Modelling and optimising the capacity and production network planning in plastics processing factories

ABSTRACT

This paper deals with the capacity planning and production network planning in plastics processing factories. We lay emphasis on the opportunity and – potentially – necessity to move machines, tools and material. Furthermore, we consider the option to outsource production to external suppliers. Demand is deterministic and has to be satisfied in the same period. We present a linear mixed integer programming model representing the problem to find a minimum-cost production plan where total cost accounts for variable production cost, setup cost, transportation cost, relocation cost and cost caused by machine purchases. The decisions to be made are the allocation of machines to plants. This includes to decide for investments or relocating machines between plants. In addition, the allocation of products to machines and the determination of the corresponding optimal quantities of production, purchase and transportation within the network of suppliers, plants and customers are decided. We provide a computational study validating the model and conduct a sensitivity analysis of the run time using an off-the-shelf solver. Finally, we present a real-world case of an international automobile supplier. Tackling the instance with an off-the-shelf solver the problem cannot be solved in reasonable time. Thus we apply a simple decomposition scheme to provide decision support for the real-world case.

KEYWORDS:

• Production
• network planning
• machine relocation
• inter-plant material flow
• multi-stage production

Acknowledgements

The first author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 425058257.

Availability of data and material

The datasets generated and analysed during the current study, in particular for sensitivity tests, are available from the corresponding author, Lena Rotfuß, upon reasonable request.

The data that support the findings of the practical example are not publicly available due to containing company-internal data but are available from the corresponding author on reasonable request and with permission of HELLA GmbH & Co. KGaA.

Code availability

The code used for validating the model during the current study is available from the corresponding author, Lena Rotfuß, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 https://www.plasticseurope.org/index.php?cID=179, accessed on 23-July-2020

2 https://www.grandviewresearch.com/press-release/global-plastics-market-analysis, accessed on 07-September-2020

Additional information

Notes on contributors

Dirk Briskorn

Dirk Briskorn received Diploma in Applied Computer Science and Business Administration from the University of Cologne, Germany, in 2004, and Dr. Sc. Pol. degree in Business Administration from the University of Kiel, Germany, in 2007. He is currently Professor for Production and Logistics at Wuppertal University in Germany. His research interests lie in scheduling theory, applied scheduling, auction theory and modelling of supply chain processes.

Lena Rotfuß

Lena Rotfuß is Research Associate and Ph.D. candidate at the Chair of Business Administration, esp. Production and Logistics at the Wuppertal University, Germany. She received a B.Sc. in Mathematics and M.Sc. in Controlling and Risk Management from the University of Siegen. Her research focuses on the capacity and production network planning.

Marcel Helmdach

Marcel Helmdach obtained his PhD degree from University of Paderborn in Germany in cooperation with Mercedes-Benz Group AG. Since 2011, he has been working in leading positions for production planning. After 7 years as Head of Capacity Planning for the lighting segment of Hella GmbH & Co. KGaA, he joined Infineon Technologies AG as head of Operations Planning and Control for the High Power Segment in 2020.