Algorithm for turnpike policies in the dynamic lot size model

Stanisław Bylka

Applicationes Mathematicae (1996)

  • Volume: 24, Issue: 1, page 57-75
  • ISSN: 1233-7234

Abstract

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This article considers optimization problems in a capacitated lot sizing model with limited backlogging. Nothing is assumed about the cost function in the case of finite restrictions of the size on the stock and backlogs. The holding and backlogging costs are functions assumed to be stationary or nearly stationary in time. In both cases, it is shown that there exists an optimal infinite inverse policy and a periodical turnpike policy. Some forward and backward procedures are adopted that determine an optimal infinite inverse policy and a strong turnpike policy relative to the class of standard or batch ordering type policies. Some remarks on the existence of planning and forecast horizons are also given.

How to cite

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Bylka, Stanisław. "Algorithm for turnpike policies in the dynamic lot size model." Applicationes Mathematicae 24.1 (1996): 57-75. <http://eudml.org/doc/219152>.

@article{Bylka1996,
abstract = {This article considers optimization problems in a capacitated lot sizing model with limited backlogging. Nothing is assumed about the cost function in the case of finite restrictions of the size on the stock and backlogs. The holding and backlogging costs are functions assumed to be stationary or nearly stationary in time. In both cases, it is shown that there exists an optimal infinite inverse policy and a periodical turnpike policy. Some forward and backward procedures are adopted that determine an optimal infinite inverse policy and a strong turnpike policy relative to the class of standard or batch ordering type policies. Some remarks on the existence of planning and forecast horizons are also given.},
author = {Bylka, Stanisław},
journal = {Applicationes Mathematicae},
keywords = {lot size models; turnpike; forecast horizon; networks; capacitated lot sizing; limited backlogging; optimal infinite inverse policy; periodical turnpike policy; batch ordering},
language = {eng},
number = {1},
pages = {57-75},
title = {Algorithm for turnpike policies in the dynamic lot size model},
url = {http://eudml.org/doc/219152},
volume = {24},
year = {1996},
}

TY - JOUR
AU - Bylka, Stanisław
TI - Algorithm for turnpike policies in the dynamic lot size model
JO - Applicationes Mathematicae
PY - 1996
VL - 24
IS - 1
SP - 57
EP - 75
AB - This article considers optimization problems in a capacitated lot sizing model with limited backlogging. Nothing is assumed about the cost function in the case of finite restrictions of the size on the stock and backlogs. The holding and backlogging costs are functions assumed to be stationary or nearly stationary in time. In both cases, it is shown that there exists an optimal infinite inverse policy and a periodical turnpike policy. Some forward and backward procedures are adopted that determine an optimal infinite inverse policy and a strong turnpike policy relative to the class of standard or batch ordering type policies. Some remarks on the existence of planning and forecast horizons are also given.
LA - eng
KW - lot size models; turnpike; forecast horizon; networks; capacitated lot sizing; limited backlogging; optimal infinite inverse policy; periodical turnpike policy; batch ordering
UR - http://eudml.org/doc/219152
ER -

References

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  1. [1] R. L. Ackoff, E. L. Arnoff and C. Churchman, Introduction to Operations Research, Wiley, New York, 1957. Zbl0079.35905
  2. [2] A. Bensoussan, J. M. Proth and M. Queyranne, A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs, Naval Res. Logist. 38 (1991), 729-742. Zbl0743.90040
  3. [3] C. Bes and S. Sethi, Concepts of forecast and decision horizons: applications to dynamic stochastic optimization problems, Math. Oper. Res. 13 (1988), 295-310. Zbl0655.90091
  4. [4] S. Bylka, Horizon theorems for the solution of the dynamic lot-size model, in: Proc. Second Internat. Sympos. on Inventories, Budapest, Publ. House Hungar. Acad. Sci., 1982, 649-660. 
  5. [5] S. Bylka and S. Sethi, Existence and derivation of forecast horizons in a dynamic lot size models with nondecreasing holding costs, Production and Operations Management 1 (1992), 212-224. 
  6. [6] S. Chand, S. P. Sethi and J. M. Proth, Existence of forecast horizons in undiscounted discrete time lot-size model, Oper. Res. 38 (1990), 884-892. Zbl0723.90013
  7. [7] A. Federgruen and M. Tzur, The dynamic lot-sizing model with backlogging: A simple O(n log n) algorithm and minimal forecast horizon procedure, Naval Res. Logist. 40 (1993), 459-478. Zbl0804.90037
  8. [8] K. Hinderer and G. Hübner, An improvement of J. F. Shapiro's turnpike theorem for the horizon of finite stage discrete dynamic programs, in: Trans. Seventh Prague Conf. on Information Theory 1974, Vol. A, Acad. Publ. House, Praha, 1977, 245-255. 
  9. [9] C. Y. Lee and E. V. Denardo, Rolling planning horizons: error bounds for the dynamic lot-size model, Math. Oper. Res. 11 (1986), 423-432. Zbl0631.90018
  10. [10] J. Łoś, Horizons in dynamic programs, in: Proc. Fifth Berkeley Sympos. on Mathematical Statistics and Probability, California University Press, Berkeley, Calif., 1967, 479-490. 
  11. [11] V. Lotfi and Y.-S. Yoon, An algorithm for the single-item capacitated lot size model with concave production and holding costs, J. Oper. Res. Soc. 45 (1994), 934-941. Zbl0809.90064
  12. [12] R. Lundin and T. Morton, Planning horizon for the dynamic lot size model: Zabel vs. protective procedures and computational results, Oper. Res. 23 (1975), 711-735. Zbl0317.90028
  13. [13] S. M. Ryan, J. C. Bean and L. Smith, A tie-breaking rule for discrete infinite horizon optimization, ibid. 40 (1992), Suppl. 2, S117-S126. Zbl0763.90090
  14. [14] R. A. Sandbothe and G. L. Thompson, A forward algorithm for the capacitated lot size model with stockouts, ibid. 38 (1990), 474-486. Zbl0727.90031
  15. [15] H. M. Wagner and T. M. Whitin, Dynamic version of the economic lot size model, Manag. Sci. 5 (1959), 89-96. Zbl0977.90500
  16. [16] Y.-S. Zheng and F. Chen, Inventory policies with quantized ordering, Naval Res. Logist. 39 (1992), 285-305. Zbl0749.90023

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