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.

本文是第一个考虑在线算法来调度配料机（PFFB）的比例灵活流水车间。调度模型的动机是个性化药物的制造过程，这些药物在现代医学中用于治疗一些严重的疾病。我们提供了两种不同的在线算法，也证明了离线问题的下界来计算它们的竞争比率。第一种算法是一种易于实现的通用局部调度启发式算法。对于具有任意数量级的 PFFB 和几个自然调度目标，它是 2 竞争的。我们还表明，对于总/平均流时间，不存在具有更好竞争比的确定性算法。对于具有两个阶段和制造期或总完成时间目标的特殊情况，\(\varphi =\frac{1+\sqrt{5}}{2}\)，黄金分割率。我们所有的结果也适用于配料机（PFB）的比例（非灵活）流水线，这也是研究在线算法的第一篇论文。