In present dynamic environment with the rapid advancement of technology the life cycle of products has been shrunk especially high-tech products like mobile phones, laptops etc. To save on capital expenditure most of the companies have their warehouses with limited capacity and they take other warehouses on rent to absorb any fluctuations in demand. The model is framed considering that the product is perishable product and demand will fall drastically after some specific time. Another assumption is that the holding cost of the rented warehouse is more than their own warehouse. Numerical Illustration has been used to check the validity of the model. 

In most of the studies it is assumed that the organization owns a single warehouse with infinite capacity. Although it is impossible for organizations to have a warehouse to manage the complete at particular time, therefore in practice, whenever a large stock is to be held, due to the limited capacity of owned warehouse (OW), one additional warehouse is taken on lease or rent. In certain practical situations, when suppliers provide price discounts for bulk purchases or when the item under consideration is a seasonal product such as the output of harvest or the replenishment cost is higher than the other related cost, etc., or the new product launched considering the large demand, the inventory manager may purchase more goods that can be stored in its own warehouse (OW) as this is a temporary phenomenon, therefore considering economical point of view, the distributors usually choose to rent other warehouses than rebuild a new warehouse. Thus, the excess quantity is stored in a rented warehouse (RW). The inventory costs (including holding cost and deterioration cost) in RW are usually higher than those in OW due to additional cost of maintenance, material handling etc. To reduce the inventory costs, it will be economical to consume the goods of RW at the earliest. Consequently, the firm stores goods in OW before RW, but clears the stocks in RW before OW. Therefore, the stocks of OW will not be released until the stocks of RW are exhausted.

Considering the above assumptions, the inventory is depleted not only by demand but also by deterioration. Therefore, differential equation model has been developed. During the interval (0, t_w), the inventory levels are positive at RW and OW considering exponentially increasing demand. At RW, the inventory is depleted by the combined effect of demand and deterioration, while at OW inventory is depleted only by the effect of deterioration as to save on holding cost the organization would be first consuming the goods of the rented warehouse. Hence, the inventory level at RW and OW are governed by the following differential equation