A generalized algebraic model for optimizing inventory decisions in a multi-stage complex supply chain

In this paper, we deal with more generalized inventory coordination mechanism in an n-stage, multi-customer, non-serial supply chain, where we extend and generalize pervious works that use algebraic methods to optimize this coordinated supply chain. We establish the recursive expressions for this multi-variable optimization problem. These expressions are used for the derivation of the optimal replenishment policy and the development of the solution algorithm. Further, we describe a simple procedure that can help in sharing the coordination cost benefits to induce all stages to adopt the inventory coordination mechanism. We provide a numerical example for illustrative purposes.