Managing Inventory for a Multidivisional Firm with Cash Pooling

We consider a multi-divisional firm in which each division replenishes its inventory and the headquarter coordinates the cash flow through a master account over a finite horizon. The demands of the divisions are stochastic and may be correlated. The objective is to find an optimal joint inventory replenishment and cash retention policy which maximizes the firm’s working capital. We show that this problem is equivalent to minimizing the total system cost. Due to curse of dimensionality, the optimal policy is difficult to obtain. Nevertheless, we characterize the properties of the optimal policy and develop a simple heuristic that possesses these properties. A numerical study shows that the heuristic is near-optimal. We explore managerial insights through the heuristic. Among others, we find that the value of cash pooling is most significant when the demands of the divisions are negatively correlated.