Assembly flow shop scheduling problem considering machine eligibility restrictions and auxiliary resource constraints

Abstract

This paper investigates a two-stage production system consists of a fabrication stage followed by an assembly stage. There are some unrelated parallel machines in the first stage to process the parts and then, the parts are assembled into the final product at an assembly workstation. To close the problem to real-world condition, machine eligibility, sequence-dependent setup times, and different release times are considered for the received parts. In addition, most of the researchers deal with machines as the only resource in conducting the scheduling problems. However, other additional resources such as specialised labours, tools, and industrial robots are usually not only required for processing jobs but also are often restricted to use. First, the problem is described and a new mixed-integer linear programming model is proposed that can solve the problem in small-sized scales. Since this problem is well known as a strong NP-hard problem, a new heuristic algorithm is proposed based on the basic idea of Johnson’s rule. Moreover, two proper lower bounds are introduced as references to evaluate the performance of the proposed heuristic algorithm. Numerical experiments show high quality of the final solutions provided by the proposed algorithm and also indicate effectiveness of two developed lower bounds.

KEYWORDS:

• Two-stage production system
• assembly flow shop
• auxiliary resource constraints
• machine eligibility
• lower bound

Disclosure statement

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

Additional information

Notes on contributors

Seyed Mohammad Hassan Hosseini

Seyed Mohammad Hassan Hosseini is currently principal and assistant professor of Industrial Engineering College at Shahrood University of Technology, where he has been since 2013. He received a B.S. from Iran University of Science and Technology in 2000, and an M.S. from the Amirkabir University of Technology. He received his Ph.D. in Industrial Engineering from the Payam-e-Noor University of Tehran in 2012. From 2002 to 2008, he worked at Iran Khodro Company (IKCO) as the most famous car manufactures in Middle East as an expert in quality control and also CRM department. His main areas of research are the modelling of scheduling (especially flow shop) and production planning and control, quality engineering and management, and decision making techniques. He has published over 40 papers in different international journals such as Journal of applied mathematical modelling, The International Journal of Advanced Manufacturing Technology, International Journal of Industrial Engineering Computations, International Journal of Supply and Operations Management, Journal of Optimisation in Industrial Engineering, Journal of Industrial and Systems Engineering, Journal of applied mathematics and computations, Environment Systems and Decisions, International Journal of Productivity and Quality Management and so on. As of 2014, Google Scholar reports over 200 citations to his work. He has given numerous invited talks and tutorials and is a founder of and consultant to companies involved in car making. His Google Scholar address is: https://scholar.google.co.in/citations?user=WehwoJ0AAAAJ&hl=en

Shib Sankar Sana

Shib Sankar Sana is currently Principal of Kishore Bharati Bhagini Nivedita College under the University of Calcutta. He served at the Department of Mathematics as Associate Professor in Bhangar Mahavidyalaya from 2001 to 2018 and Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi as an Associate Lecturer during 1999–2001. His main areas of research are the modelling of production planning and inventory control, Biomathematics and Soft Computing. He has published over 175 papers in Journal of cleaner Production, European Journal of Operational Research, International Journal of Production Economics, Computers and Mathematics with Application, Mathematical and Computer Modelling, Applied Mathematics and Computation, Journal of Modelling in Management, American Journal of Mathematical and Management Sciences, International Journal of Systems Science, Far East Journal of Applied Mathematics, Non-linear Phenomena in Complex Systems, Advanced Modelling and Optimisation, Vietnam Journal of Mathematics, Yugoslav Journal of Operational Research, International Journal of Operational Research, International Journal of Services Operations Management, International Journal of Modelling, Identification and Control, International Journal of Innovative Computing and Application, International Journal of Procurement Management, International Journal of Mathematics and Operations Research, IMA Journal of Management Mathematics, International Journal of Information and Decision Science, Indian Journal of Industrial and Applied Mathematics, International Journal of Management Science and Engineering Management, Applied Mathematical Modelling, Decision Support Systems, Service Science, Review in Aquaculture, International Journal of Production Research, Expert Systems with Application, Economic Modelling, Journal of Manufacturing Systems, Journal of Advanced Manufacturing Systems, Journal of Industrial & Management Optimisation, Annals of Operations Research, International Journal of Logistics Research and Applications, Computers & Industrial Engineering, Journal of Intelligent Manufacturing, International Journal of Applied and Computational Mathematics, RAIRO-Operations Research, CIRP Journal of Manufacturing Science and Technology, Control and Cybernetics, Cybernetics and Systems, etc. He is a member of the editorial board of American Journal of Computational and Applied Mathematics, Universal Journal of Applied Mathematics, International Journal of Advanced Mathematics, American Journal of Industrial and Business Management. My Google Scholar address is: https://scholar.google.co.in/citations?user=WehwoJ0AAAAJ&hl=en

Mohammad Rostami

Mohammad Rostami is a Professor in the Department of Industrial Engineering and Management at Shahrood University of Technology, where he has been since 2018. He received a B.S. in 2012, M.S. in 2014, and he received his Ph.D. in 2018 all of them from the Iran University of Science and Technology. From 2012 to 2018 he worked as an expert in production planning and control in different manufacturing industries. He interests to research in scheduling, hub location, project scheduling, and robust optimisation. Much of his work has been on modelling and solving the project scheduling and location-routing problems. He has also investigated the implications of linear and non-linear programing models, heuristics, and metaheuristics to solve such NP-hard problem with large-sized scales. As of 2014, Google Scholar reports over 200 citations to his work. He has given numerous invited talks and tutorials and is a founder of and consultant to companies involved in the project. He has over 25 publications in different academic journals such as Journal of Computers & Industrial Engineering, Engineering Applications of Artificial Intelligence, Applied Mathematical Modelling, Management Science Letters. His Google scholar address is: https://scholar.google.com/citations?hl=en&user=TPCdJoMAAAAJ