An Algorithm for Infinite Horizon Lot Sizing with Deterministic Demand

Author(s)
Milan Horniaček

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.

Cite this paper

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.

M. Horniaček, "An Algorithm for Infinite Horizon Lot Sizing with Deterministic Demand,"

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

[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