994.
[3]	A. Wagelmans, S. V. Hoesel and A. Kolen, “Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in Wagner-Whitin Case,” Operations Research, Vol. 40, 1992, pp. S145-S156. http://dx.doi.org/10.1287/opre.40.1.S145
[4]	H. M. Wagner and T. M. Whitin, “Dynamic Version of the Economic Lot Size Model,” Management Science, Vol. 5, No. 1, 1958, pp. 89-96. http://dx.doi.org/10.1287/mnsc.5.1.89