The Fourth Industrial Revolution means the digital transformation of production systems. Cyber-physical systems allow for the horizontal and vertical integration of these production systems as well as the exploitation of the benefits via optimization tools. This article reviews the impact of Industry 4.0 solutions concerning optimization tasks and optimization algorithms, in addition to the identification of the new R&D directions driven by new application options. The basic organizing principle of this overview of the literature is to explore the requirements of optimization tasks, which are needed to perform horizontal and vertical integration. This systematic review presents content from 900 articles on Industry 4.0 and optimization as well as 388 articles on Industry 4.0 and scheduling. It is our hope that this work can serve as a starting point for researchers and developers in the field.

The current work reveals a methodology that provides an adequate basis to portray and model supply chains mathematically and formally as well as to synthesize optimal and alternative supply scenarios algorithmically while taking into account structural redundancy. The proposed methodology is based on the combinatorial foundations of algorithmic process synthesis or more specifically on the P-graph framework. A biodiesel supply network involving blending and transportation serves as an illustrative example. A novel algorithm generates the mathematical model and alternative solutions to increase reliability of supply scenarios. Major steps of the generation are the structure generation and estimation of reliability of a supply scenario.

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