Dynamic inventory control with payment delay and credit limit

Abstract

AbstractThe credit limit is the maximum amount of accounts payable (AP) that a firm owes to its supplier. This limit establishes a tie between the effective purchasing cost and the order quantity as well as the AP level. We present a multi‐period stochastic inventory model with payment delay and credit limit. Our model aims to capture the property of the optimal ordering policy with respect to the AP and inventory states. For the backlogging and lost‐sales cases, we present the method to reduce the dimension of state space. In both cases, the optimal order quantity is demonstrated to be decreasing in the AP and inventory level of each age. In addition, the sensitivity of the optimal order quantity with respect to the AP decreases with age. That is, the optimal order quantity is more sensitive to the younger AP. In the backlogging case, the base‐stock policy is not optimal due to the presence of credit limits. Somewhat surprisingly, our numerical example shows that the optimal order quantity is not necessarily increasing in the credit limit. Finally, based on the L♮‐convexity of the cost‐to‐go function, we design a linear programming greedy heuristic policy for the infinite‐horizon version of our model with independent and identically distributed demands. Numerical results show that our heuristic policy performs well.