# Cafeteria Line Balancing Problem ## Given Data | Task | Description | Service Time (seconds) | |------|-------------------|------------------------| | A | Serve vegetables | 25 | | B | Serve entrée | 30 | | C | Serve soup | 20 | | D | Serve dessert | 15 | | E | Serve drink | 10 | | F | Collect money | 60 | **Precedence:** - Only restriction: Collect money (F) must be last; all other tasks can be in any order before F. --- ## Step 1: Calculate Desired Cycle Time **Output required:** 60 customers per hour \[ \text{Cycle Time} = \frac{\text{Available Time per Hour}}{\text{Output Required per Hour}} \] There are **360 seconds** in one hour: \[ \text{Cycle Time} = \frac{360 \text{ seconds}}{60 \text{ customers}} = 60 \text{ seconds per customer} \] --- ## Step 2: Calculate Total Task Time Sum all service times: \[ \text{Total Task Time} = 25 + 30 + 20 + 15 + 10 + 60 = 160 \text{ seconds} \] --- ## Step 3: Calculate Minimum Number of Workstations \[ \text{Minimum Number of Stations} = \frac{\text{Total Task Time}}{\text{Cycle Time}} \] \[ = \frac{160}{60} \approx 2.67 \] **Since you can't have a fraction of a station, round up:** \[ \boxed{3 \text{ stations (workers) minimum}} \] --- ## Step 4: Summary Table | Metric | Value | |-----------------------------|------------------------| | Cycle time | 60 seconds/customer | | Total task time | 160 seconds | | Minimum stations (workers) | 3 | --- ## Step 5: Explanation - **Cycle time** is how long you can spend serving one customer to meet your target output. - **Total task time** is how much actual work is required for each customer. - **Minimum stations** is the smallest number of workers needed so that, with the tasks split among them, the line can serve customers at the required pace. The longest single task (F: Collect Money, 60 seconds) sets a practical lower limit as well. --- ## Precedence Diagram (Text) ``` [A] [B] [C] [D] [E] ---> [F] ``` *Tasks A, B, C, D, E can be done in any order, but all must be done before F.* --- ## Conclusion **To serve 60 customers per hour, you need a cycle time of 60 seconds per customer and at least 3 workstations (workers) in the cafeteria line.**

# Cafeteria Line Balancing Problem ## Given Data | Task | Description | Service Time (seconds) | |------|-------------------|------------------------| | A | Serve vegetables | 25 | | B | Serve entrée | 30 | | C | Serve soup | 20 | | D | Serve dessert | 15 | | E | Serve drink | 10 | | F | Collect money | 60 | **Precedence:** - Only restriction: Collect money (F) must be last; all other tasks can be in any order before F. --- ## Step 1: Calculate Desired Cycle Time **Output required:** 60 customers per hour \[ \text{Cycle Time} = \frac{\text{Available Time per Hour}}{\text{Output Required per Hour}} \] **Available Time:** There are **360 seconds** in one hour. \[ \text{Cycle Time} = \frac{360 \text{ seconds}}{60 \text{ customers}} = 60 \text{ seconds per customer} \] **Explanation:** Cycle time determines how long each customer can take in the service process to meet the desired output. In this case, each customer must be served within 60 seconds. --- ## Step 2: Calculate Total Task Time Sum all service times: \[ \text{Total Task Time} = 25 + 30 + 20 + 15 + 10 + 60 = 160 \text{ seconds} \] **Explanation:** Total task time is the cumulative time required to serve one customer through all tasks. This gives an idea of the total workload that needs to be managed by the workers. --- ## Step 3: Calculate Minimum Number of Workstations \[ \text{Minimum Number of Stations} = \frac{\text{Total Task Time}}{\text{Cycle Time}} \] \[ = \frac{160}{60} \approx 2.67 \] **Since you can't have a fraction of a station, round up:** \[ \boxed{3 \text{ stations (workers) minimum}} \] **Explanation:** The minimum number of workstations indicates how many workers are needed to handle the workload within the constraints of the cycle time. Rounding up ensures that the operation can be completed within the required time frame. --- ## Step 4: Summary Table | Metric | Value | |-----------------------------|------------------------| | Cycle time | 60 seconds/customer | | Total task time | 160 seconds | | Minimum stations (workers) | 3 | **Explanation:** This table summarizes the key metrics derived from the calculations, providing a quick reference for understanding the service line requirements. --- ## Step 5: Explanation of Precedence Diagram ### Precedence Diagram (Text) ``` [A] [B] [C] [D] [E] ---> [F] ``` *Tasks A, B, C, D, E can be done in any order, but all must be done before F.* **Explanation:** The precedence diagram visually represents the order in which tasks can be performed. It clarifies that while tasks A through E can be arranged flexibly, task F (Collect Money) must always be the last step. --- ## Conclusion **To serve 60 customers per hour, you need a cycle time of 60 seconds per customer and at least 3 workstations (workers) in the cafeteria line.** **Explanation:** The conclusions drawn from the calculations directly inform how the cafeteria should be structured to meet its service goals efficiently. Understanding these parameters allows for effective staffing and workflow management.