Optimal sustainable order quantities for growing items

Some industries, such as the livestock and poultry industries, produce “growing items,” which can be defined as items whose weight and value constantly increase over time. This paper details the design and optimization of a sustainable inventory model for such items that considers the environmental effects of Greenhouse Gases (GHGs) emitted from produced manure, fermentation processes, and transportation, as well as their cost with respect to carbon tax. Furthermore, the proposed model also considers the growth patterns for all dead and live grown items, along with mortality and survival probabilities. Additionally, the sustainability of the period length and order quantity of items is optimized in order to minimize the cost function, while still satisfying the environmental constraints on the main sources of emissions. Through a series of examples, we show that our sustainable Economic Order Quantity (EOQ) model is suitable for applications dealing with growing items. To solve these examples, we utilized the “HHO-GWO” algorithm, which is a novel hybrid metaheuristic that combines the advantages of the Harris Hawks Optimizer (HHO) and Grey Wolf Optimization (GWO) algorithms to find much better solutions in fewer iterations. The performance of the HHO-GWO algorithm is compared to that of the HHO and GWO algorithms, as well as Interior Point (IP) solver, with respect to different measures such as quality of generated solutions and CPU-Time. The results indicated that, compared to the HHO and GWO algorithms on their own, the HHO-GWO algorithm generates much better solutions for the proposed model, while also minimizing CPU-Time. The results obtained for the model showed that considering sustainability factors for growing items not only increases the order quantity, but it also shortens the growth cycle significantly. Finally, sensitivity analyses of the parameters and decision variables identified some practical approaches that can be utilized by inventory managers in agriculture industries.