A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.

► Soni and Shah’s model is extended to allow for non-zero ending-inventory, limited inventory space and profit maximization.
► Sufficient conditions for the existence and uniqueness of the optimal solution are established.
► Economic interpretations for the theoretical results are provided.
► The numerical examples indicate that our optimal solution leads to increase the profit in relation with that of Soni and Shah.