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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 679736, 24 pages
Research Article

Order Level Inventory Models for Deteriorating Seasonable/Fashionable Products with Time Dependent Demand and Shortages

1Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
2Hellenic Army Academy, Vari 16673, Attica, Greece

Received 18 September 2008; Revised 3 July 2009; Accepted 20 July 2009

Academic Editor: Wei-Chiang Hong

Copyright © 2009 K. Skouri and I. Konstantaras. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.