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.

一些行业，例如畜牧业和家禽业，会产生“生长的物品”，可以将其定义为重量和价值随时间不断增加的物品。本文详细介绍了此类物品的可持续库存模型的设计和优化，该模型考虑了粪便产生的温室气体（GHG）对环境的影响，发酵过程和运输以及其碳税成本。此外，提出的模型还考虑了所有死活活物的生长方式，以及死亡率和生存率。此外，优化了物料的期间长度和订单数量的可持续性，以使成本函数最小化，同时仍满足主要排放源的环境约束。通过一系列示例，我们表明我们的可持续经济订单数量（EOQ）模型适用于处理增长项目的应用。为了解决这些示例，我们利用了“ HHO-GWO”算法，这是一种新颖的混合元启发式算法，结合了Harris Hawks Optimizer（HHO）和Gray Wolf Optimization（GWO）算法的优势，可以在更少的迭代中找到更好的解决方案。关于HHO-GWO算法的性能与HHO和GWO算法以及内部点（IP）求解器的性能进行了比较，例如生成的解决方案的质量和CPU时间。结果表明，与单独使用HHO和GWO算法相比，HHO-GWO算法为所提出的模型生成了更好的解决方案，同时还最大程度地减少了CPU时间。该模型获得的结果表明，考虑增长项目的可持续性因素不仅增加了订单数量，而且显着缩短了增长周期。最后，对参数和决策变量的敏感性分析确定了一些实用的方法，可供农业行业的库存管理人员使用。