基于Excel的办公座位轮值自动化咨询：Assignment Problem与线性规划可行性

Great question! Since you're tackling an office seat rotation (not academic work) and need to automate this using only Excel, the Assignment Problem (a classic linear programming use case) is exactly the right approach. Let me break this down into actionable steps tailored to your office needs:

The Assignment Problem is designed to match a set of "workers" (your employees) to a set of "tasks" (your office seats) with specific constraints—exactly what you need for rotation. It ensures:

• Every employee gets exactly one seat per day/week
• Every seat is assigned to exactly one employee
• You can enforce rules like "no repeating the same seat two weeks in a row" or "employee X can’t use seat Y" by adjusting a "cost matrix" (more on that below)

First, set up 4 key sheets in your workbook:

• Employee Roster: Column A lists all your team members (e.g., E1, E2, ..., En)
• Seat Inventory: Column A lists all available seats (e.g., S1, S2, ..., Sn—make sure the count matches your employee count for a balanced problem; we’ll cover unbalanced later)
• Constraint Table: An n×n grid where you mark 0 if an employee can’t use a specific seat (e.g., due to accessibility needs) and 1 if they can
• Cost Matrix: Another n×n grid. Here, "cost" is a tool to drive rotation:
  • Set a low cost (e.g., 1) for all valid seat-employee pairs
  • Set a high cost (e.g., 100) for pairs you want to avoid (like last week’s assigned seat for an employee)
  • Use Excel formulas to auto-update this: =IF(LastWeek!B2=1, 100, 1) to flag last week’s assignment as high-cost

Excel’s built-in Solver add-in will handle the optimization for you. First, enable it if you haven’t:

File > Options > Add-ins > Manage: Excel Add-ins > Go > Check "Solver Add-in" > OK

Then configure Solver for your rotation:

1. Objective: Select the total cost cell (sum of your Cost Matrix multiplied by a binary assignment matrix) and set it to Min (we want the lowest total cost, which means avoiding high-cost "forbidden" pairs)
2. Variable Cells: Select an empty n×n grid—these will be binary values (1 = assigned, 0 = not assigned)
3. Constraints:
   • Add a constraint that each row in the variable grid sums to 1 (each employee gets one seat)
   • Add a constraint that each column in the variable grid sums to 1 (each seat gets one employee)
   • Add a constraint that variable cells ≤ the corresponding cell in your Constraint Table (blocks forbidden seat-employee pairs)
   • Set variable cells to Binary (only 0 or 1 values allowed)

Click Solve, and Excel will generate your optimized seat assignment.

To make this repeatable every week:

• Save your Solver settings (click "Save Model" in the Solver window) so you don’t have to reconfigure constraints each time
• Use Excel macros or formula references to auto-update the Cost Matrix with last week’s assignments (so employees don’t get the same seat two weeks running)
• For daily rotation, just duplicate the setup for each day of the week, adjusting the Cost Matrix to avoid recent seats

• Unbalanced counts: If you have more seats than employees (or vice versa), adjust the constraints: allow some columns (seats) to sum to 0 (empty seats) or some rows (employees) to sum to 0 (flexible seating for remote workers)
• Group constraints: If you need to keep certain employees adjacent (or separate), adjust the Constraint Table to block or prioritize those pairs
• Test small first: Start with 3-4 employees/seats to validate the setup before scaling to your full team

内容的提问来源于stack exchange，提问作者PSP