Optimal economic growing quantity for reproductive farmed animals under profitable by-products and carbon emission considerations

Some agricultural industries such as livestock and poultry farming produce "growing items" whose weight and value constantly increase over time. Growing items and their related industries are vital in supplying the needed food and fiber for the world population. More importantly, concerns for the preservation of natural resources have led to sustainable goals of reducing greenhouse gas emissions (GHGEs) released by growing items. Recently, an inventory system called "economic growing quantity (EGQ)" was designed for growing items. This paper designs, develops, and optimizes a sustainable model for EGQ system, entitled "sustainable EGQ (SEGQ)", where the hidden costs and revenues associated with the sustainability of growing items are considered under a carbon tax policy. The cost function incorporates purchasing, transportation, feeding, shortage, setup, holding, and carcass disposal costs as well as the tax costs of greenhouse gas (GHG) emitted from manure, feed fermentation, carcasses, holding and transportation processes. The revenue function takes the earned income from the sale of grown items as well as their byproducts into account. Accordingly, a nonlinear program (NLP) is developed to maximize the total profit. The novelty of this paper resides in its consideration of the reproductive patterns and byproducts of growing items, gradual sales, shortage costs, major sources of GHGEs and their hidden costs, and finally a design of the main variables to mitigate the GHGs emitted by the growing items. Findings demonstrate that the SEGQ model with reproducible items and profitable byproducts increases the growth cycle and decreases the quantity of growing items needed at the start of the inventory cycle.