Growing items inventory model for carbon emission under the permissible delay in payment with partially backlogging

Growing inventory is the set of commodities whose level enhances during the stocking period. This kind of product is normally seen in the poultry industry and livestock farming. In this model, the live newborn is considered to be the initial inventory of the retailer. These are procured and fed until they grow to an ideal weight during the breeding period. Afterward, these are slaughtered and converted to deteriorating items prone to the customer's demand during the consumption period. The poultry industry is responsible for greenhouse gas emissions during feeding, farming, slaughtering, and handling. Consequently, the retailers are enforced to make efforts to reduce the emission which also affects the inventory demeanor. Therefore, the effect of the carbon emissions from the poultry industry has been investigated here. Generally, customers prefer food over the preserved items so shortages are permitted which has been assumed here with partial backlogging. The study has been carried out to investigate the optimum breeding period and optimum livestock inventory. A numerical example and illustrations validate the analytical results. Lastly, a sensitivity analysis has been provided concerning some key parameters.