Effective inventory control in supply chains with large uncertain decay factor using robust model predictive control

Abstract

This paper deals with the inventory control in supply chains under the following assumptions: 1) highly perishable goods with uncertain decay factor, 2) a future customer demand belonging to a known compact uncertainty set. The problem is to define a control policy keeping the on hand stock level as close as possible to a desired level despite the above uncertainties. The contribution of this paper focuses on a Robust Model Predictive Control (RMPC) approach. This implies solving a min-max optimization problem with hard constraints on some physical variables. To drastically reduce the numerical complexity of this problem, the control signal (i.e. the sequence of replenishment orders) is sought in the space of B-spline functions, which are known to be universal approximators admitting a parsimonious parametric representation. This allows us: 1) to reduce the number of both decision variables and constraints involved in the optimization procedure, 2) to reformulate the numerically involved minimization of the worst case cost functional as a Weighted Constrained Robust Least Squares (WCRLS) estimation problem. The WCRLS algorithm can be efficiently implemented using second order cone programming. A rigorous analysis of stability and feasibility conditions is provided.