A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system

Chung and Huang (2007) designed recently a two-warehouse inventory model for deteriorating items when the supplier offers the retailer a delay period and in turn the retailer provides a delay period to their customers. They assumed that the stocks of RW are transported to OW via a continuous release pattern and the transportation costs are ignored. The holding cost in RW is exceeding that in OW. The deterioration rate of RW is assumed to be identical to that in OW. For practical purpose, it is observed that due to demand, the retailer needs to rent warehouse to store items sometimes. If the retailer's facility about deterioration is not newer than that of the rented warehouse, then α≥β. Otherwise, α<β. This paper extends the model of Chung and Huang (2007) by considering β>α which means that the rate of deterioration in RW exceeds that of OW. First, expressions are obtained for the total variable cost of the inventory system. Second, this study demonstrates that a unique optimal solution exists. Third, two lemmas and one theorem are designed for determining the optimal cycle time. Finally, numerical examples are presented to illustrate the procedure for solving the model and sensitivity analysis of the optimal solution with respect to the parameters of the system is conducted.