Excel is a powerful tool that many use for optimization problems through its Solver and Goal Seek features. However, users often encounter frustrating scenarios where Solver fails to find a feasible solution, and Goal Seek does not seem to solve the entire problem. Understanding the root causes of these issues can enhance your Excel experience and lead to successful problem-solving.
Common Problem Scenario
You may find yourself in a situation where you set up an optimization problem in Excel using the Solver add-in. You define the objective, constraints, and variable cells, but when you hit “Solve,” you receive a message stating that the Solver could not find a feasible solution. Similarly, with Goal Seek, you might set a target value but discover that it does not adjust all relevant variables as expected.
Original Problem Code Snippet
Assuming you have the following basic setup for Solver:
Set Objective: Cell A1 (to maximize)
By Changing Cells: Cells B1:B5
Subject to Constraints:
1. Cell C1 <= 100
2. Cell D1 >= 0
Analyzing the Problem
Excel Solver Issues
When Solver does not find a feasible solution, several factors could contribute to this problem:
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Conflicting Constraints: If the constraints are mutually exclusive, Solver will struggle to find a solution. For example, if one constraint requires a variable to be less than a certain number while another requires it to exceed a larger number, there’s no feasible solution.
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Incorrect Objective Function: Ensure that the objective function is correctly defined. If the function has errors or is improperly set up, it can lead to Solver being unable to find a feasible solution.
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Variable Bounds: If your variable cells have boundaries that prevent them from reaching any feasible point given the constraints, Solver will also fail.
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Model Complexity: Complex models with nonlinear constraints may require specific settings in Solver, such as changing the solving method from Simplex LP to GRG Nonlinear or Evolutionary.
Goal Seek Limitations
Goal Seek is limited compared to Solver and is primarily designed to find a single variable that achieves a specified value. Therefore, its limitations often arise from:
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Single Variable Focus: Goal Seek only adjusts one variable to meet the target cell value. If other variables also need adjusting to reach a desired state, Goal Seek won’t handle it.
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Non-linear Relationships: If the relationship between the input and the target cell is non-linear, Goal Seek may not provide the correct solution.
Practical Examples and Solutions
Example 1: Solver
Imagine you are optimizing a production schedule for two products, A and B, with the following constraints:
- You can produce a maximum of 100 units of Product A.
- The total production must not exceed 150 units.
If you accidentally define your constraints as follows:
- A <= 100
- B <= 60
- A + B <= 100
Excel Solver will fail to find a feasible solution because A + B will never satisfy both A + B <= 100 and the lower boundary of Product B (if it is forced below a certain minimum).
Solution: Review and adjust the constraints to ensure they do not conflict, and ensure you properly specify the maximum production capacity.
Example 2: Goal Seek
Suppose you have a formula in cell B1 that calculates profit based on sales in cell A1. You want to achieve a profit of $200.
Using Goal Seek:
- Set cell: B1
- To value: 200
- By changing cell: A1
If your profit formula is non-linear (e.g., involves multiplication with other variables), Goal Seek may yield a value for A1 but may not represent a feasible production scenario.
Solution: In such cases, consider using Solver to adjust multiple variables simultaneously or revise the profit equation to ensure it operates linearly.
Conclusion
Encountering issues with Excel Solver and Goal Seek can be frustrating. However, understanding the underlying problems can empower you to troubleshoot effectively. Always ensure that your constraints do not conflict, your objective function is correctly defined, and recognize the limitations of Goal Seek.
Useful Resources
By utilizing these insights and resources, you can enhance your productivity in Excel and effectively tackle optimization challenges. Happy solving!
