Energy consumption control in the two-machine Bernoulli serial production line with setup and idleness

Abstract

In recent years, the topic of sustainable manufacturing system design with energy saving features has received increasing attention. For a typical production line setting, the machines are subject to random breakdown and restart besides blockage and starvation, and they are usually connected via buffer areas with finite capacity. In the present study, the energy consumption of the serial production line with two Bernoulli machines is considered, with an aim to minimise the total energy consumption under a desired production rate. The energy consumption of the two-machine system is composed of the energy needed to setup, to remain idle, and for actual manufacturing. In order to minimise the total energy expenditure, a nonlinear fractional polynomial optimisation model is constructed, which is first converted to a nonlinear polynomial optimisation problem. Then the property of the total energy cost is analysed via the sum of squares (SOS) method. To speed up the solving process, a new heuristic approach named energy consumption saving (ECS) algorithm is proposed considering the monotonicity and local optimality of the energy cost function. Finally, by presenting optimal configurations of the production line with different throughputs, buffer capacities, and energy parameters, a simulation-based study is performed to validate the SOS and ECS algorithms.

Keywords:

• Serial production line
• Bernoulli machine
• nonlinear polynomial optimisation
• energy consumption
• heuristics

Disclosure statement

No potential competing interest was reported by the authors.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

The authors are grateful for the financial support partly from the Natural Science Foundation of China [grant numbers 71871203, L1924063].

Notes on contributors

Zhi Pei

Zhi Pei (Member, IEEE) received the B.S. and Ph.D. degrees in industrial engineering from Tsinghua University, Beijing, China, in 2005 and 2011, respectively. He was a visiting professor with North Carolina State University, Raleigh, NC, USA, in 2015. He is currently a professor with the Department of Industrial Engineering, Zhejiang University of Technology, Hangzhou, China. He has published academic articles in many journals, such as the European Journal of Operational Research, Annals of Operations Research, Computers & Operations Research, Service Science, Omega, and IEEE Transactions on Automation Science and Engineering. He is an associate editor for the journal IEEE Transactions on Automation Science and Engineering. His current research interests include manufacturing system modelling, machine scheduling, nonlinear optimisation, and queueing theory.

Peiqi Yang

Peiqi Yang received the B.S. degree in industrial engineering form Zhejiang University of Technology, Hangzhou, China, in 2020. She is currently pursuing the master's degree with College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou. Her research interests include modelling, analysis, and optimisation of production systems.

Yujuan Wang

Yujuan Wang received the B.S. degree in industrial engineering form North China University of Science and Technology, Tangshan, China, in 2018, and the M.S. degrees in mechanical engineering form Zhejiang University of Technology, Hangzhou, China, in 2021. Her research interests include modelling, analysis, and optimisation of production systems.

Chao-Bo Yan

Chao-Bo Yan (Senior Member, IEEE) received the B.S. degree from Xi'an Jiaotong University, Xi'an, China, in 2004, and the M.S. and Ph.D. degrees in control science and engineering from Tsinghua University, Beijing, China, in 2007 and 2012, respectively. He was a Visiting Scholar with the University of Michigan, Ann Arbor, MI, USA, from 2009 to 2010, and a Post-Doctoral Research Fellow from 2012 to 2014. He is currently a Professor with the School of Automation Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University. His research interests include modelling, analysis, and optimisation of production systems, and cyber-physical systems (CPS) theory and its applications to manufacturing, logistics, and inventory systems. Dr. Yan is an Associate Editor of the IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, an Editor on the Conference Editorial Board (CEB) of the IEEE CONFERENCE ON AUTOMATION SCIENCE AND ENGINEERING, and the General Co-Chair of 2022 IEEE CONFERNCE ON AUTOMATION SCIENCE ENGINEERING. He was an Associate Editor of the IEEE ROBOTICS AND AUTOMATION LETTERS and a Guest Editor of IISE TRANSACTIONS and INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH.