An exact method for machining lines design with equipment selection and line balancing

Abstract

We consider the context of machining systems design where both equipment selection and line balancing decisions have to be taken in order to minimise the total cost of the system. The designed flow line employs multi-positional machines with rotary tables where vertical and horizontal machining modules can be used for the realisation of machining processes. For this challenging optimisation problem in production research, we develop an innovative mathematical model based on a mixed-integer linear programme and a heuristic algorithm for an approximate solution. An extensive numerical experiment is conducted in order to evaluate the performances of the proposed mathematical model and the developed heuristic. The obtained results show that the decision makers can use the elaborated methods for solving efficiently even large-scale industrial problems.

KEYWORDS:

• Machining systems design
• machining processes
• flow lines
• line balancing
• combinatorial optimisation
• decision support systems

Acknowledgments

The series of research studies on line balancing for machining lines was started by our team in our INTAS projects for which Dr. Jean-Marie Proth was the scientific coordinator: INTAS-96-0820 (Discrete optimisation problems in scheduling and computer-aided design, 1997–2000); and INTAS-00-0217 (Scheduling and assignment models under uncertainty and real-time constraints with application to manufacturing, communication, computer-aided design, and transportation, 2001–2004). This work is in continuation of that and later projects that was partially funded by ANR project ANR-21-CE10-0019. Such an approach was often used in the research work of Dr. Jean-Marie Proth. Additionally, the work of the second author was partially funded by the European project ASSISTANT, project 101000165 of H2020-ICT-2018-20.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

All used data are provided in the paper. If readers have any questions about the data used in this research they are invited to contact the corresponding author who will share all available information.

Additional information

Funding

This work was supported by Agence Nationale de la Recherche: [Grant Number ANR-21-CE10-0019]; European Commission: [Grant Number 101000165 of H2020-ICT-2018-20].

Notes on contributors

Olga Battaïa

Prof. Olga Battaïa has a Full Professor position in Department of Operations Management and Information Systems at Kedge Business School. She serves as Associated Editor for several international peer-reviewed journals, including the Journal of Manufacturing Systems, IISE Transactions and Omega-the International Journal of Management Science. She is also a Member of IFAC Technical Committee 5.2. Management and Control in Manufacturing and Logistics. Her research interests lie in the domains of Supply Chain Management, Sustainable manufacturing, Business Analytics, Decision Support Systems. Olga Battaïa co-authored more than 200 scientific publications and supervised or co-supervised 13 PhD students. She was invited to present her research at several renowned international conferences and universities in Europe, America, Asia and Africa.

Alexandre Dolgui

Dr. Alexandre Dolgui is an IISE Fellow, Distinguished Professor and the Head of Automation, Production and Computer Sciences Department at the IMT Atlantique. His research and teaching activities focuse on manufacturing line design, production planning and supply chain optimisation, resilience of global supply networks. He is the co-author of 5 books, the co-editor of 25 books or conference proceedings, the author of over 300 refereed papers in international journals. He is the Editor-in-Chief of the International Journal of Production Research, an Area Editor of Computers & Industrial Engineering. He is an Active Fellow of the European Academy for Industrial Management, Member of the Board of the International Foundation for Production Research, Vice-chair Chair (former Chair 2011 - 2017) of IFAC TC 5.2 Management and Control in Manufacturing and Logistics, Member of IFIP WG 5.7 Advances in Production Management Systems, IEEE System Council Analytics and Risk Technical Committee, he has been Scientific Chair of many leading scientific conferences. He received various international awards and distinctions.

Nikolai Guschinsky

Nikolai N. Guschinsky received B.S. and MSc degrees in applied mathematics from the Byelorussian State University, Minsk, Belarus, and a Ph.D. degree in mathematical cybernetics from the Institute of Mathematics of Byelorussian Academy of Sciences, Minsk, Belarus, in 1978, 1984, and 1991, respectively. He served as a Junior Researcher and Researcher of the Mathematical Cybernetics Laboratory, then as a Senior Researcher of Operation Research Laboratory, Minsk, Belarus. Now he is a Leading Researcher of Mathematical Cybernetics Laboratory at the United Institute of Informatics Problems of the National Academy of Sciences of Belarus. His research interests include graph optimisation and computer-aided design of complex engineering systems. He is the author of 2 books, about 50 journal papers and book chapters and over 130 papers in conference proceedings and research reports. Dr. N. Guschinsky is the Byelorussian Operations Research Society Secretary. He received the IIE Transactions Award — 2008 Best Paper in Design and Manufacturing focus issue and the National Academy of Sciences of Belarus Prize in 2008.