use solver to find the combination of procedures

Breiz Heurope

3 min read

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09-03-2025

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Solver, an add-in available in Microsoft Excel, is a powerful tool for finding the best combination of variables to optimize a given objective. This article will guide you through using Solver to determine the optimal combination of procedures, a common problem in various fields like operations research, finance, and healthcare. We'll explore the process with a practical example and discuss key considerations.

Understanding the Problem: Optimizing Procedure Combinations

Imagine you're a medical facility managing different procedures with varying costs, durations, and patient benefits. Your goal is to find the combination of procedures that maximizes patient benefit while staying within budget and time constraints. This is a classic optimization problem perfectly suited for Solver.

Setting up your Excel Spreadsheet for Solver

Before we begin, ensure the Solver Add-in is enabled in Excel. (File > Options > Add-ins > Manage: Excel Add-ins > Go... > Check "Solver Add-in" > OK).

Here's how to structure your spreadsheet:

1. Procedures: List each procedure in a column (e.g., Column A).
2. Cost per Procedure: In the next column (e.g., Column B), enter the cost associated with each procedure.
3. Duration per Procedure: Enter the duration (e.g., in minutes or hours) of each procedure in another column (e.g., Column C).
4. Benefit per Procedure: Assign a numerical value representing the benefit of each procedure (e.g., patient improvement score, profit margin). This goes in another column (e.g., Column D).
5. Number of Procedures: Create a column (e.g., Column E) where you'll input the number of times each procedure is performed. These are your decision variables, which Solver will adjust. Initially, set these to 0.
6. Totals: Calculate the total cost, total duration, and total benefit. Use formulas to sum the products of the "Number of Procedures" and the respective cost, duration, and benefit columns (e.g., =SUMPRODUCT(B2:B10,E2:E10) for total cost).

Defining the Solver Parameters

Now, let's configure Solver:

1. Data > Solver: Open the Solver Parameters dialog box.

2. Set Objective: Select the cell containing your total benefit (this is what you want to maximize).

3. To: Choose "Max" (since we want to maximize benefit).

4. By Changing Variable Cells: Select the range containing the "Number of Procedures" (your decision variables).

5. Subject to the Constraints: Click "Add" to define constraints. These are crucial:

   • Budget Constraint: Add a constraint limiting the total cost (e.g., Total Cost <= Budget).
   • Time Constraint: Add a constraint limiting the total duration (e.g., Total Duration <= Available Time).
   • Non-negativity Constraint: Ensure the number of each procedure is non-negative (e.g., Number of Procedures >= 0). This prevents Solver from suggesting negative numbers of procedures.
   • Integer Constraint (Optional): If you can only perform whole numbers of procedures, add an integer constraint for each decision variable. This ensures Solver provides realistic solutions.

6. Solving Method: Select a solving method. "GRG Nonlinear" is a good starting point for many problems. Experiment with others if necessary.

7. Solve: Click "Solve" to let Solver find the optimal combination.

Interpreting the Results

Solver will display the optimal number of each procedure to perform, along with the resulting total cost, duration, and maximum benefit. Carefully review the results to ensure they make sense in your context.

Example: A Simple Healthcare Scenario

Let's say we have three procedures:

Our budget is $500, and we have 120 minutes available. Using Solver, we might find the optimal combination is 3 of Procedure A, 4 of Procedure B, and 1 of Procedure C, maximizing our benefit while staying within constraints.

Advanced Considerations

• Multiple Objectives: Solver can handle multiple objectives (e.g., maximizing benefit while minimizing cost) using techniques like goal programming.
• Non-linear Relationships: Solver can handle non-linear relationships between variables, though it may require more advanced settings and potentially longer solving times.
• Sensitivity Analysis: After finding a solution, perform sensitivity analysis to see how the optimal combination changes when constraints are altered slightly. This helps understand the robustness of the solution.

By following these steps and understanding the capabilities of Solver, you can efficiently determine the optimal combination of procedures to meet your specific needs and objectives. Remember to thoroughly check the results and consider the limitations of the model.