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Preparation

NOTE: INSERT1 and INSERT2 (see below) have been emailed to you.

1. If you have a Mac, visit and read www.solver.com/using-frontline-solvers-macintosh. To use the software for this course, you’ll need to install Windows alongside Mac OSX, and install Excel or Office for Windows. This will also allow you to use other Windows software, as well as Mac software on your machine.

2. Check whether you have 32-bit or 64-bit Excel – this determines which software version you should download. You probably have 32-bit Excel. You have 64-bit ONLY if (i) in Excel 2010, you click File – Help, and you see 64-bit in the lower right, or (ii) in Excel 2013, you click File – Account – About Excel, and you see 64-bit at the top of the dialog.

Registration

1. Point your browser to www.solver.com/student. (Do not attempt to register or download anywhere else on Solver.com – this will cause trouble later.)

2. Fill out the form on this page. Enter your email address (to ensure you receive your license activation code), enter a login password you can remember, enter your first and last name, and University of Notre Dame for your school.

3. Enter INSERT1 for the Textbook Code and INSERT2 for the Course Code. These are special for our course – entering these will give you a 140-day license. (Leaving them blank will give you a 15-day license.)

4. Check the box to acknowledge that you accept the Frontline Systems license agreement. Note: Frontline receives no money from you, or the textbook publisher, or the university; this free 140-day license is a courtesy that they offer to students.

5. Click the button Register to Download. If everything is OK, this will take you to the Download page.

Download

1. On the Download page, change 32-bit to 64-bit ONLY if you’ve confirmed that you have 64-bit Excel (see above). Click the blue Download Now button.

2. In some browsers you will see a dialog 'Do you want to run or save this file?' Click Save to save the file, named either SolverSetup.exe or SolverSetup64.exe.

3. Now check your email, at the email address you entered above, for a message containing an installation password and a license activation code. Frontline sends this email twice, from different servers, to ensure that you receive it. If you don’t get it, visit www.solver.com/installation-password-request and login to request another email message.

Installation

1. Make sure that Excel is closed (not running), then run the program SolverSetup.exe (or SolverSetup64.exe). SolverSetup will prompt you to enter the password and activation code from the email message above – enter them exactly as shown in the email (you can copy and paste).

2. The SolverSetup program will prompt you to choose between Analytic Solver Platform, Risk Solver Platform and XLMiner. Choosing Analytic Solver Platform gives you all the features of Risk Solver Platform and XLMiner, so this is usually the best choice. You can CHANGE this choice later in Excel, by choosing a menu option Help – Change Product on the Ribbon.

3. When the SolverSetup program finishes, start Excel (the last Setup dialog prompts you to do this). You should see new tabs on the Ribbon for Analytic Solver Platform or Risk Solver Platform, and XLMiner. Click the Solver Platform tab – you should see a “Welcome” dialog with various links. Use the Help dropdown menu to open Help text, the User Guide and Reference Guide, and load example workbooks.

If all has gone well, you’re ready for our class exercises. If you have problems, the best avenues to get help are to email support@solver.com (this creates a support ticket in Frontline’s Help Desk) or start a Live Chat from any page on www.solver.com, or from within Excel (Help – Support Live Chat).

Load the Solver Add-in | Formulate the Model | Trial and Error | Solve the Model

Excel includes a tool called solver that uses techniques from the operations research to find optimal solutions for all kind of decision problems.

Load the Solver Add-in

To load the solver add-in, execute the following steps.

1. On the File tab, click Options.

2. Under Add-ins, select Solver Add-in and click on the Go button.

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3. Check Solver Add-in and click OK.

4. You can find the Solver on the Data tab, in the Analyze group.

Formulate the Model

The model we are going to solve looks as follows in Excel.

1. To formulate this linear programming model, answer the following three questions.

a. What are the decisions to be made? For this problem, we need Excel to find out how much to order of each product (bicycles, mopeds and child seats).

b. What are the constraints on these decisions? The constrains here are that the amount of capital and storage used by the products cannot exceed the limited amount of capital and storage (resources) available. For example, each bicycle uses 300 units of capital and 0.5 unit of storage.

c. What is the overall measure of performance for these decisions? The overall measure of performance is the total profit of the three products, so the objective is to maximize this quantity.

2. To make the model easier to understand, create the following named ranges.

3. Insert the following three SUMPRODUCT functions.

Explanation: The amount of capital used equals the sumproduct of the range C7:E7 and OrderSize. The amount of storage used equals the sumproduct of the range C8:E8 and OrderSize. Total Profit equals the sumproduct of UnitProfit and OrderSize.

Trial and Error

With this formulation, it becomes easy to analyze any trial solution.

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For example, if we order 20 bicycles, 40 mopeds and 100 child seats, the total amount of resources used does not exceed the amount of resources available. This solution has a total profit of 19000.

It is not necessary to use trial and error. We shall describe next how the Excel Solver can be used to quickly find the optimal solution.

Solve the Model

To find the optimal solution, execute the following steps.

1. On the Data tab, in the Analyze group, click Solver.

Enter the solver parameters (read on). The result should be consistent with the picture below.

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You have the choice of typing the range names or clicking on the cells in the spreadsheet.

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2. Enter TotalProfit for the Objective.

3. Click Max.

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4. Enter OrderSize for the Changing Variable Cells.

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5. Click Add to enter the following constraint.

6. Check 'Make Unconstrained Variables Non-Negative' and select 'Simplex LP'.

7. Finally, click Solve.

Result:

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The optimal solution:

Conclusion: it is optimal to order 94 bicycles and 54 mopeds. This solution gives the maximum profit of 25600. This solution uses all the resources available.