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class__11 -Designation/Exer_2b-Mathematical Model and Hungarian Method Solution and Minimum Cost/Exercise_2b-Excel Solver.md

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+## Exercise 2b: Solved Excel Solver
+
+### Problem Statement :
+
+Make the mathematical model and determining the designation and the minimum cost of the process.
+
+
+## **Step 1: Enter the Cost Matrix in Excel**
+
+|  | A | B | C | D | E |
+| :-- | :-- | :-- | :-- | :-- | :-- |
+|  |  | T1 | T2 | T3 | T4 |
+| 2 |  |  |  |  |  |
+| 3 | A | 5 | 24 | 13 | 7 |
+| 4 | B | 10 | 25 | 3 | 23 |
+| 5 | C | 28 | 9 | 8 | 5 |
+| 6 | D | 10 | 17 | 15 | 3 |
+
+
+---
+
+## **Step 2: Create the Assignment Matrix**
+
+Next to your cost matrix, create a 4x4 grid for assignments (let’s say in G3:J6).
+Each cell will be a binary variable (0 or 1):
+
+- 1 if the operator is assigned to that task, 0 otherwise.
+
+|  | G | H | I | J |
+| :-- | :-- | :-- | :-- | :-- |
+|  | T1 | T2 | T3 | T4 |
+| 3 |  |  |  |  |
+| 4 |  |  |  |  |
+| 5 |  |  |  |  |
+| 6 |  |  |  |  |
+
+
+---
+
+## **Step 3: Objective Function (Total Cost)**
+
+In a cell (say, **L2**), calculate the total cost using the SUMPRODUCT function:
+
+```excel
+=SUMPRODUCT(B3:E6, G3:J6)
+```
+
+This multiplies each cost by its assignment (0 or 1) and sums the result.
+
+---
+
+## **Step 4: Add Constraints for Solver**
+
+You need to ensure:
+
+- Each worker is assigned to **exactly one** task.
+- Each task is assigned to **exactly one** worker.
+
+**For each row (worker):**
+In K3: `=SUM(G3:J3)` (copy down to K6)
+Set each to **equal 1** in Solver.
+
+**For each column (task):**
+In G7: `=SUM(G3:G6)` (copy right to J7)
+Set each to **equal 1** in Solver.
+
+---
+
+## **Step 5: Configure Solver**
+
+1. Go to **Data** > **Solver**.
+2. **Set Objective:**
+    - Set Objective: `L2` (or wherever your total cost is).
+    - To: **Min**
+3. **By Changing Variable Cells:**
+    - `G3:J6` (your assignment matrix)
+4. **Add Constraints:**
+    - `G3:J6` = binary (use "bin" in Solver)
+    - `K3:K6` = 1 (each worker assigned to one task)
+    - `G7:J7` = 1 (each task assigned to one worker)
+5. Click **Solve**.
+
+---
+
+## **Step 6: Interpret the Results**
+
+Solver will fill the assignment matrix with 0s and 1s.
+For each row, the "1" indicates which task that worker is assigned to.
+
+### **Example Solution (Optimal):**
+
+| Worker | Task Assigned | Cost |
+| :-- | :-- | :-- |
+| A | 1 | 5 |
+| B | 3 | 3 |
+| C | 2 | 9 |
+| D | 4 | 3 |
+| **Total** |  | **20** |
+
+
+---
+
+## **Summary Table for README**
+
+| Worker | Task 1 | Task 2 | Task 3 | Task 4 | Assignment |
+| :-- | :-- | :-- | :-- | :-- | :-- |
+| A | 5 | 24 | 13 | 7 | 1 (T1) |
+| B | 10 | 25 | 3 | 23 | 3 (T3) |
+| C | 28 | 9 | 8 | 5 | 2 (T2) |
+| D | 10 | 17 | 15 | 3 | 4 (T4) |
+
+**Minimum total time: 20**
+
+---
+
+## **Tips**
+
+- Use **conditional formatting** to highlight the "1"s in the assignment matrix for clarity.
+- If Solver is not enabled, go to **File > Options > Add-ins > Solver Add-in**.
+
+---
+
+**Ready! You have solved the assignment problem step by step in Excel using Solver, ensuring the minimum total cost is 20.**
+