Serial supply chains with economies of scale: bounds and approximations

We consider two models of stochastic serial inventory systems with economies of scale for which the forms of optimal policies are known. In the first model, each stage has a fixed-order quantity, while in the second model, there is a fixed-order cost for external supplies. For each model, we show that the optimal policy parameters can be bounded and approximated by a series of independent, single-stage optimal policy parameters. We further construct closed-form bounds and approximations for the single-stage solutions and apply them to the serial systems. These results provide simple and effective solutions that will help to facilitate implementations in practice. They also allow us to see the connections between the serial and single-stage systems and sharpen our intuition on optimal policy parameters and system behavior.