To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, you can use Excel’s Solver add-in. Solver is a powerful tool that can find the optimal solution to optimization problems like this one. Here’s a step-by-step guide on how to do it:

Step 1: Prepare Your Data

First, make sure you have your data in an Excel spreadsheet. In this case, the data represents the time it takes each employee to perform each job. Create a table that looks something like this:

Make sure to input the correct time values and leave blank cells where an employee cannot perform a specific job.

Step 2: Install and Activate Solver

If you haven’t already installed Solver, you can do so by going to “File” > “Options” > “Add-Ins.” In the Excel Options window, select “Add-Ins” on the left, choose “Solver Add-in,” and click “Go…” to install it. Make sure to check the box for Solver Add-in and click “OK.”

Step 3: Set Up the Objective Function

Now, you need to set up the objective function that Solver will minimize. In this case, the objective is to minimize the total time required. To do this:

1. Create a cell where you’ll calculate the total time. Let’s say you put this in cell B8.
2. In cell B8, enter the formula to calculate the total time. You can use the SUMPRODUCT function to multiply each employee’s time by their assignment to a job. For example, the formula might be:
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   =SUMPRODUCT(B2:F6, $B$14:$F$18)


   Here, B2:F6 represents the range of employee-job times, and $B$14:$F$18 will be the range where you will specify the assignments later.

Step 4: Define Constraints

You need to define constraints to ensure that each job is assigned to one employee and each employee is assigned to one job. Here’s how to set up these constraints:

1. Create a new section in your spreadsheet to define the constraints. For this example, let’s say you use cells B14:F18.
2. In each cell in the constraints section, enter 0 or 1 to represent whether an employee is assigned to a job. For example, if Employee 1 is assigned to Job 1, cell B14 should contain 1, and the rest should contain 0.
3. Use Excel’s Data Validation feature to ensure that each row and each column in the constraint section contains only one “1” and the rest are “0”s.

Step 5: Set Up Solver

Now that you’ve prepared your data, objective function, and constraints, it’s time to set up Solver:

1. Go to the “Data” tab in Excel.
2. Click on “Solver” in the “Analysis” group to open the Solver Parameters window.
3. In the Solver Parameters window:
   • Set the objective to “Minimize.”
   • In the “Objective” field, enter the cell reference of the total time calculation (B8 in this example).
   • In the “By Changing Variable Cells” field, enter the cell range where you defined the constraints (B14:F18 in this example).
   • Add constraints:
     • Add constraints to ensure that each row and each column in the constraints section sum to 1.
   • Click “Add” for each constraint and make sure they are set up correctly.
4. Click the “Options” button to configure Solver options if needed.
5. Click “OK” to close the Options window.
6. Click “Solve” in the Solver Parameters window to let Excel find the optimal solution.

Step 6: Review the Results

Once Solver finds a solution, it will populate the assignment cells in the constraints section (B14:F18 in this example). Each cell will contain either 0 or 1, indicating whether an employee is assigned to a job. The total time in cell B8 will also update to show the minimized total time.

Review the results to ensure that each job is assigned to one employee, each employee is assigned to one job, and the total time is minimized.

In this step-by-step guide, you’ve learned how to use Excel’s Solver add-in to solve an assignment problem that minimizes total time while considering employee-job compatibility and constraints. This approach ensures that you make efficient job assignments while optimizing your resource allocation.