数学建模(工业工程).

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数学建模,工业工程

Mathematical Modeling

Mathematical Modeling means to solve a practical problem, after making necessary hypotheses and simplification, we use mathematical language, symbols and other appropriate mathematical tools to describe the problem. Finally, we get a mathematical expression or structure of the practical problem. 数学建模就是解决一个实际问題.在作出必要的假设和简化后，运用数学语言、符号等适当的数学工具来描述间題。最后，我们得到了实际问题的数学表达式或结构。

In this course, we learn four kinds of mathematical models in order to apply to practical problems. The first one is basic optimization model. The optimization problem is one of the most frequently encountered problems in the fields of Engineering technology, economic management and scientific research. This part introduces a simpler optimization model, which can be reduced to the function extremum problem in calculus, and can be solved directly by differential method. For example, we can solve the problem of the best time to sell pigs. A pig weighs 200 pounds and gains 5 pounds a day, which costs 45 cents per day. The market price of the pig is 65 cents per pound, but it drops by 1 cent per day, we want to know the best time to sell pigs.

在本课程中，我们学习四种数学模型，以应用于实际问题。

第一种是基本优化模型。优化问题是工程技术、经济管理和科学研究领域中经常遇到的问题之一。这一部分介绍了一个简単的优化模型，它可以化为微积分中的函数极值问題，并可以直接用微分法求解。例如，我们可以解决卖猪的最佳时机问题。一头猪重200磅，每天增重5磅，每天45美分。这头猪的市价是每磅65美分，但每天下降1美分，我们想知道卖猪的最佳时机。 The second one is mathematical programming model. The three elements of it are decision variable, objective function and constraints. The most typical problem that can be solved by this model is assignment problem. Several tasks are assigned to some candidates. As each person has different expertise, the benefits or resources needed to complete each task are different. We want to know how to assign tasks and gain maximal total benefits or spend minimal total resources.

二是数学规划模型。它的三个要素是决策变量、目标函数和约束条件。该模型能解决的最典型问題是分配问题。一些候选人被分配了几项任务。由于每个人都有不同的专长，完成每项任务所需的好处或资源是不同的。我们想知道如何分配任务和获得最大的总收益或花费最少的总资源。

The third one is curve fitting model. A set of discrete points is given, and a simple function is

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