Computing base-stock levels for a two-stage supply chain with uncertain supply

We consider independent decision makers in a two-stage supply chain subject to uncertainty in upstream supply, and we use a recently published computational algorithm to generate independent, single-stage (ISS) base-stock inventory solutions for each stage in the system. These solutions are computed by employing straightforward, linear functions to estimate the parameters that must be set to seed the single-stage computational algorithm. Those linear functions are derived from the system-optimal solutions, which are found by solving a Markov chain model of the two-stage system. We demonstrate that the ISS solutions are often quite close to the system-optimal solution, and moreover, we develop a fast, descent-based search to quickly find the system-optimal solutions starting from the ISS solutions. We use our solution algorithm to generate optimal solutions to 1100 randomly-generated problem instances, allowing us to explore the behavior of the two-stage inventory system under various cost, demand uncertainty, and supply uncertainty conditions. We find that the downstream stocking levels are strongly influenced by the properties of the downstream demand, while the upstream stocking level is very strongly influenced by the holding costs and supply uncertainty, and only marginally by the retailer penalty cost. Moreover, the system responds to changes in the cost and uncertainty environment mostly by shifting the burden of holding cost either upstream or downstream, leaving the downstream penalty cost relative stable across the large set of problem instances we study.