Technical note—managing inventory for firms with trade credit and deficit penalty

This paper considers a firm that periodically orders inventory to satisfy demand in a finite horizon. The firm operates under two-level trade credit—that is, it offers trade credit to its customer while receiving one from its supplier. In addition to standard inventory-related costs, the firm also incurs periodic cash-related costs, which include a deficit penalty cost due to cash shortage and an interest gain (negative cost) due to excess cash after inventory payments. The objective is to obtain an inventory policy that maximizes the firm’s working capital at the end of the horizon. We show that this problem is equivalent to one that minimizes the total inventory- and cash-related costs within the horizon. For this general model, we prove that a state-dependent policy is optimal. To facilitate implementation and reveal insights, we consider a simplified model in which a myopic policy is optimal under nondecreasing demand. A numerical study suggests that this myopic policy is an effective heuristic for the original system. The heuristic policy generalizes the classic base-stock policy and resembles practical working capital management under which a firm orders according to its working capital level. The policy parameters have closed-form expressions, which show the impact of demand and cost parameters on the inventory decision. Our study assesses the value of considering financial flows when a firm makes the inventory decision and reveals insights consistent with empirical findings.

Duke Scholars

Author Kevin H. Shang Fuqua School of Business