The return and remanufacturing rates in a multi-stage green supply chain system with rework, variable shipping cost and ordering cost reduction

Abstract

This paper focuses on an integrated multi-stage green supply model where the remanufacturing and manufacturing are taken together. The return rate and remanufacturing rate are both stochastic in nature. The remanufacturing rate depends on the return rate. The defective products which are generated during the manufacturing as well as the remanufacturing process are immediately reworked. To reduce the ordering costs of the buyers, additional investments are taken into consideration. The manufacturer’s shipment cost depends on the number of deliveries. Close-loop formulae are obtained for the decision variables. Numerical study shows that an additional investment in ordering cost reduction helps the buyers to save more money as well as to reduce the integrated expected total cost of the entire green supply chain system. Sensitivity analyses for both of the models, with and without ordering cost reduction, are carried out.

KEYWORDS:

• Green supply chain
• stochastic return and remanufacturing rate
• rework
• ordering cost reduction
• variable transportation cost

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Notes on contributors

Monami Das Roy

Dr. Monami Das Roy is an Assistant Professor in the Department of Mathematics, Haldia Government College, Vidyasagar University, West Bengal, India. She obtained her B.Sc. in Mathematics and M.Sc. in Applied Mathematics from Vidyasagar University. In 2013, she received her Ph.D. in Production Planning and Inventory Control from Jadavpur University, Kolkata. Dr. Das Roy served at the Department of Mathematics, Bethune College, University of Calcutta, West Bengal, India, from 2006–2015. Her research interests are mainly in the area of Inventory Control, Production Planning, Supply Chain Systems, Optimization, and Just-in-time (JIT) modelling. She has published a number of papers in various reputed international journals such as International Journal of Systems Science, Mathematical and Computer Modelling, International Journal of Production Research, International Journal of Management Science and Engineering Management, IMA Journal of Management Mathematics, Journal of Advances in Management Research, RAIRO Operations Research, Computers & Industrial Engineering, OPSEARCH, Sādhanā and so on. She has also acted as a potential reviewer of several reputed journals.

Shib Sankar Sana

Dr. 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 200 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, Nonlinear Phenomena in Complex Systems, Advanced Modeling and Optimization, Vietnam Journal of Mathematics, Yugoslav Journal of Operational Research, International Journal of Operational Research, International Journal of Services Operations Management, International Journal of Modeling, 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 Optimization, 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