使用LINGO解决线性非线性优化问题指南

需积分: 9 167 浏览量更新于2024-07-31 收藏 3.89MB PDF 举报

"LINGO 11 用户手册是关于使用 LINGO 软件解决线性和非线性优化问题的指南。此软件提供了一种专有的建模语言，便于构建大规模优化模型，并配备了高效的求解器，能快速找到解决方案并进行结果分析。手册中包含了版权信息、商标声明以及免责声明等内容。" 在《Lingo 11 用户手册》中，用户将了解到 LINGO 软件的重要功能和用途。LINGO 是一款强大的工具，设计用于解决各种优化问题，无论是线性的还是非线性的。其核心特性在于其内置的建模语言，使得用户能够方便地表示复杂的数学模型，即使面对大规模的问题也能轻松处理。此外，LINGO 配备了高效的求解引擎，能够快速找到最优解，极大地提高了问题求解的速度和效率。关于软件的法律方面，手册指出 LINGO 软件及其相关文档受版权保护。用户仅能在授权的范围内复制或使用，未经 LINDO Systems Inc. 的书面许可，不得擅自复制。同时，LINGO 和 LINDO 分别是 LINDO Systems Inc. 的商标和注册商标，手册中可能提及的其他产品和公司名称可能是其各自所有者的财产。手册中的免责声明强调，LINDO Systems Inc. 在收到付款时保证提供的软件磁盘包含准确的 LINGO 软件复制品，以及相关文档的准确复制。然而，由于计算机程序和模型的复杂性，软件可能存在错误。因此，用户在依赖软件结果做决策之前，应先验证答案的准确性。LINDO Systems Inc. 及其关联方不对软件或文档提供任何其他明示保修，也不作任何形式的暗示保修。整体而言，《Lingo 11 用户手册》是学习和掌握如何使用 LINGO 解决实际优化问题的重要参考资料，涵盖了软件的使用方法、注意事项以及法律条款，对于科研、工程、经济等领域需要进行优化计算的用户来说极具价值。通过深入阅读和实践，用户将能够有效地运用 LINGO 处理各类优化任务。

2 CHAPTER 1

Most copies of LINGO come with their licenses preinstalled. However, some versions of LINGO

require you to input a license key. If your version of LINGO requires a license key, you will be

presented with the following dialog box when you start LINGO:

Your license key may have been included in an email sent to you when you ordered your software.

The license key is a string of letters, symbols and numbers, separated into groups of four by hyphens

(e.g., r82m-XCW2-dZu?-%72S-fD?S-Wp@). Carefully enter the license key into the edit field,

including hyphens. License keys are case sensitive, so you must be sure to preserve the case of the

individual letters when entering your key. Click the OK button and, assuming the key was entered

correctly, LINGO will then start. In the future, you will be able to run LINGO directly without

entering the key.

Note: If you received your license key by email, then you have the option of cutting-and-pasting it

into the license key dialog box. Cut the key from the email that contains it with the Ctrl+C

key, then select the key field in LINGO dialog box and paste the key with the Ctrl+V key.

If you don’t have a key, you can choose to run LINGO in demo mode by clicking the Demo button. In

demo mode, LINGO has all the functionality of a standard version of LINGO with the one exception

that the maximum problem size is restricted. Demo licenses expire after 30 days.

4 CHAPTER 1

Developing a LINGO Model in Windows

The Problem

For our sample model, we will create a small product-mix example. Let’s imagine that the

CompuQuick Corporation produces two models of computers—Standard and Turbo. CompuQuick can

sell every Standard unit it produces for a profit contribution of $100, and each Turbo unit for a

contribution of $150. At the CompuQuick factory, the Standard computer production line can produce,

at most, 100 computers per day. At the same time, the Turbo computer production line can turn out

120 computers per day. Furthermore, CompuQuick has a limited supply of daily labor. In particular,

there is a total of 160 hours of labor available each day. Standard computers require 1 hour of labor,

while Turbo computers are relatively more labor intense requiring 2 hours of labor. The problem for

CompuQuick is to determine the mix of Standard and Turbo computers to produce each day to

maximize total profit without exceeding line and labor capacity limits.

In general, an optimization model will consist of the following three items:

• Objective Function - The objective function is a formula that expresses exactly

what it is you want to optimize. In business oriented models, this will usually be

a profit function you wish to maximize, or a cost function you want to minimize.

Models may have, at most, one objective function. In the case of our

CompuQuick example, the objective function will compute the company’s profit

as a function of the output of Standards and Turbos.

• Variables - Variables are the quantities you have under your control. You must

decide what the best values of the variables are. For this reason, variables are

sometimes also called decision variables. The goal of optimization is to find the

values of a model’s variables that generate the best value for the objective

function, subject to any limiting conditions placed on the variables. We will

have two variables in our example−one corresponding to the number of

Standards to produce and the other corresponding to the number of Turbos to

produce.

• Constraints - Almost without exception, there will be some limit on the values

the variables in a model can assume—at least one resource will be limited (e.g.,

time, raw materials, your department’s budget, etc.). These limits are expressed

in terms of formulas that are a function of the model’s variables. These formulas

are referred to as constraints because they constrain the values the variables can

take. In our CompuQuick example, we will have one constraint for each

production line and one constraint on the total labor used.

GETTING STARTED 5

Entering the Model

We will now construct the objective function for our example. We will let the variables STANDARD

and TURBO denote the number of Standard and Turbo computers to produce, respectively.

CompuQuick’s objective is to maximize total profit. Total profit is calculated as the sum of the profit

contribution of the Standard computer ($100) multiplied by the total Standard computers produced

(STANDARD) and the profit contribution of the Turbo computer ($150) multiplied by the total Turbo

computers produced (TURBO). Finally, we tell LINGO we want to maximize an objective function by

preceding it with “MAX =”. Therefore, our objective function is written on the first line of our model

window as:

MAX = 100 * STANDARD + 150 * TURBO;

Note: Each mathematical expression in LINGO is terminated with a semicolon. These semicolons

are required. Your model will not solve without them. For more information on the syntax of

LINGO, see below.

Next, we must input our constraints on line capacity and labor supply. The number of Standard and

Turbo computers produced must be constrained to the production line limits of 100 and 120,

respectively. Do this by entering the following two constraints just below the objective function:

STANDARD <= 100;

TURBO <= 120;

In words, the first constraint says the number of Standard computers produced daily (STANDARD)

must be less-than-or-equal-to (<=) the production line capacity of 100. Likewise, the second constraint

says the number of Turbo computers produced daily (TURBO) must be less-than-or-equal-to (<=) its

line capacity of 120.

Note: Since most computers do not have less-than-or-equal-to keys (≤), LINGO has adopted the

convention of using the two character symbol <= to denote ≤. As an alternative, you may

simply enter < to signify less-than-or-equal-to. In a similar manner, >= or > are used to

signify greater-than-or-equal-to (≥).

The final constraint on the amount of labor used can be expressed as:

STANDARD + 2 * TURBO <= 160;

Specifically, the total number of labor hours used (STANDARD + 2 * TURBO) must be

less-than-or-equal-to (<=) the amount of labor hours available of 160.

剩余697页未读，继续阅读

brucewch

粉丝: 0
资源: 7

使用LINGO解决线性非线性优化问题指南

LINGO优化建模教程：深入实例应用

Lingo V18.44+ 中文版：专业优化模型求解软件介绍

LINGO软件学习教程与优化建模资料大全

Lingo_18_Users_Manual.pdf

Lingo与线性规划.pdf

LINGO语言应用讲座.pdf

LINGO软件的使用.pdf

lingo错误代码实用.pdf

用LINGO解决数学问题.pdf

Lingo-11-Users-Manual.rar_lingo

最新资源