Abstract For the production of complex products, this study investigates a flexible production system with a variable production rate as an alternative method to overcome the stock-out risk because of the uncertainty of fuzzy-stochastic demand in an integrated model. The variable production rate enables vendors to fulfill demand uncertainties and reduce the lead time. To establish the relationship between the process quality and production rate three functions, linear, quadratic, and cubic, have been introduced in the mode. The development of such an advanced flexible production system requires a considerably higher setup cost and increases the supply chain cost. To overcome this, the authors introduce a discrete investment function to control setup costs. Authors utilize a crashing cost to reduce the duration of the lead time within the supply chain (SC) structure. In real-life, vendors and buyers face different constraints and set some targets for themselves. Here, the authors consider the storage space and budget constraint for the vendor and customers’ service level constraint for the buyer. An SC model is proposed to find the optimal order quantity, reorder point, lead time, investment for setup cost reduction, and production rate with the minimized total expected cost of the chain. To get the optimal solutions to decision variables, the authors employed a classical optimization technique in the proposed model. An improved algorithm for the global minimum expected cost of SC is designed under the flexible production system. Three numerical examples with comparative study to the previous model and the sensitivity analysis are included to test and validate the proposed model. The numerical analysis and comparative study prove that the proposed model attains the minimum SC cost at the decision variables' optimal values.

中文翻译：

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随机模糊需求下与产品质量相关的最优生产率的多约束供应链模型

摘要 针对复杂产品的生产，本研究研究了一种可变生产率的柔性生产系统，作为克服由于集成模型中模糊随机需求的不确定性导致的缺货风险的替代方法。可变生产率使供应商能够满足需求的不确定性并缩短交货时间。为了建立过程质量和生产率之间的关系，模型中引入了线性、二次和三次函数。开发这种先进的柔性生产系统需要相当高的设置成本并增加供应链成本。为了克服这个问题，作者引入了一个离散投资函数来控制设置成本。作者利用崩溃成本来减少供应链 (SC) 结构内的提前期的持续时间。在现实生活中，卖家和买家面临不同的约束，并为自己设定了一些目标。在这里，作者考虑了供应商的存储空间和预算约束以及买方的客户服务水平约束。提出了一个 SC 模型，以在链的总预期成本最小的情况下找到最佳订货数量、再订货点、提前期、降低设置成本的投资和生产率。为了获得决策变量的最优解，作者在所提出的模型中采用了经典的优化技术。设计了柔性生产系统下SC全局最小预期成本的改进算法。三个数值例子与之前的模型进行了比较研究和敏感性分析，以测试和验证所提出的模型。数值分析和比较研究证明，所提出的模型在决策变量的最优值下达到了最小的 SC 成本。