Two layers green supply chain imperfect production inventory model under bi-level credit period

This article focuses on an integrated production inventory model with rework of the imperfect units and stock dependent demands of the customer from several retailers. There is an opportunity to build a model to measure the amount of carbon emissions during the time of production and the corresponding rate of carbon emission parameters are random which follows Beta distribution. Here, the rate of imperfectness is assumed to be a function of time and production rate. In this paper, a manufacturer–retailer–customer chain system is developed in which the retailer gets an upstream trade credit period from the manufacturer and retailers offer a downstream trade credit period to customers to stimulate demand as well as sales and reduce inventory. The model has been developed as a profit maximization problem with respect to the manufacturer and retailers. Finally, several numerical examples and sensitivity analysis are provided to illustrate the model.