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Mixed integer predictive control deals with optimizing integer and realcontrol variables over a receding horizon. The mixed integer nature of controlsmight be a cause of intractability for instances of larger dimensions. Totackle this little issue, we propose a decomposition method which turns theoriginal $n$-dimensional problem into $n$ indipendent scalar problems of lotsizing form. Each scalar problem is then reformulated as a shortest path oneand solved through linear programming over a receding horizon. This lastreformulation step mirrors a standard procedure in mixed integer programming.The approximation introduced by the decomposition can be lowered if we operatein accordance with the predictive control technique: i) optimize controls overthe horizon ii) apply the first control iii) provide measurement updates ofother states and repeat the procedure.

Mixed integer predictive control and shortest path reformulation