A two-phase production inventory model for imperfect quality items with multivariate demand, upstream and downstream credit period offers under a carbon tax, and green subsidy

Abstract

Generating customer-friendly products is a big task nowadays. Green products are famous all over the world now. In quite few manufacturing processes, carbon emissions become an unavoidable fact. To reduce emissions, the government enacted enormous rules and regulations. This developed model consists of a supply chain with two phase production containing defective products and rework through the same manufacturing system, where the product deterioration is considered after production and rework (i.e. where the deterioration starts when the product is out for sale), as three cases: (1) no deterioration, (2) instantaneous deterioration and (3) non-instantaneous deterioration. Demand function is selling price, green product price, advertisement and credit period dependent for first two cases and for case 3, the market scale of the demand is exponentially increasing considering uncertainty. Supplier offers a full credit period offer to the retailer and the retailer gives a partial credit period offer to his customer. Various methods are implemented to reduce carbon emissions during various production processes, and we have implemented preservation technology to reduce emissions even with a carbon tax policy involved. With government subsidies, the greenness of the product is considered to make it more environmental friendly. Numerical examples and sensitivity analysis are carried out to verify the results of the developed model.

KEYWORDS:

• Two-phase imperfect production system
• green product
• green innovation cost
• green subsidy
• cap and trade mechanism
• instantaneous and non-instantaneous deteriorating items
• upstream and downstream credit period offers

AMS CLASSIFICATIONS:

• 90B05
• 90B29
• 90B31

Disclosure statement

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

Additional information

Notes on contributors

C. Jayasankari

Jayasankari Chandramohan is now working as an assistant professor in Department of Science and Humanities in Sree Sakthi Engineering College, Karamadai, Coimbatore. She pursued her doctoral degree as a full-time research scholar in the Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, Tamil Nadu, India, in 2023. She completed her Post Graduate degree (mathematics) in the School of Sciences in Bharathidasan University, Palakalaiperur, Trichy, in 2018. She completed her UG degree (mathematics) in Devanga Arts College, Aruppukottai, in 2016. Her research interests are inventory systems, production inventory management, operations research and supply chain management.

R. Uthayakumar

R. Uthayakumar is currently a professor in the Department of Mathematics at The Gandhigram Rural Institute – Deemed to be University, Gandhigram, India. He received his M.Sc. in Mathematics from the American College, Madurai, India, in 1989 and Ph.D. in Mathematics from The Gandhigram Rural Institute – Deemed to be University, Gandhigram, India, in 2000. He has published about 200 papers in international and national journals. His research interests include the following fields: operations research, industrial engineering and fractal analysis.