Joint Inventory and Cash Management for Multi-Divisional Supply Chains

Abstract

Cash pooling is a powerful tool to consolidate intragroup liquidity for multi-divisional corporations. This paper develops a centralized supply chain model that aims to assess the value of cash pooling. The supply chain is owned by a single corporation with two divisions, where the downstream division (headquarter), facing random customer demand, replenishes materials from the upstream one. The downstream division receives cash payments from customers and determines a system-wide inventory replenishment and cash retention policy. We consider two cash management systems that represent different levels of cash concentration. For cash pooling, the supply chain adopts a financial services platform which allows the headquarter to create a corporate master account that aggregates the divisions' cash. For transfer pricing, on the other hand, each division owns its cash and pays for the ordered material according to a fixed price. Comparing both systems yields the value of adopting such financial services. We prove that the optimal policy for the cash pooling model has a surprisingly simple structure -- both divisions implement a base-stock policy for material control; the headquarter monitors the corporate working capital and implements a two-threshold policy for cash retention. Solving the transfer pricing model is more involved. We derive a lower bound on the optimal cost by connecting the model to an assembly system. Our results show that the value of cash pooling can be very significant when demand is increasing (stationary) and the markup for the upstream division is small (high). Nevertheless, a big portion of the pooling benefit may be recovered if the headquarter can decide the optimal transfer price and the lead time is short.