Define and solve a problem by using Solver

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're related to the formula objective cell F7, =SUM (Q1 Profit:Q2 Profit).

1. Variable cells

2. Constrained cell

3. Objective cell

After Solver runs, the new values are as follows.

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

   Note: If the Solver command or the Analysis group isn't available, you need to activate the Solver add-in. For more information, see How to activate the Solver add-in.

   

2. In the Set Objective box, enter a cell reference or name for the objective cell. The objective cell must contain a formula.

3. Do one of the following steps.

   • If you want the value of the objective cell to be as large as possible, select Max.

   • If you want the value of the objective cell to be as small as possible, select Min.

   • If you want the objective cell to be a certain value, select Value of, and then type the value in the box.

   • 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.

4. In the Subject to the Constraints box, enter any constraints that you want to apply by doing the following steps.

   1. In the Solver Parameters dialog box, select 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. Select the relationship ( <=, =, >=, int, bin, or dif ) that you want between the referenced cell and the constraint. If you select ​​​​​​​int, integer appears in the Constraint box. If you select bin, binary appears in the Constraint box. If you select ​​​​​​​dif, alldifferent appears in the Constraint box.

   4. If you choose <=, =, or >= for the relationship in the Constraint box, type a number, a cell reference or name, or a formula.

   5. Do one of the following steps.

      • To accept the constraint and add another, select Add.

      • To accept the constraint and return to the Solver Parameters dialog box, select OK.

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

   6. You can change or delete an existing constraint by doing the following actions.

      • In the Solver Parameters dialog box, select the constraint that you want to change or delete.

      • Select Change and then make your changes or select Delete.

5. Select Solve and do one of the following actions.

   • To keep the solution values on the worksheet, in the Solver Results dialog box, select Keep Solver Solution.

   • To restore the original values before you selected Solve, select Restore Original Values.

   • You can interrupt the solution process by pressing Esc. Excel recalculates the worksheet with the last values that it found for the decision variable cells.

   • To create a report that's based on your solution after Solver finds a solution, select a report type in the Reports box and then select 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, select Save Scenario in the Solver Results dialog box, and then type a name for the scenario in the Scenario Name box.

1. After you define a problem, select 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 select OK.

3. In the Solver Parameters dialog box, select Solve.

4. In the Show Trial Solution dialog box, do one of the following actions.

   • To stop the solution process and display the Solver Results dialog box, select Stop.

   • To continue the solution process and display the next trial solution, select Continue.

1. In the Solver Parameters dialog box, select Options.

2. Choose or enter values for any of the options on the All Methods, GRG Nonlinear, and Evolutionary tabs in the dialog box.

1. In the Solver Parameters dialog box, select Load/Save.

2. Enter a cell range for the model area and select either Save or Load.

   When you save a model, enter the reference for the first cell of a vertical range of empty cells where 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 can have its own Solver selections, and all of them are saved. You can also define more than one problem for a worksheet by selecting Load/Save to save problems individually.

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.

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 D5), until the total profit (objective cell D7) reaches the maximum possible amount. The values in the variable cells are used to calculate the profit for each quarter, so they're related to the formula objective cell D7, =SUM(Q1 Profit:Q2 Profit).

Variable cells

Constrained cell

Objective cell

After Solver runs, the new values are as follows.

1. Select Data > Solver.

   

2. In Set Objective, enter a cell reference or name for the objective cell.

   Note: The objective cell must contain a formula.

3. Do one of the following steps.

   To	Do this
   Make the value of the objective cell as large as possible	Select Max.
   Make the value of the objective cell as small as possible	Select Min.
   Set the objective cell to a certain value	Select Value Of and then type the value in the box.

4. 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.

5. In the Subject to the Constraints box, add any constraints that you want to apply.

   To add a constraint, follow these steps.

   1. In the Solver Parameters dialog box, select 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. On the <= relationship pop-up menu, select the relationship that you want between the referenced cell and the constraint. If you choose <=, =, or >=, in the Constraint box, type a number, a cell reference or name, or a formula.

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

   4. Do one of the following actions.

   To	Do this
   Accept the constraint and add another	Select Add.
   Accept the constraint and return to the Solver Parameters dialog box	Select OK.

6. Select Solve, and then do one of the following actions.

   To	Do this
   Keep the solution values on the sheet	Select Keep Solver Solution in the Solver Results dialog box.
   Restore the original data	Select Restore Original Values.

1. Select Data > Solver.

   

2. After you define a problem, in the Solver Parameters dialog box, select Options.

3. Select the Show Iteration Results check box to see the values of each trial solution, and then select OK.

4. In the Solver Parameters dialog box, select Solve.

5. In the Show Trial Solution dialog box, do one of the following actions.

   To	Do this
   Stop the solution process and display the Solver Results dialog box	Select Stop.
   Continue the solution process and display the next trial solution	Select Continue.

1. Select Data > Solver.

   

2. Select Options, and then in the Options or Solver Options dialog box, choose one or more of the following options:

   To	Do this
   Set solution time and iterations	On the All Methods tab, under Solving Limits, in the Max Time (Seconds) box, type the number of seconds that you want to allow for the solution time. Then, in the Iterations box, type the maximum number of iterations that you want to allow. Note: If the solution process reaches the maximum time or number of iterations before Solver finds a solution, Solver displays the Show Trial Solution dialog box.
   Set the degree of precision	On the All Methods tab, in the Constraint Precision box, type the degree of precision that you want. The smaller the number, the higher the precision.
   Set the degree of convergence	On the GRG Nonlinear or Evolutionary tab, in the Convergence box, type the amount of relative change that you want to allow in the last five iterations before Solver stops with a solution. The smaller the number, the less relative change is allowed.

3. Select OK.

4. In the Solver Parameters dialog box, select Solve or Close.

1. Select Data > Solver.

   

2. Select Load/Save, enter a cell range for the model area, and then select either Save or Load.

   When you save a model, enter the reference for the first cell of a vertical range of empty cells where 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 sheet by saving the workbook. Each sheet 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 sheet by selecting Load/Save to save problems individually.

1. Select Data > Solver.

   

2. On the Select a Solving Method pop-up menu, select one of the following: