Integrating Inventory Replenishment and Cash Payment Decisions in Supply Chains

The recent nancial crisis demonstrates that an upstream member in a supply chain usually has a weaker cash liquidity. Cash shortage a ects material supply to a downstream member, which, in turn, a ects the performance of the entire chain. This paper provides a supply chain model that integrates material and cash ows and investigates the impact of payment policies on the system performance. Speci cally, we consider a two-stage system in which a retailer replenishes inventory from a supplier in a nite horizon. The retailer has stronger cash liquidity in the sense that it can transfer cash from or to an investment account in each period. To quantify the value of payment exibility, we consider two payment schemes. For the exible payment (FP) scheme, the retailer may delay the payment or subsidize cash to the supplier; for the strict payment (SP) scheme, the retailer pays exactly what it orders. We prove that the optimal joint policy for the FP model has a surprisingly simple structure both stages implement an echelon base-stock policy for inventory replenishment; the retailer monitors the system's working capital and implements a two-threshold policy for cash transfers and a pay-up-to policy for payment. Solving the SP model is more involved. We rst provide a lower bound on the optimal cost by connecting the SP model to an assembly system. We then propose a simple and intuitive heuristic. Our numerical study characterizes circumstances under which the value of exible payment is most signi cant and identi es factors that a ect the optimal cash to inventory ratio. In addition, the volatility of payment from the retailer to the supplier is larger (smaller) than that from the supplier to the external vendor under the FP (SP) scheme. Thus, the material and nancial bullwhip e ects may not amplify in the same direction.