Sử dụng hàm Solver trong Excel

Cách sử dụng hàm Solver trong Excel, ứng dụng vào tính toán trong môn Quy hoạch tuyến tính

Linear Programming Using Excel

Subject: Linear Programming using Excel

Application: Microsoft Excel 2007

Task: Solving a Linear Program Using Excel

Install the Solver Add-In

1 In the Microsoft Office button, go to excel options to click Add-ins

2 In the Add-Ins box, select Solver Add-In and click Go

3 In the Add-Ins available box, check the Analysis ToolPak and then OK

4.2 Exercises 307

To initiate the program, select PRGM <SMPLX> ENTER , and you will see the screens

Enter the first pivot column, column 1 and ENTER , to obtain the screens

The ratios 240 and 150 indicate the second row is the pivot row Press ENTER and enter 2

Press ENTER to obtain the next tableau

A B C D

1

3

Using Solver

Excel has a program, Solver, that does the computations for a linear programming problem We use the

follow-ing example to illustrate how it is used

Maximize z 5 5x1 1 8x2 1 7x3 subject to

3x1 1 2x2 1 x3 660

x1 1 4x2 1 2x3 740

2x1 1 x2 1 3x3 853

x1 0, x2 0, x3 0 Here’s how we set up the problem

We use the cells A1:C1 for the values of the variables x1, x2, and x3 Solver will adjust the values of the

variables until the objective function reaches the optimal value We begin by entering x1 5 0 in A1, x2 5 0 in

B1, and x3 5 0 in C1 Next we enter the formulas for the left side of the constraints, the nonnegative conditions and the objective function in column D, and the number on the right side in column E

Unless otherwise noted, all content on this page is © Cengage Learning.

Copyright 2012 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has

To start up Solver, click on the Data tab Move to the Analysis group and click on Solver.

• Place the cursor in the box next to Set Target Cell, or Set Objective, depending on your version of Excel.

• Select cell D7, since this is the location of the formula for the objective function.

• Check the button to maximize, since this is a maximization problem.

Place the cursor in the box under By changing cells: and then select cells A1:C1 (the cells containing the

variables)

You are now ready to enter the constraints

Move the cursor to the box under Subject to the Constraints: and click on the button shown as Add to

obtain

Make sure the cursor is in the box under Cell Reference: and select cell D1; then move the cursor to the box

under Constraint: and select the cell E1.

Click the Add button Repeat the preceding step using cells D2 and E2, then D3 and E3 Click Ok.

You have entered the constraints Note that the constraints have the symbol ,5 between Cell Reference:

and Constraint: (this represents #).

4.2 Exercises 309

Click on the Add button to enter the nonnegative conditions Again place the cursor in the Cell Reference: box and select cell D4 Then select E4 for the Constraint: box Since this is a nonnegative condition, we need the $ symbol; get it by selecting 5 Then click Add.

In the same way, enter the nonnegative constraints using D5, E5 and D6, E6 You will then have the screen

Now set the options for Solver, depending on your version.

Click into the Options box, and make sure Make sure the Simplex LP method is selected in the

that the Assume Linear Model checkbox is dialog box

checked, as in the following figure

Leave all other options as is, and click Ok.

Click on the Solve button to obtain the solution.

The maximum value of z 5 2386 at (116, 63, 186).

Unless otherwise noted, all content on this page is © Cengage Learning.

Copyright 2012 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has