Hybrid model predictive control applied to production-inventory systems

Hybrid production-inventory systems are characterized by discrete decisions on production levels and/or capacity. These systems have broad applicability to important, emerging applications of process control concepts, among them time-varying adaptive behavioral interventions and supply chain management. This paper examines the usefulness of hybrid model predictive control (HMPC) in these two novel application settings. In a hypothetical adaptive behavioral intervention inspired by Fast Track (a preventive intervention for reducing conduct disorder in at-risk children), HMPC is presented as a means to improve the assignment of frequency of home-based counseling visits to families with low parental function. In supply chain management, the usefulness of HMPC for assigning production capacity in an inventory control problem under conditions of varying customer demand is presented. These problems are modeled as mixed logical dynamical (MLD) systems, with HMPC consisting of a Mixed Integer Quadratic Program (MIQP) that employs a three-degree-of-freedom parametrization for achieving ease of tuning and facilitating robust performance under uncertainty.