Using Excel's Built-In Solver - Product Mix Example
Understanding the Excel Solver Dialogs
To let the Excel Solver know which cells on the worksheet represent the decision variables, constraints and objective function, we click Solver button on the Excel Data tab, or the Premium Solver button on the Add-Ins tab, which displays the Solver Parameters dialog. In the Set Objective (or Set Target Cell) edit box, we type or click on cell F5, the objective function. In the By Changing Variable Cells edit box, we type B4:E4 or select these cells with the mouse. (Click on the image to see it full-size.)
To add the constraints, we click on the Add button in the Solver Parameters dialog and select cells F8:F11 in the Cell Reference edit box (the left hand side), and select cells G8:G11 in the Constraint edit box (the right hand side); the default relation <= is OK. (Click on the image to see it full-size.)
We choose the Add button again (either from the Add Constraint dialog above, or from the main Solver Parameters dialog) to define the non-negativity constraint on the decision variables. (Alternatively, we can check the Make Unconstrainted Variables Non-Negative option in the Solver Parameters dialog.)
When we've completely entered the problem, the Solver Parameters dialog appears as shown below. This is the Excel Solver dialog from Excel 2010; the Solver in earlier versions of Excel have similar elements. Frontline's Premium Solver products can emulate either style, and they also offer a new Ribbon-based user interface. (Click on the image to see it full-size.)
Finding and Using the Solution
To find the optimal solution, we simply click on the Solve button. After a moment, the Excel Solver returns the optimal solution in cells B4 through E4. This means that we should build 23 pallets of Tahoe panels, 15 pallets of Pacific panels, 39 pallets of Savannah panels, and 0 pallets of Aspen panels. This results in a total profit of $58,800 (shown in cell F5). (Click on the image to see it full-size.)
The message "Solver found a solution" appears in the Solver Results dialog, as shown above. (Click on the image to see it full size). We now click on "Answer" in the Reports list box to produce an Answer Report, and click OK to keep the optimal solution values in cells B4:E4.
After a moment, the Solver creates another worksheet containing an Answer Report, like the one below, and inserts it to the left of the problem worksheet in the Excel workbook. (Click on the image to see it full-size.)
This report shows the original and final values of the objective function and the decision variables, as well as the status of each constraint at the optimal solution. Notice that the constraints on glue, pressing, and pine chips are binding and have a slack value of 0. The optimal solution would use up all of these resources; however, there were 28,000 pounds of oak chips left over. If we could obtain additional glue, pressing capacity, or pine chips we could further increase total profits, but extra oak chips would not help in the short run.
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If you've gotten to this point, congratulations! You've successfully set up and solved a simple optimization problem using Microsoft Excel. If you'd like, you can see how to set up and solve the same Product Mix problem using Risk Solver Platform in Excel or using a Visual Basic .NET program that calls Frontline's Solver Platform SDK. If you haven't yet read the other parts of the tutorial, you may want to return to the Tutorial Start and read the overviews "What are Solvers Good For?", "How Do I Define a Model?", "What Kind of Solution Can I Expect?" and "What Makes a Model Hard to Solve?"
This was an example of a linear programming problem. Other types of optimization problems may involve quadratic programming, mixed-integer programming, constraint programming, smooth nonlinear optimization, and nonsmooth optimization. To learn more, click Optimization Problem Types. For a more advanced explanation of linearity and sparsity in optimization problems, continue with our Advanced Tutorial.