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

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.