Resilient and robust management policy for multi-stage supply chains with perishable goods and inaccurate forecast information: A distributed model predictive control approach

An efficient supply chain (SC) management requires that decisions are taken to minimize the effects of parametric uncertainties and unpredictable external disturbances. In this article, we consider this problem with reference to a multi-stage SC (MSSC) whose dynamics is characterized by the following elements of complexity: perishable goods with uncertain perishability rate, an uncertain future customer demand that is only known to fluctuate inside a given compact set. The problem we face is to define a resilient and robust Replenishment Policy (RP) such that at any stage the following requirements are satisfied: the fulfilled demand is maximized, overstocking is avoided, the bullwhip effect (BE) is mitigated. These objectives should be pursued despite the mentioned uncertainties and unexpected customer demand behaviors violating the bounds of the compact set. Robustness is here intended with respect to uncertainty on the perishability rate, and resiliency as the ability to quickly react to the mentioned unforeseen customer demands. We propose a method based on a distributed resilient robust model predictive control (DRRMPC) approach. Each local robust MPC (RMPC) involves solving a Min-Max constrained optimization problem (MMCOP). To drastically reduce the numerical complexity of each MMCOP, we parametrize its solution by means of B-spline functions