# American Institute of Mathematical Sciences

October  2013, 9(4): 855-883. doi: 10.3934/jimo.2013.9.855

## Two-warehouse inventory models for deteriorating products with ramp type demand rate

 1 Department of Mathematics, University of Ioannina, 451 10, Ioannina, Greece 2 Department of Business Administration, Business Excellence Laboratory, University of Macedonia, 156 Egnatia Street, 54006 Thessaloniki, Greece

Received  August 2011 Revised  February 2013 Published  August 2013

In today's business environment, there are various reasons, namely, bulk purchase discounts, seasonality of products, re-order costs, etc., which force the buyer to order more than the warehouse capacity (owned warehouse). Such reasons call for additional storage space to store the excess units purchased. This additional storage space is typically a rented warehouse. It is known that the demand of seasonal products increases at the beginning of the season up to a certain moment and then is stabilized to a constant rate for the remaining time of the season (ramp type demand rate). As a result, the buyer prefers to keep a higher inventory at the beginning of the season and so more units than can be stored in owned warehouse may be purchased. The excess quantities need additional storage space, which is facilitated by a rented warehouse.
In this study an order level two-warehouse inventory model for deteriorating seasonal products is studied. Shortages at the owned warehouse are allowed subject to partial backlogging. This two-warehouse inventory model is studied under two different policies. The first policy starts with an instant replenishment and ends with shortages and the second policy starts with shortages and ends without shortages. For each of the models, conditions for the existence and uniqueness of the optimal solution are derived and a simple procedure is developed to obtain the overall optimal replenishment policy. The dynamics of the model and the solution procedure have been illustrated with the help of a numerical example and a comprehensive sensitivity analysis, with respect to the most important parameters of the model, is considered.
Citation: Konstantina Skouri, Ioannis Konstantaras. Two-warehouse inventory models for deteriorating products with ramp type demand rate. Journal of Industrial & Management Optimization, 2013, 9 (4) : 855-883. doi: 10.3934/jimo.2013.9.855
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