Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem
AbstractWe consider a single-stage inventory system facing non-stationary stochastic demand of the customers in a finite planning horizon. Motivated by the practice, the replenishment times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact replenishment quantities can be deferred until the replenishment time. This operating scheme is refereed to as a “static-dynamic uncertainty” strategy in the literature . We consider dynamic fixed-ordering and linear end-of-period holding costs, as well as dynamic penalty costs, or service levels. We prove that the optimal ordering policy is a base stock policy for both penalty cost and service level constrained models. Since an exponential exhaustive search based on dynamic programming yields the optimal ordering periods and the associated base stock levels, it is not possible to compute the optimal policy parameters for longer planning horizons. Thus, we develop two heuristics. Numerical experiments show that both heuristics perform well in terms of solution quality and scale-up efficiently; hence, any practically relevant large instance can be solved in reasonable time. Finally, we discuss how our results and heuristics can be extended to handle capacity limitations and minimum order quantity considerations.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Omega.
Volume (Year): 40 (2012)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description
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.:
- Paul Zipkin, 1989. "Critical Number Policies for Inventory Models with Periodic Data," Management Science, INFORMS, vol. 35(1), pages 71-80, January.
- Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
- Tarim, S. Armagan & Kingsman, Brian G., 2006. "Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand," European Journal of Operational Research, Elsevier, vol. 174(1), pages 581-599, October.
- Thomas E. Morton & David W. Pentico, 1995. "The Finite Horizon Nonstationary Stochastic Inventory Problem: Near-Myopic Bounds, Heuristics, Testing," Management Science, INFORMS, vol. 41(2), pages 334-343, February.
- Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
- Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
- Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2011. "The cost of using stationary inventory policies when demand is non-stationary," Omega, Elsevier, vol. 39(4), pages 410-415, August.
- Joseph D. Blackburn & Dean H. Kropp & Robert A. Millen, 1986. "A Comparison of Strategies to Dampen Nervousness in MRP Systems," Management Science, INFORMS, vol. 32(4), pages 413-429, April.
- Vargas, Vicente, 2009. "An optimal solution for the stochastic version of the Wagner-Whitin dynamic lot-size model," European Journal of Operational Research, Elsevier, vol. 198(2), pages 447-451, October.
- Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
- James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
- Tempelmeier, Horst, 2007. "On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 181(1), pages 184-194, August.
- Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2013. "A simple approach for assessing the cost of system nervousness," International Journal of Production Economics, Elsevier, vol. 141(2), pages 619-625.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
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.