Solver in Excel

The solver in excel is an analysis tool that helps find solutions to complex business problems requiring crucial decisions to be made. For every problem, the goal (objective), variables, and constraints are identified. The solver returns an optimal solution which sets accurate values of the variables, satisfies all constraints, and meets the goal.

For example, the solver helps create the most appropriate project schedule, minimize an organization’s expenses on transportation of its employees, maximize the profits generated by a given marketing plan, and so on.

The solver can solve the following types of problems:

• Optimization problems where profits need to be maximized and costs need to be minimized
• Arithmetic equations
• Linear and nonlinear problems

In optimization problems, the solver in excel helps to minimize or maximize the objective based on certain variables. Being known as a “what-if analysis” tool, the solver is enabled by the “add-ins” option or the Developer tab of Excel.

For solving a problem, the user has to input certain parameters based on which the solver operates. The tasks of the user followed by the functions of the solver are listed as under:

• Identify the goal (objective) of the problem–This tells the solver what has to be done, thereby lending a direction to the solver.
• Choose the variables of the problem–This tells the solver the areas it has to work upon. The solver in excel returns the most appropriate values of the variables that meet the goal.
• Set the constraints of the problem–This tells the solver to work within the limits defined by the constraints. The solver returns a solution that meets the goal and, at the same time, does not go beyond these limitations.

Hence, the entire solution is focused on the goal of the problem. The solver returns the best possible solution for a problem keeping in mind the set of controls.

The “solver add-in” is not enabled by default in Excel. The two ways to activate the “add-in” are stated as follows:

a. With the “add-ins” option of the File menu

b. With the Developer tab

b. The steps under the Developer tab option are listed as follows:

• In the Developer tab, click on “Excel add-ins” in the “add-ins” group. Select the checkbox “solver add-in” and click “Ok.”

• Once installed, the “solver” button appears in the “analysis” group of the Data tab.

The solver model consists of the objective cells, variable cells, constraints, and formulas that interconnect these components. The excel solver finds an optimal solution to the formula mentioned in the objective cell by changing the variable data cells, given the restrictions of the constraint cells.

Let us understand the terminologies used in the “solver parameters” dialog box. This will be helpful when running the solver. The terms are defined as follows:

• Objective cell: This is a single cell which contains a formula. The formula is decision-based and subject to the restrictions of the constraint cells. The value of the objective cell can be minimized, maximized, or set equal to the specified target value.

• Decision variable or variable cells: These are the cells in which the solver returns the values based on the objective of the problem. Since these data cells are variable, they can be changed with respect to the objective. In Excel, up to 200 variable cells can be specified.
• Constraint cells: These are the limitations within which the given problem is solved. In other words, they are the conditions that should be satisfied.

The three methods to solve the data in the excel solver are listed as follows:

1. GRG nonlinear

The acronym “GRG” stands for “generalized reduced gradient nonlinear.” This method helps solve nonlinear problems. A nonlinear problem may have more than one feasible region. Alternatively, it may have a set of similar values for the variable cells with all the constraints being satisfied.

2. Simplex LP

The acronym “LP” stands for linear problems. This method helps solve linear programming problems and works faster than the GRG nonlinear method. In a linear programming problem, a single objective has to be maximized or minimized subject to certain conditions.

The simplex LP and GRG nonlinear method both are used for smooth problems.

3. Evolutionary

This method helps solve non-smooth problems, which consist of discontinuous functions. The non-smooth problems are the most challenging optimization models to solve.

Let us consider some examples to understand the solver tool of Excel.

Example #1

We want to find the value of X and Y in the following arithmetic equation with the help of the solver tool.

56=2X-5+Y²

Step 1: Formulate the equation on an Excel sheet, as shown in the following image.

Step 2: Click the “solver” button in the “analysis” group of the Data tab. The “solver parameters” dialog box opens. Enter cell “$D$9” in the objective cell, as shown in the succeeding image. The variable cells are “$C$7:$D$7.”

In the “value of” box, type 56. This is because the right-hand side value of the given equation should be equal to 56.

Step 3: Select GRG nonlinear in the “select a solving method” box. Click “solve.”

Note: The GRG nonlinear is the default solving method.

Step 4: The “solver results” box appears. This box may take some time to display depending on the complexity of the model. Select “keep solver solution” and click “Ok,” as shown in the following image.

Step 5: The results are shown in the following image. The solver has calculated X as 30.5 and Y as 0. The right-hand and left-hand sides both are equal now.

Example #2

The succeeding image provides the details of an organization that manufactures a television set, stereo, and speaker. The raw materials used are chassis, picture tube, speaker cone, power supply, and electronics. The leftover stock of raw materials is given in G10:G14.

We want to maximize the overall profits given the limited availability of the raw materials.

The variable cells, constraint cells, and the objective cell are highlighted.

Step 1: Calculate the “used inventory” in F10:F14. The formula is shown in the following image.

Step 2: Click the “solver” button in the “analysis” group of the Data tab. In the “solver parameters” dialog box, click “add” to the right of the “subject to the constraints” box.

Step 3: The “add constraint” box appears, as shown in the succeeding image. The constraints are defined as follows:

• The leftover stock of raw materials should be greater than or equal to zero. So, enter “$G$10:$G$14” in the “cell reference” box. In the box to the right, type the comparison operator “>=.” In the “constraint” box, enter “0.”
• The quantity of the three products (television set, stereo, and speaker) should be greater than or equal to zero. So, enter “$C$6:$E$6>=0” as done for the preceding point.

After entering every constraint, click the “add” button to add it to the “solver parameters” box. Once all constraints have been entered, click “Ok.”

Step 4: In the “solver parameters” box, enter “$C$18” in the “set objective” box. Select the “max” option. In the “by changing variable cells” box, enter “$C$6:$E$6.” Select the solving method as GRG nonlinear. Click “solve.”

Step 5: The output is shown in the following image. The organization must produce 250 television sets, 50 stereos, and 50 speakers to make a profit of $28,000. The product-wise profits are also displayed in C17:E17.

This is an optimal solution given the constraints. With these numbers, the organization will be able to utilize its resources efficiently.

The major applications of the excel solver are listed as follows:

• It helps take decisions at the top level of management. For instance, an organization may want to maximize the profits and minimize the costs given the limited resources of inventory and manpower.
• It helps solve the day-to-day problems of life which can be converted into arithmetic equations. For instance, a housewife may require an optimal monthly budget to be created which can meet the family’s financial needs, given the limitations.