Different from previous researches, our study considers a perishable item with collaborative vendor–buyer ordering policy and finite replenishment rate. Furthermore, due to the importance of inventory and capital investment in today’s fuzzy marketing environments, researches in fuzzy collaborative inventory models have become very popular research in recent decades. Therefore, in our integrated model with deteriorating inventory replenishment policy, we construct the crisp/fuzzy models with inventory investment constraints with fuzzy environments. Two different fuzzy decision-making methods are used to formulate the models. Convex fuzzy programming (CFP) method is used to maximize the weighted sum for each achievement level of the joint cost and constraints. An inverse weighted fuzzy non-linear programming (IWFNLP) is then proposed to satisfy the decision-maker’s desirable achievement level of service. A heuristic algorithm with mixed-integer hybrid differential evolution (MIHDE) is developed to solve the crisp/fuzzy models. Numerical examples and sensitivity analysis are developed to investigate the effectiveness of the proposed method in the fuzzy environment. From the numerical analysis, it can be seen that the IWFNLP method is a more efficient decision-making tool than the CFP method.

与以前的研究不同，我们的研究考虑了具有协同供应商-购买者订购政策和有限补货率的易腐物品。此外，由于在当今的模糊营销环境中库存和资本投资的重要性，近几十年来，模糊协作库存模型的研究已成为非常流行的研究。因此，在具有恶化的库存补货策略的集成模型中，我们构建了带有模糊环境的具有库存投资约束的明晰/模糊模型。使用两种不同的模糊决策方法来建立模型。凸模糊规划（CFP）方法用于使联合成本和约束的每个实现水平的加权总和最大化。然后提出逆加权模糊非线性规划（IWFNLP），以满足决策者所期望的服务水平。提出了一种混合整数混合差分进化算法（MIHDE）的启发式算法，用于求解清晰/模糊的模型。通过数值算例和灵敏度分析，研究了该方法在模糊环境下的有效性。从数值分析可以看出，与CFP方法相比，IWFNLP方法是一种更有效的决策工具。通过数值算例和灵敏度分析，研究了该方法在模糊环境下的有效性。从数值分析可以看出，与CFP方法相比，IWFNLP方法是一种更有效的决策工具。通过数值算例和灵敏度分析，研究了该方法在模糊环境下的有效性。从数值分析可以看出，与CFP方法相比，IWFNLP方法是一种更有效的决策工具。