State reduction in a dependent demand inventory model given by a time series

The dependent demand inventory model given by the time series with a stochastic trend and seasonality was considered. A two-state variable dynamic programming problem was reduced to the one-state variable problem under linear cost structure. The demand distribution was shown to be normal with the no...

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Published in	European journal of operational research Vol. 41; no. 2; pp. 174 - 180
Main Author	Reyman, Grzegorz
Format	Journal Article
Language	English
Published	Amsterdam Elsevier B.V 25.07.1989 Elsevier Elsevier Sequoia S.A
Series	European Journal of Operational Research
Subjects	Applied sciences Demand Dynamic programming Exact sciences and technology Inventory Inventory control Inventory control, production control. Distribution Lagermanagement Mathematical models Operational research and scientific management Operational research. Management science Operations research Reduction State Theorie Time series Zeitreihenanalyse time series demand Inventory Demand Stockpile control Reduction method Seasonal demand Time series Bayes forecasting Models Dynamic programming Two variables function
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ISSN	0377-2217 1872-6860
DOI	10.1016/0377-2217(89)90381-0

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Abstract	The dependent demand inventory model given by the time series with a stochastic trend and seasonality was considered. A two-state variable dynamic programming problem was reduced to the one-state variable problem under linear cost structure. The demand distribution was shown to be normal with the nonstationary mean and the constant variance. The optimal ordering levels are characterized by single critical numbers.
AbstractList	The dependent demand inventory model given by the time series with a stochastic trend and seasonality was considered. A two-state variable dynamic programming problem was reduced to the one-state variable problem under linear cost structure. The demand distribution was shown to be normal with the nonstationary mean and the constant variance. The optimal ordering levels are characterized by single critical numbers. In practice, researchers are very often confronted with dynamic inventory problems of dependent demand. However, not much research has been conducted on this subject. Generally, stochastic models assume that demand distributions in inventory in different periods are independent. Recently, more attention has been given to dependent demand inventory models. Generally, the exponential forecasting model is considered. However, a more general model for a dependent demand is examined. The time series is given by a stochastic trend component and a seasonal component. A 2-state variable dynamic programming problem is reduced to the one-state variable problem under a linear cost structure. The demand distribution is shown to be normal with the nonstationary mean and the constant variance. The optimal ordering levels are attained by single critical numbers.
Author	Reyman, Grzegorz
Author_xml	– sequence: 1 givenname: Grzegorz surname: Reyman fullname: Reyman, Grzegorz organization: Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
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Keywords	time series demand Inventory Demand Stockpile control Reduction method Seasonal demand Time series Bayes forecasting Models Dynamic programming Two variables function
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References_xml	– volume: 6 start-page: 61 year: 1974 end-page: 74 ident: BIB3 article-title: Consistency conditions for probability estimators and integrals of density estimators publication-title: Utilitas Mathematica – volume: 6 start-page: 231 year: 1960 end-page: 258 ident: BIB5 article-title: Dynamic inventory policy with varying stochastic demand publication-title: Management Science – volume: 72 start-page: 334 year: 1982 end-page: 348 ident: BIB2 article-title: Inventories and sticky prices: More on the microfoundations of macroeconomics publication-title: American Economic Review – volume: 31 start-page: 1150 year: 1985 end-page: 1160 ident: BIB1 article-title: Bayes solution to dynamic inventory models under unknown demand distribution publication-title: Management Science – volume: 34 start-page: 83 year: 1986 end-page: 90 ident: BIB7 article-title: Scarf's state reduction method, Flexibility, and a dependent demand inventory model publication-title: Operations Research – year: 1983 ident: BIB6 article-title: Theory and Practice of Recursive Identification – year: 1960 ident: BIB4 article-title: Planning Production, Inventories, and Work Force – volume: 7 start-page: 561 year: 1960 end-page: 569 ident: BIB9 article-title: Some remarks on Bayes solutions to the inventory problem publication-title: Naval Research Logistics Quarterly – volume: Vol. 16 start-page: 253 year: 1981 end-page: 277 ident: BIB8 article-title: Managing reparable item inventory systems: A review publication-title: Multi-Level Production Inventory Control Systems: Theory and Practice – year: 1960 ident: 10.1016/0377-2217(89)90381-0_BIB4 – volume: 31 start-page: 1150 year: 1985 ident: 10.1016/0377-2217(89)90381-0_BIB1 article-title: Bayes solution to dynamic inventory models under unknown demand distribution publication-title: Management Science doi: 10.1287/mnsc.31.9.1150 – volume: 34 start-page: 83 year: 1986 ident: 10.1016/0377-2217(89)90381-0_BIB7 article-title: Scarf's state reduction method, Flexibility, and a dependent demand inventory model publication-title: Operations Research doi: 10.1287/opre.34.1.83 – volume: 6 start-page: 61 year: 1974 ident: 10.1016/0377-2217(89)90381-0_BIB3 article-title: Consistency conditions for probability estimators and integrals of density estimators publication-title: Utilitas Mathematica – year: 1983 ident: 10.1016/0377-2217(89)90381-0_BIB6 – volume: 6 start-page: 231 year: 1960 ident: 10.1016/0377-2217(89)90381-0_BIB5 article-title: Dynamic inventory policy with varying stochastic demand publication-title: Management Science doi: 10.1287/mnsc.6.3.231 – volume: 72 start-page: 334 year: 1982 ident: 10.1016/0377-2217(89)90381-0_BIB2 article-title: Inventories and sticky prices: More on the microfoundations of macroeconomics publication-title: American Economic Review – volume: 7 start-page: 561 year: 1960 ident: 10.1016/0377-2217(89)90381-0_BIB9 article-title: Some remarks on Bayes solutions to the inventory problem publication-title: Naval Research Logistics Quarterly doi: 10.1002/nav.3800070428 – volume: Vol. 16 start-page: 253 year: 1981 ident: 10.1016/0377-2217(89)90381-0_BIB8 article-title: Managing reparable item inventory systems: A review
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Title	State reduction in a dependent demand inventory model given by a time series
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