Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment

Abstract

In this paper, we develop a closed-loop supply chain model with two suppliers, one manufacturer and one retailer. The manufacturer produces a single product in batches using fresh raw materials and used items. Fresh raw materials can be obtained from primary and secondary suppliers. The primary supplier is cheaper but may not provide the exact ordered quantity, whereas the secondary supplier is expensive but always offers the exact ordered quantity. Random return of used product and stochastic lead time at the retailer are assumed in this model. The market demand of the finished product is linearly dependent on the retail price and quality, and the production process is subject to learning. A numerical example is taken to illustrate the developed model and perform sensitivity analysis. It is observed that learning in production has significant positive effect on the optimal decisions of the closed-loop supply chain.

Keywords:

• Supply chain
• stochastic lead time
• learning
• price and quality dependent
• demand
• random return

Acknowledgments

Authors are sincerely thankful to the esteemed reviewers for their comments and suggestions based on which the manuscript has been improved.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research support from Department of Science and Technology, Government of India (IF160066) is gratefully acknowledged.

Notes on contributors

B. C. Giri

B. C. Giri is a Professor in the Department of Mathematics, Jadavpur University, Kolkata, India. He did his M.S. in Mathematics and Ph.D. in Operations Research both from Jadavpur University, Kolkata, India. His research interests include inventory/supply chain management, production planning and scheduling, reliability and maintenance, and his research papers have appeared in Naval Research Logistics, International Journal of Production Research, OMEGA, Journal of the Operational Research Society, European Journal of Operational Research, International Journal of Production Economics, Journal of Cleaner Production, and other journals. He was a JSPS Research Fellow at Hiroshima University, Japan, during the period 2002–2004, Humboldt Research Fellow at Mannheim University, Germany, during the period 2007–2008 and a Fulbright-Nehru Senior Research Fellow at Louisiana State University, USA, in 2012.

M. Masanta

M. Masanta is a Ph.D. scholar in the Department of Mathematics, Jadavpur University, Kolkata, India. She received her B.Sc. and M.Sc. degrees in Mathematics from Jadavpur University, India. Her research interests include inventory/supply chain management, production planning, learning, etc.