Joint inventory and cash management for multidivisional supply chains

This paper develops a centralized supply chain model that integrates material flows with cash flows. The supply chain is owned by a single firm with two divisions. The downstream division (headquarters), facing random customer demand, replenishes materials from the upstream division. The firm installs a financial services platform that pools the divisions cash into a master account managed by the headquarters. In each period, cash is received from customers and paid to the outside vendor after materials are delivered. The headquarters determines how much cash to retain for inventory replenishment. The objective is to determine an optimal joint inventory replenishment and cash retention policy for the entire supply chain. We prove that the optimal policy has a surprisingly simple structureboth divisions implement a base-stock policy for inventory replenishment; the headquarters monitors the corporate working capital and implements a two-threshold policy for cash retention. This result is obtained by extending the well-known Clark-Scarf decomposition with newly derived cash-related penalty functions. The optimal policy enables us to investigate the interaction between cash and inventory decisions. We show that in the presence of transaction costs, a firm may stock more even if the inventory holding cost increases. To quantify the value of financial integration, we compare the cash pooling model with systems under different levels of financial integration. Our study suggests that the value of cash pooling can be significant when demand is increasing (respectively, stationary) and the internal transfer price is low (respectively, high). Nevertheless, a significant amount of cash pooling benefit may be recovered if the headquarters can optimize the internal transfer price.

Duke Scholars

Author Kevin H. Shang Fuqua School of Business