Nonlinear Short-Term Scheduling Model

The presented concept leads to a mixed-integer nonlinear programming (MINLP) model. The binary variables representing assignment decisions and sequencing decisions are complemented by continuous variables representing timings, durations, hold-ups, feed streams, supplied product, under- and overproduction. The 

In the polymerization stage, the number of events, i.e., of the polymerization starts, N, is given and the events are identified by the index n = 1... N. Start times of polymerizations are represented by continuous variables in e [0, H] in with H denoting the given scheduling horizon. As an initial condition, the first polymerization is defined to start at tn= i = t°. 

The reactors are not considered individually but they are aggregated to a group of identical processing units with an overall capacity of four. The allocation of the reactors is not modeled explicitly, but they induce constraints on the start times of the polymerizations. Based on the as sumption that all four reactors can be used and that they are allocated in turns, the intervals between tn and tn+4 [n = 1... N — 4) must be greater than or equal to the processing time of a polymerization dp (with dp= 17)  

Similar to the reactors, the allocation of the safety ventilation system is not modeled explicitly. It induces lower bounds on the variable intervals dn (n = 1... N — 1) between two consecutive polymerization starts n and n + 1 given by the duration of the first polymerization phase q, i.e., dn [q, H] Vn N — 1 with q = 4. The intervals dn are calculated from equality constraints  

Note that in contrast to the intervals between tn and tn+4, the intervals between successive polymerization starts tn and tn+i are calculated explicitly, since they are essential for the capacity constraints of the mixing vessels (see below). 

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