Optimal Inventory Level Control in the Case of Perishable Goods With Unknown Time-Varying Decay Factor: A Data-Driven Supervised Robust Model Predictive Control Approach

We consider the optimal inventory control problem of a periodically reviewed supply chain with perishable goods. The deterioration process is characterized by an unknown decay factor time-varying over a given arbitrarily large uncertainty subset of all admissible values. In this context we face the problem of defining an effective inventory control policy reconciling control requirements like maximizing the satisfied customer demand, avoiding overstocking, attenuating the bullwhip effect. The conflict of these requirements and the uncertainty on the time varying decay factor define a highly involved problem that necessarily calls for an optimal and robust control synthesis approach. To define a general synthesis procedure of the inventory control policy, we take into account the time varying uncertainty on the decay factor through weak “a priori” assumptions that are verified in the vast majority of practical cases, regardless of the actual dynamics of the deterioration process. To reduce the conservatism of any robust optimization procedure we propose a novel approach based on a data driven reconfigurable min-max model predictive control (MPC). In brief, the synthesis procedure consists of the following steps: 1) the whole set of possible values assumed by the time-varying decay factor is partitioned into a family of small subintervals; 2) the subinterval containing the current and unknown decay factor is identified on the basis of a data-driven test; 3) a supervisor exploits this information to instantly update the current configuration of a reconfigurable min-max MPC strategy. We provide theoretical guarantee of asymptotic stability and satisfaction of the hard constraints on the inventory control policy. The numerical simulations confirm the validity of the proposed method.