A two-warehouse inventory model for items with stock-level-dependent demand rate

As we all know, the capacity of any warehouse is limited. In practice, however, there usually exist various factors that induce the decision-maker of the inventory system (especially those with inventory-dependent demand rate) to order more items than can be held in his own warehouse. Therefore, for the decision maker, it is very practical to determine whether or not to rent other warehouses and what order or shipment policy to adopt if other warehouses are indeed needed. In this paper, a deterministic inventory model with inventory-dependent demand rate and two separate warehouses (own warehouse, abbreviated as OW and rented warehouse, abbreviated as RW) is developed to help the decision-maker to make the decision. The model is formulated by assuming that the demand rate is a polynomial form of current inventory level, the stock is transferred from RW to OW under a bulk release pattern and the transportation cost is taken to be dependent on the transported amount. Shortages are not allowed. Presented here are sufficient and necessary conditions of judging whether to rent RW and the solution procedure of the proposed model. The solution procedure is illustrated with some numerical examples. Sensitivity analysis of parameters is also shown.