小婧研学(78):运筹学运输问题的计算机解法

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运筹学运输问题的计算机解法通常借助专业的数学软件或编程语言来实现，以下介绍几种常见的方法：

Computer solutions to transportation problems in operations research are usually implemented with the help of specialized mathematical software or programming languages, and the following are some common methods:

一、使用Excel求解

1. Use Excel to solve

建立模型：在Excel中创建表格，输入运输问题的相关数据，包括产地、销地、产量、销量以及单位运输成本等。

Build a model: Create a table in Excel and enter data related to transportation problems, including origin, sales location, production volume, sales volume, and unit transportation cost.

设置目标函数和约束条件：通过公式计算总运输成本作为目标函数，利用“规划求解”工具设置产量和销量的约束条件。

Set Objective Functions and Constraints: Use formulas to calculate total transportation costs as objective functions, and use the Solver tool to set constraints for production and sales.

求解：运行“规划求解”，Excel会自动找到使总运输成本最小的运输方案。

Solve: Run Solver and Excel will automatically find the transportation solution that minimizes the total transportation cost.

二、使用Python求解

2. Use Python to solve

使用PuLP库：PuLP是一个用于线性规划的Python库。首先定义问题，然后设置变量、目标函数和约束条件，最后调用求解器求解。

Use the PuLP library: PuLP is a Python library for linear programming. Start by defining the problem, then set the variables, objective functions, and constraints, and finally call the solver to solve.

使用SciPy库：SciPy的 optimize 模块也可用于解决运输问题，通过定义目标函数和约束条件，调用优化算法求解。

Using the SciPy library: SciPy's optimize module can also be used to solve transportation problems, by defining objective functions and constraints, and invoking optimization algorithms to solve.

三、使用MATLAB求解

3. Use MATLAB to solve

建立模型：将运输问题转化为线性规划模型，定义目标函数系数向量、约束条件矩阵和向量。

Build a model: Transform the transportation problem into a linear programming model, and define the objective function coefficient vectors, constraint matrices, and vectors.

调用函数：使用 linprog 函数求解线性规划问题，得到最优解和目标函数值。

Call Function: Use the linprog function to solve the linear programming problem and get the optimal solution and the value of the objective function.

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部分参考内容来自百度

翻译来源：谷歌翻译