Model Answer
0 min readIntroduction
Line balancing is a crucial aspect of operations management, aiming to distribute tasks evenly across a production line to maximize efficiency and minimize idle time. In a competitive market, like the toy industry, optimizing production processes is vital for cost control and responsiveness to rivals. A well-balanced line reduces bottlenecks, lowers work-in-progress inventory, and ultimately enhances profitability. This problem requires us to design a production line for an electronic football game, considering task times and precedence constraints to compete effectively with an existing model. The goal is to minimize the number of workstations needed to complete the production process.
Understanding the Problem
The problem presents a classic line balancing scenario. We are given a set of tasks, each with a specific processing time, and a set of precedence constraints that dictate the order in which tasks must be performed. The objective is to assign these tasks to workstations in a way that minimizes the number of workstations required, while adhering to both the task times and precedence rules.
Determining the Cycle Time
Before balancing the line, we need to determine the cycle time. The cycle time is the maximum time allowed at each workstation. It is typically determined by the total task time divided by the desired number of workstations. Since the number of workstations is what we are trying to optimize, we will start by calculating the theoretical minimum number of workstations and then refine it.
First, we need the task data. Let's assume the following task data (as it was missing from the question):
| Task | Task Time (seconds) | Predecessor(s) |
|---|---|---|
| A | 30 | - |
| B | 40 | A |
| C | 20 | A |
| D | 50 | B, C |
| E | 30 | D |
| F | 20 | D |
| G | 40 | E, F |
Total task time = 30 + 40 + 20 + 50 + 30 + 20 + 40 = 230 seconds.
Let's start by assuming we want to complete one unit every minute (60 seconds). This would require 230/60 = 3.83 workstations. Therefore, we need at least 4 workstations.
Line Balancing Algorithm
We will use a heuristic approach to line balancing. The steps are as follows:
- Step 1: Create a precedence diagram to visualize the task dependencies.
- Step 2: Assign tasks to workstations, starting with the first workstation.
- Step 3: Prioritize tasks based on their longest processing time and number of successors.
- Step 4: Assign tasks to a workstation as long as the workstation's cumulative time does not exceed the cycle time (60 seconds).
- Step 5: If a task cannot be assigned to the current workstation, move to the next workstation.
- Step 6: Repeat steps 3-5 until all tasks are assigned.
Balanced Production Line
Applying the algorithm, a possible balanced production line is as follows:
| Workstation | Tasks | Total Time (seconds) |
|---|---|---|
| 1 | A, C | 30 + 20 = 50 |
| 2 | B | 40 |
| 3 | D, F | 50 + 20 = 70 (Exceeds cycle time - needs adjustment) |
| 4 | E, G | 30 + 40 = 70 (Exceeds cycle time - needs adjustment) |
The initial attempt shows that Workstations 3 and 4 exceed the cycle time. We need to re-arrange the tasks. A better arrangement is:
| Workstation | Tasks | Total Time (seconds) |
|---|---|---|
| 1 | A, C | 30 + 20 = 50 |
| 2 | B | 40 |
| 3 | D | 50 |
| 4 | E, F, G | 30 + 20 + 40 = 90 (Exceeds cycle time - needs adjustment) |
Still exceeding the cycle time. Let's try a cycle time of 70 seconds. Total task time is 230, so 230/70 = 3.29. We still need 4 workstations.
| Workstation | Tasks | Total Time (seconds) |
|---|---|---|
| 1 | A, C | 30 + 20 = 50 |
| 2 | B | 40 |
| 3 | D, F | 50 + 20 = 70 |
| 4 | E, G | 30 + 40 = 70 |
This arrangement satisfies the precedence constraints and the cycle time of 70 seconds. Therefore, 4 workstations are required.
Conclusion
In conclusion, balancing the production line for the electronic football game requires careful consideration of task times and precedence constraints. By applying a line balancing algorithm, we have determined that a cycle time of 70 seconds and 4 workstations are necessary to efficiently manufacture the product. This balanced line minimizes idle time and maximizes throughput, enabling the toy company to compete effectively with its rival. Further optimization could involve exploring different cycle times or using more sophisticated line balancing techniques.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.