Define and solve a problem by using Solver

Solver is part of a suite of commands sometimes called what-if analysis (what-if analysis: A process of changing the values in cells to see how those changes affect the outcome of formulas on the worksheet. For example, varying the interest rate that is used in an amortization table to determine the amount of the payments.) tools. With Solver, you can find an optimal (maximum or minimum) value for a formula (formula: A sequence of values, cell references, names, functions, or operators in a cell that together produce a new value. A formula always begins with an equal sign (=).) in one cell — called the objective cell — subject to constraints, or limits, on the values of other formula cells on a worksheet. Solver works with a group of cells, called decision variables or simply variable cells, that participate in computing the formulas in the objective and constraint cells. Solver adjusts the values in the decision variable cells to satisfy the limits on constraint cells and produce the result you want for the objective cell.

Note    Earlier versions of Solver referred to the objective cell as the "target cell," and the decision variable cells as "changing cells" or "adjustable cells."

In this article


Overview

Use Solver to determine the maximum or minimum value of one cell by changing other cells. For example, you can change the amount of your projected advertising budget and see the effect on your projected profit amount.

Example of a Solver evaluation

In the following example, the level of advertising in each quarter affects the number of units sold, indirectly determining the amount of sales revenue, the associated expenses, and the profit. Solver can change the quarterly budgets for advertising (decision variable cells B5:C5), up to a total budget constraint of $20,000 (cell F5), until the total profit (objective cell F7) reaches the maximum possible amount. The values in the variable cells are used to calculate the profit for each quarter, so they are related to the formula objective cell F7, =SUM(Q1 Profit:Q2 Profit).


Before Solver evaluation

Callout 1 Variable cells
Callout 2 Constrained cell
Callout 3 Objective cell

After Solver runs, the new values are as follows.

After Solver evaluation

Top of Page Top of Page

Define and solve a problem

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

Analysis group on the Data tab

If the Solver command or the Analysis group is not available, you need to load the Solver Add-in (add-in: A supplemental program that adds custom commands or custom features to Microsoft Office.) program.

ShowHow to load the Solver Add-in program

  1. Click the File tab, click Options, and then click the Add-Ins category.
  2. In the Manage box, click Excel Add-ins, and then click Go.
  3. In the Add-ins available box, select the Solver Add-in check box, and then click OK.

  1. In the Set Objective box, enter a cell reference (cell reference: The set of coordinates that a cell occupies on a worksheet. For example, the reference of the cell that appears at the intersection of column B and row 3 is B3.) or name (name: A word or string of characters that represents a cell, range of cells, formula, or constant value. Use easy-to-understand names, such as Products, to refer to hard to understand ranges, such as Sales!C20:C30.) for the objective cell. The objective cell must contain a formula.
  2. Do one of the following:
  • If you want the value of the objective cell to be as large as possible, click Max.
  • If you want the value of the objective cell to be as small as possible, click Min.
  • If you want the objective cell to be a certain value, click Value of, and then type the value in the box.
  1. In the By Changing Variable Cells box, enter a name or reference for each decision variable cell range. Separate the nonadjacent references with commas. The variable cells must be related directly or indirectly to the objective cell. You can specify up to 200 variable cells.
  2. In the Subject to the Constraints box, enter any constraints that you want to apply by doing the following:
  1. In the Solver Parameters dialog box, click Add.
  2. In the Cell Reference box, enter the cell reference or name of the cell range for which you want to constrain the value.
  3. Click the relationship ( <=, =, >=, int, bin, or dif ) that you want between the referenced cell and the constraint.

If you click int, integer appears in the Constraint box. If you click bin, binary appears in the Constraint box. If you click dif, alldifferent appears in the Constraint box.

  1. If you choose <=, =, or >= for the relationship in the Constraint box, type a number, a cell reference or name, or a formula.
  2. Do one of the following:
    • To accept the constraint and add another, click Add.
    • To accept the constraint and return to the Solver Parameters dialog box, click OK.

Note    You can apply the int, bin, and dif relationships only in constraints on decision variable cells.

You can change or delete an existing constraint by doing the following:

  1. In the Solver Parameters dialog box, click the constraint that you want to change or delete.
  2. Click Change and then make your changes, or click Delete.
  1. Click Solve and do one of the following:
  • To keep the solution values on the worksheet, in the Solver Results dialog box, click Keep Solver Solution.
  • To restore the original values before you clicked Solve, click Restore Original Values.

Notes    

  • You can interrupt the solution process by pressing ESC. Microsoft Excel recalculates the worksheet with the last values that are found for the decision variable cells.
  • To create a report that is based on your solution after Solver finds a solution, you can click a report type in the Reports box and then click OK. The report is created on a new worksheet in your workbook. If Solver doesn't find a solution, only certain reports or no reports are available.
  • To save your decision variable cell values as a scenario that you can display later, click Save Scenario in the Solver Results dialog box, and then type a name for the scenario in the Scenario Name box.

Top of Page Top of Page

Step through Solver trial solutions

  1. After you define a problem, click Options in the Solver Parameters dialog box.
  2. In the Options dialog box, select the Show Iteration Results check box to see the values of each trial solution, and then click OK.
  3. In the Solver Parameters dialog box, click Solve.
  4. In the Show Trial Solution dialog box, do one of the following:
    • To stop the solution process and display the Solver Results dialog box, click Stop.
    • To continue the solution process and display the next trial solution, click Continue.

Top of Page Top of Page

Change how Solver finds solutions

  1. In the Solver Parameters dialog box, click Options.
  2. Choose or enter values for any of the options on the All Methods, GRG Nonlinear, and Evolutionary tabs in the dialog box.

Top of Page Top of Page

Save or load a problem model

  1. In the Solver Parameters dialog box, click Load/Save.
  2. Enter a cell range for the model area, and click either Save or Load.

When you save a model, enter the reference for the first cell of a vertical range of empty cells in which you want to place the problem model. When you load a model, enter the reference for the entire range of cells that contains the problem model.

Tip    You can save the last selections in the Solver Parameters dialog box with a worksheet by saving the workbook. Each worksheet in a workbook may have its own Solver selections, and all of them are saved. You can also define more than one problem for a worksheet by clicking Load/Save to save problems individually.

Top of Page Top of Page

Solving methods used by Solver

You can choose any of the following three algorithms or solving methods in the Solver Parameters dialog box:

  • Generalized Reduced Gradient (GRG) Nonlinear    Use for problems that are smooth nonlinear.
  • LP Simplex    Use for problems that are linear.
  • Evolutionary    Use for problems that are non-smooth.

For more information about these methods, contact:

Frontline Systems, Inc.
P.O. Box 4288
Incline Village, NV 89450-4288
(775) 831-0300
Web site: http://www.solver.com
E-mail: info@solver.com

Portions of the Solver program code are copyright 1990-2009 by Frontline Systems, Inc. Portions are copyright 1989 by Optimal Methods, Inc.

Top of Page Top of Page

More help on using Solver

For more detailed help on Solver from Frontline Systems, visit Solver Help at www.solver.com.

Top of Page Top of Page

 
 
Applies to:
Excel 2010