excel tutorialExcel Solver
Excel includes a tool called solver that uses techniques from the operations research to find optimal solutions for all kind of decision problems. This chapter describes how to enable the solver, how to formulate a model on a spreadsheet, how to analyze a trial solution, and how to use the solver to quickly find the optimal solution.
Enable Solver
To enable the solver in Excel 2010, execute the following steps.
1. On the File tab, click on Options.
2. Under Add-ins, select Solver Add-in and click on the Go button.
3. Check Solver Add-in and click on OK.
4. You can find the Solver under the Data tab.
Formulating the Model
The model we are going to solve looks as follows in Excel. You can download the accompanied Excel file if you want.
To formulate this linear programming model we have answered the following three questions.
1. 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).
2. 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.
3. What is the overall measure of performance of these decisions? The cycle trader's measure of performance is the total profit from the three products, so the objective is to maximize this quantity.
To make our model easier to understand we have named the following ranges.
| Range Name | Cells |
| OrderSize | C12:E12 |
| ResourcesAvailable | H7:H8 |
| ResourcesUsed | F7:F8 |
| TotalProfit | H12 |
| UnitProfit | C4:E4 |
To implement the answers on the questions, insert the following formulas.
4. The amount of capital used equals the sumproduct of range("C7:E7") and OrderSize.
5. The amount of storage used equals the sumproduct of range("C8:E8") and OrderSize.
6. Total profit equals the sumproduct of OrderSize and UnitProfit.
Result:
Trial and Error
With this formulation, it becomes easy to analyze any trial solution.
For example, when 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, click on Solver.
Enter the Solver Parameters. You have the choice of typing the range names or clicking on the cells in the spreadsheet. The result should be consistent with the picture below.
2. Enter TotalProfit for the Objective.
3. Click on Max.
4. Enter OrderSize for the Changing Variable Cells.
5. Click on Add to enter the constraint.
6. Make sure 'Make Unconstrained Variables Non-Negative' is checked and 'Simplex LP' is selected as the solving method.
7. Finally, click on Solve.
Result:
The 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.
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