Optimal Backlogging Over an Infinite Horizon Under Time-Varying Convex Production and Inventory Costs
We consider an infinite horizon production planning problem with nonstationary, convex production and inventory costs. Backlogging is allowed, unlike as in related previous work, and inventory cost is interpreted as backlogging cost when inventory is negative. We create finite horizon truncations of the infinite horizon problem and employ classic results on convex production planning to derive a closed-form formula for the minimum forecast horizon. We show that optimal production levels are monotonically increasing in the length of horizon, leading to solution convergence and a rolling horizon procedure for delivering an infinite horizon optimal production plan. The minimum forecast horizon formula is employed to illustrate how cost parameters affect how far one must look into the future to make an infinite horizon optimal decision today.
Volume (Year): 11 (2009)
Issue (Month): 2 (June)
|Contact details of provider:|| Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA|
Web page: http://www.informs.org/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert L. Smith & Rachel Q. Zhang, 1998. "Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs," Management Science, INFORMS, vol. 44(9), pages 1313-1320, September.
- Howard C. Kunreuther & Thomas E. Morton, 1973. "Planning Horizons for Production Smoothing with Deterministic Demands," Management Science, INFORMS, vol. 20(1), pages 110-125, September.
- Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
- Gerald L. Thompson & Suresh P. Sethi, 1980. "Turnpike Horizons for Production Planning," Management Science, INFORMS, vol. 26(3), pages 229-241, March.
- Gary D. Eppen & F. J. Gould & B. Peter Pashigian, 1969. "Extensions of the Planning Horizon Theorem in the Dynamic Lot Size Model," Management Science, INFORMS, vol. 15(5), pages 268-277, January.
- Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
- Suresh Chand & Suresh P. Sethi & Gerhard Sorger, 1992. "Forecast Horizons in the Discounted Dynamic Lot Size Model," Management Science, INFORMS, vol. 38(7), pages 1034-1048, July.
- Howard C. Kunreuther & Thomas E. Morton, 1974. "General Planning Horizons for Production Smoothing with Deterministic Demands," Management Science, INFORMS, vol. 20(7), pages 1037-1046, March.
- Dwight R. Lee & Daniel Orr, 1977. "Further Results on Planning Horizons in the Production Smoothing Problem," Management Science, INFORMS, vol. 23(5), pages 490-498, January.
- Edward Zabel, 1964. "Some Generalizations of an Inventory Planning Horizon Theorem," Management Science, INFORMS, vol. 10(3), pages 465-471, April.
- Joseph D. Blackburn & Howard Kunreuther, 1974. "Planning Horizons for the Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 21(3), pages 251-255, November.
- Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
When requesting a correction, please mention this item's handle: RePEc:inm:ormsom:v:11:y:2009:i:2:p:362-368. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.