This paper studies the problem of pricing and inventory planning for a vendor of non-instantaneous deteriorating items under partially backlogged shortages with greening investment. The demand of customers and inventory control variables are affected by greening programs. The primary objective of this paper is to determine the optimal sales price, replenishment schedule, and order quantity per inventory cycle under different greenness levels, which will help maximize the vendor’s total profit. The problem is formulated as a non-linear optimization model in which an analytical approach is applied in order to find the optimal solution. Using several mathematical theorems, it has been proven that the optimal solution not only exists but also is unique. In order to show the efficacy of the proposed model, a real case study in the round beef industry is analyzed. Furthermore, a sensitivity analysis is conducted to help find managerial insights. The results indicate the range of greening cost that positively influences the demand and total profit for the vendor. Additionally, the vendor’s inventory planning is designed and differentiated according to the demand function and greenness level.

本文研究了在绿色投资的情况下部分积压的短缺情况下非瞬时恶化物品供应商的定价和库存计划问题。客户的需求和库存控制变量受绿化程序影响。本文的主要目的是确定在不同绿色水平下的最佳销售价格，补货时间表和每个库存周期的订单数量，这将有助于最大化卖方的总利润。该问题被表述为非线性优化模型，在该模型中，为了找到最优解，应用了一种分析方法。使用几个数学定理，已证明最佳解决方案不仅存在，而且是唯一的。为了显示所提出模型的功效，分析了圆形牛肉行业的实际案例。此外，进行了敏感性分析以帮助找到管理上的见解。结果表明，绿化成本的范围对供应商的需求和总利润有积极影响。此外，根据需求函数和绿色程度设计和区分供应商的库存计划。