Multi-echelon Supply Chain Optimization: Methods and Application Examples

Optimization and optimal control of multi-echelon supply chain operations is difficult due to the interdependencies across the stages and the various stock nodes of inventory networks. While network inventory control problems can be formulated as Markov decision processes, the resulting models can usually not be solved numerically due to the high dimension of the state space for instances of realistic size. In this paper the application of a recently developed approximation technique based on piece-wise linear convex approximations of the underlying value function is discussed for two well-known examples from supply chain optimization: multiple sourcing and dynamic inventory allocations. The examples show that the new technique can lead to policies with lower costs than the best currently known heuristics and at the same time yields further insights into the problem such as lower bounds for the achievable cost and an estimation of the value function.