use solver to find the combination of procedures

Daniel Parker

3 min read

·

28-02-2025

1

0

Share

Solver, a powerful add-in in Microsoft Excel, allows you to find the best combination of variables to optimize a target outcome. This article explores how to leverage Solver to determine the ideal mix of procedures, given specific constraints and objectives. We'll cover various scenarios and provide a step-by-step guide. This is particularly useful in fields like healthcare resource allocation, manufacturing process optimization, and portfolio management.

Defining the Problem: What are we Optimizing?

Before diving into Solver, clearly define your problem. This includes:

• Objective Function: What are you trying to maximize or minimize? This is your target—e.g., maximizing profit, minimizing cost, or balancing workload.
• Decision Variables: What are the procedures you can combine? These are the variables Solver will adjust to find the optimal solution. Represent each procedure with a cell containing its quantity or frequency.
• Constraints: What limitations exist? These could include budgetary constraints, time limitations, resource availability (staff, equipment), or minimum/maximum requirements for specific procedures. Express these as mathematical inequalities or equations.

Let's illustrate with a simplified example:

Imagine a medical clinic optimizing its use of three procedures (A, B, C) to maximize revenue, subject to constraints on available doctor time and patient demand.

Setting up your Excel Spreadsheet

1. Data Input: Create a table to input data regarding each procedure: revenue per procedure, doctor time required per procedure, and maximum patient demand.

2. Decision Variables: Assign cells to represent the number of times each procedure is performed. Let's say:

   • Cell D2: Number of procedure A
   • Cell D3: Number of procedure B
   • Cell D4: Number of procedure C

3. Calculated Values: Calculate the total revenue, total doctor time, and the total number of procedures. You will use formulas for this:

   • Total Revenue (Cell F2): =D2*B2 + D3*B3 + D4*B4
   • Total Doctor Time (Cell F3): =D2*C2 + D3*C3 + D4*C4
   • Total Procedures (Cell F4): =SUM(D2:D4)

4. Constraints: In separate cells, define your constraints:

   • Maximum Doctor Time Available (e.g., 25 hours in cell G2)
   • Other Constraints (e.g., minimum number of procedure A)

Using Solver

1. Install Solver: If you don't have Solver installed, go to File > Options > Add-Ins > Manage: Excel Add-ins > Go. Check "Solver Add-in" and click "OK".

2. Open Solver: Go to Data > Solver.

3. Set Parameters:

   • Set Objective: Select the cell containing your objective function (Total Revenue - F2 in our example). Choose "Max" (to maximize revenue).
   • By Changing Variable Cells: Select the cells containing your decision variables (D2:D4).
   • Subject to the Constraints: Click "Add" to add your constraints. For example:
     • Cell F3 <= G2 (Total Doctor Time <= Max Doctor Time)
     • D2:D4 >= 0 (Non-negativity constraint - can't perform negative procedures)
     • Add other constraints as needed based on patient demand.

4. Solve: Click "Solve". Solver will find the optimal combination of procedures. Choose "Keep Solver Solution" to retain the results.

5. Analyze Results: Review the Solver results in your decision variable cells (D2:D4). These cells will now contain the optimal number of each procedure to perform. Examine the total revenue achieved.

Advanced Considerations

• Integer Constraints: If you can only perform whole numbers of procedures (no fractions), add an integer constraint to your decision variables.
• Non-Linear Problems: Solver can also handle non-linear optimization problems, although they may require more careful setup and interpretation.
• Sensitivity Analysis: After solving, consider performing a sensitivity analysis to see how changes in constraints affect the optimal solution. This assesses the robustness of your solution.

Conclusion

Solver is a valuable tool for finding the optimal combination of procedures in various contexts. By clearly defining your problem, setting up your spreadsheet correctly, and utilizing Solver's features, you can efficiently determine the ideal allocation of resources to achieve your objectives, whether maximizing profits, minimizing costs, or balancing workloads. Remember to always review and interpret the results to ensure they align with real-world limitations and considerations.