标题： 酸奶供应链中在需求不确定性下的生产与分销计划、调度和路径优化：一个案例研究 显示英文标题

标题： Production and distribution planning, scheduling, and routing optimization in a yogurt supply chain under demand uncertainty: A case study

摘要： 考虑到食品工业的发展及其挑战，如高易腐性，管理食品工业供应链是研究人员和决策者关注的重点。 决策中的不确定性变得尤为重要，特别是在酸奶行业，该行业以复杂性著称。 本研究涉及酸奶供应链中的生产与分销计划、调度和路线安排。 该问题的特点包括多种产品、一个工厂、多个配送中心、多个时期和多种运输方式。 使用混合整数非线性规划（MINLP）模型来最小化总成本，包括生产、设置、加班、未满足需求和运输成本。 此外，在不确定性下应用了鲁棒模糊规划方法，并提出了线性化程序将其转换为线性化的混合整数规划公式。 该问题通过两种数据类型进行测试：三个规模（小、中、大）的示例问题和伊朗Kalle乳制品公司的实际数据。 开发了一种遗传算法（GA）来解决问题，并对其应用进行了必要的修改。 GA的性能与一种精确算法（分支与切割）进行了比较，结果显示公司的生产政策能够每天适应以精确满足需求。 转向小批量生产和更长的保质期使得更好的库存分配成为可能，并避免在不确定情况下出现短缺。 公司的政策能够适应商业环境中的剧烈波动，尽管这需要较高的成本，例如库存维护。 显示英文摘要

摘要： Considering the evolution of the food industry and its challenges, like high perishability, managing the food industry supply chain is a key focus for researchers and decision-makers. Uncertainty in decision-making has gained importance, particularly in the yogurt industry, known for its complexity. This study addresses production and distribution planning, scheduling, and routing in the yogurt supply chain. The problem is characterized by multiple products, a single plant, multiple distribution centers, multiple periods, and various transportation methods. A mixed-integer non-linear programming (MINLP) model is used to minimize total costs, including production, setup, overtime, unmet demand, and transportation. Additionally, a robust fuzzy programming approach is applied under uncertainty, with linearization procedures proposed to convert it into a linearized mixed-integer programming formulation. The problem is tested with two data types: a sample problem in three sizes (small, medium, and large) and real data from Kalle Dairy Company, Iran. A Genetic Algorithm (GA) is developed to solve the problem, with necessary modifications made for its application. The GA's performance is compared to an exact algorithm (Branch & Cut), showing that the company's production policy adapts daily to meet demand precisely. The shift to smaller batch production and longer shelf life allows better stock allocation and avoids shortages in uncertain conditions. The company's policies adapt to severe fluctuations in the business environment, though this requires high costs, such as inventory maintenance.