  This paper is the first to consider online algorithms to schedule a
proportionate flexible flow shop of batching machines (PFFB). The scheduling
model is motivated by manufacturing processes of individualized medicaments,
which are used in modern medicine to treat some serious illnesses. We provide
two different online algorithms, proving also lower bounds for the offline
problem to compute their competitive ratios. The first algorithm is an
easy-to-implement, general local scheduling heuristic. It is 2-competitive for
PFFBs with an arbitrary number of stages and for several natural scheduling
objectives. We also show that for total/average flow time, no deterministic
algorithm with better competitive ratio exists. For the special case with two
stages and the makespan or total completion time objective, we describe an
improved algorithm that achieves the best possible competitive ratio
$\varphi=\frac{1+\sqrt{5}}{2}$, the golden ratio. All our results also hold for
proportionate (non-flexible) flow shops of batching machines (PFB) for which
this is also the first paper to study online algorithms.
