linear programming

简明释义

线性规划

英英释义

例句

1.The company used linear programming to optimize its production schedule.

该公司使用线性规划来优化其生产计划。

2.The university offers a course on linear programming as part of its operations research curriculum.

该大学在其运筹学课程中提供关于线性规划的课程。

3.Using linear programming, the chef maximized the use of ingredients while minimizing waste.

厨师利用线性规划最大化原材料的使用，同时最小化浪费。

4.By applying linear programming, the logistics team improved their delivery routes.

通过应用线性规划，物流团队改善了他们的配送路线。

5.The marketing department applied linear programming to allocate budgets across different campaigns effectively.

市场部门应用线性规划有效地分配不同活动的预算。

作文

Linear programming is a mathematical technique used for optimization, where the objective is to maximize or minimize a linear function subject to a set of linear constraints. This method has wide applications in various fields such as economics, business, engineering, and military operations. Understanding linear programming (线性规划) can significantly enhance decision-making processes, especially when resources are limited and must be allocated efficiently.The core of linear programming (线性规划) involves defining a problem in terms of variables, an objective function, and constraints. The variables represent the quantities we want to determine, while the objective function expresses what we aim to optimize—be it profit, cost, time, or any other measurable factor. Constraints are the limitations or requirements that must be satisfied, often expressed as inequalities.For instance, consider a factory that produces two products, A and B. The goal is to maximize profit, which could be represented by the equation: Profit = 40A + 30B, where A and B are the quantities of products A and B produced, respectively. However, the factory has limited resources such as labor hours and raw materials. These limitations can be expressed as constraints, such as:- 2A + B ≤ 100 (labor hours)- A + 3B ≤ 90 (raw materials)- A, B ≥ 0 (non-negativity constraints)By using linear programming (线性规划), one can find the optimal values of A and B that maximize profit without violating any constraints. This process typically involves graphical methods for simple problems or more complex algorithms like the Simplex method for larger problems.Another significant aspect of linear programming (线性规划) is its ability to handle multiple objectives. In real-life scenarios, decisions often involve competing goals. For example, a company might want to maximize profit while minimizing environmental impact. Multi-objective linear programming (线性规划) allows decision-makers to find solutions that balance these conflicting objectives effectively.Moreover, linear programming (线性规划) can also be applied to network flows, transportation problems, and scheduling issues. For example, in transportation problems, the goal may be to minimize shipping costs while meeting demand at various locations. By modeling this scenario with linear programming (线性规划), businesses can determine the most cost-effective way to distribute products.In conclusion, linear programming (线性规划) is a powerful tool that provides a structured approach to solving optimization problems. Its applications are vast and varied, making it an essential technique for anyone involved in decision-making processes. By mastering linear programming (线性规划), individuals and organizations can make informed choices that lead to better resource allocation and enhanced outcomes across multiple sectors.

线性规划是一种用于优化的数学技术，其目标是最大化或最小化一个线性函数，同时满足一组线性约束。这种方法在经济学、商业、工程和军事行动等多个领域有广泛应用。理解线性规划（linear programming）可以显著增强决策过程，尤其是在资源有限且必须有效分配的情况下。线性规划（linear programming）的核心涉及将问题定义为变量、目标函数和约束条件。变量代表我们想要确定的数量，而目标函数则表达了我们希望优化的内容——无论是利润、成本、时间还是其他可测量的因素。约束条件是必须满足的限制或要求，通常以不等式的形式表达。例如，考虑一家生产两种产品A和B的工厂。目标是最大化利润，可以用以下方程表示：利润 = 40A + 30B，其中A和B分别是生产的产品A和B的数量。然而，工厂的资源有限，例如劳动小时和原材料。这些限制可以表达为约束条件，如：- 2A + B ≤ 100（劳动小时）- A + 3B ≤ 90（原材料）- A, B ≥ 0（非负约束）通过使用线性规划（linear programming），人们可以找到最大化利润而不违反任何约束的A和B的最佳值。这个过程通常涉及简单问题的图形方法或更复杂的算法，如单纯形法，用于更大规模的问题。线性规划（linear programming）的另一个重要方面是它能够处理多个目标。在现实生活中，决策往往涉及竞争目标。例如，一家公司可能希望最大化利润的同时最小化环境影响。多目标线性规划（linear programming）允许决策者有效地找到平衡这些相互冲突目标的解决方案。此外，线性规划（linear programming）还可以应用于网络流、运输问题和调度问题。例如，在运输问题中，目标可能是最小化运输成本，同时满足各个地点的需求。通过用线性规划（linear programming）对这一场景建模，企业可以确定最具成本效益的产品分配方式。总之，线性规划（linear programming）是一种强大的工具，为解决优化问题提供了结构化的方法。它的应用广泛多样，使其成为任何参与决策过程的人的基本技术。通过掌握线性规划（linear programming），个人和组织可以做出明智的选择，从而在多个领域实现更好的资源分配和提升结果。