"静态数学优化模型应用与案例分析"

本文参考了数学模型第3版和第2版，首先介绍了静态优化问题的基本概念和建模过程。以第三章简单的优化模型为例，详细讨论了存贮模型、生猪出售时机、森林救火、最优价格、血管分支、消费者均衡等具体问题，展示了在现实世界中普遍存在的优化问题。静态优化问题指最优解是数而非函数，建立静态优化模型的关键在于确定恰当的目标函数，并且一般使用微分法来求解静态优化模型。 在存贮模型问题中，一配件厂需要安排产品的生产计划，考虑到生产准备费和贮存费的影响。厂家生产能力很大，可以在很短时间内产出所需数量。通过分析每天生产一次的情况以及不同生产周期和产量的情况，找出使总费用最小的生产周期和产量，建立了生产周期、产量与需求量、准备费、贮存费之间的关系，并得出了每次1000件、10天生产一次的最优生产方案。 本文通过具体的数学模型问题，展示了如何应用静态优化模型来解决实际生产和管理中的优化问题，强调了确定目标函数和灵活运用微分法的重要性。同时，也提醒了在处理优化问题时需要综合考虑各项费用和因素，寻找最优的决策方案以达到最大效益。Mathematical Modeling, Third Edition, compiled by Jiang Qiyuan, et al., which provide students with the knowledge and skills necessary to successfully model and solve real-world problems. The third chapter of the book focuses on simple optimization models, such as storage models, optimal pricing, and consumer equilibrium. These models are essential in helping businesses and organizations make informed decisions and optimize their resources. One of the key concepts discussed in the text is the idea of static optimization problems where the optimal solution is a number, rather than a function. This chapter also emphasizes the importance of determining the appropriate objective function based on the modeling purpose and using differential calculus to solve static optimization models. Through practical examples like the storage model problem discussed in the text, readers are introduced to the process of establishing relationships between production cycles, product quantities, demand, preparation costs, and storage fees to minimize total costs. Overall, this text provides a comprehensive overview of static optimization models and their application in various real-world scenarios. By understanding the fundamental principles and techniques presented in the book, readers can develop the analytical skills and problem-solving abilities needed to tackle complex optimization problems and make informed decisions in their professional careers.