Optimal Lot Size under Trade Credit Financing When Demand and Deterioration Are Fluctuating with Time

This paper considers a generalized lot size inventory model with deteriorated products under trade credit financing. The demand and deterioration rates are known, continuous, and differentiable functions of time. In addition, the trade credit policy adopted in this paper assumes that the supplier offers the retailer the permissible delay period M, and the retailer also offer the trade credit period N to his/her customer, where M ≥ N. Under these general assumptions, the inventory model is formulated to attain the minimum total cost per unit time. For each circumstance, sufficient condition which lead to a minimal solution of the considered problem is also derived. Then, a rigorous mathematical analysis is used to prove that such a minimal solution is unique and global-optimal. Finally, some numerical examples are used to illustrate the model