## 1 Introduction  
Production companies have to apply the solutions of cyber-physical systems to improve their availability, efficiency, reliability, and productivity. The ever-changing manufacturing industry requires the improvement of these attributes. Statistical surveys suggest that by the end of 2019, about 75% of large manufacturing companies will update their operations with Internet of Things solutions [1] and transform their conventional manufacturing environment to cyber-physical systems. The integration of IoT solutions leads to hyperconnected value chains, where not only manufacturing but also the related supply chain and logistics processes are operating in a cyber-physical environment.  
KUKA AG (a German manufacturer of industrial robots and solutions having 25 subsidiaries worldwide) created a new versatile solution that compensates for peak capacity utilization or bottlenecks in resources. In a matrix production system, configurable production or assembly cells are arranged in a grid layout, and the in-plant supply is based on electric automated guided vehicles [2]. The matrix production system integrates a wide range of Internet of Things technologies and solutions, like standardized configurable production and assembly cells; in-plant transfer system based on configurable material handling machines; digital twin solutions to support prediction and optimization performance; intelligent tools and gentelligent products. A gentelligent product can collect and store lifecycle data about itself and its environment with integrated sensors and send feedback for product design or process engineering.  
The design and operation of the in-plant supply of a matrix production system is an important part of this cyber-physical system because in matrix production logistics and manufacturing are separated, and a logistics system must answer dynamically changing supply-demands and perform them for an uninterrupted value chain. The role of in-plant supply has changed in these highly flexible, responsive manufacturing systems, where manufacturing and assembly cells can be removed or added. In this respect, the motivation of our research is analytic, as we describe a mathematical model and a suitable heuristic optimization algorithm to offer a solution for the design and control problems of in-plant supply in a matrix production environment. This paper studies the design aspects of the in-plant supply of matrix production from sustainability and emission reduction points of view. As the literature review section will show, the majority of the articles in the field of in-plant supply are focusing on the optimization in a conventional manufacturing environment and only a few of them describe the design aspects of in-plant logistics solutions in a cyber-physical environment. The application of suitable design and control methods can increase the efficiency, availability, and sustainability.  
This paper is organized as follows. Section 2 presents a systematic literature review, which summarizes the research background of in-plant manufacturing supply. Section 3 describes the model framework of in-plant supply in a cyber-physical production environment. Section 4 presents a multiphase optimization model including clustering, routing, and scheduling problems based on a black hole algorithm and a flower pollination algorithm and demonstrates the scenario analysis, which validates the model and the optimization algorithm. Conclusions and future research directions are discussed in Section 5.