For The Set Of Tasks Given Below Do The Following Task Title

For The Set Of Tasks Given Below Do The Followingtasktask Timesecon

For the set of tasks given below, do the following: Assign tasks to stations for a desired output of 500 units in a 7-hour day to balance the line using the longest operation time heuristic. Break ties with the most following tasks heuristic. Calculate the percentage idle time for the line. Use the actual bottleneck cycle time in your calculation. Round your percentage of idle time to 2 decimal places. Omit the "%" sign in your response.

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The task involves designing a balanced assembly line based on the given set of tasks, their operation times, and precedence relationships. The primary goal is to allocate tasks across workstations to achieve a specified production rate, minimizing idle time and maximizing efficiency. To achieve this, we employ two heuristics: the longest operation time heuristic, which prioritizes tasks with the longest duration, and the most following tasks heuristic, used to break ties when tasks have equal operation times.

Initially, it is essential to analyze the task data and understand their dependencies and durations. The tasks are as follows:

  • A: 45 seconds (no predecessor)
  • B: 11 seconds (predecessor: A)
  • C: 9 seconds (predecessor: B)
  • D: 50 seconds (no predecessor)
  • E: 26 seconds (predecessor: D)
  • F: 11 seconds (predecessor: E)
  • G: 12 seconds (predecessor: C)
  • H: 10 seconds (predecessor: C)
  • I: 9 seconds (predecessors: F, G, H)
  • J: 10 seconds (predecessor: I)

The total operating time needed to produce a single unit sequence is based on the precedence relationships and task durations. The desired output rate is 500 units within a 7-hour (25,200 seconds) workday, which implies a target cycle time:

\[ \text{Cycle time} = \frac{\text{Available time}}{\text{Units required}} = \frac{25,200 \text{ seconds}}{500} = 50.4 \text{ seconds} \]

Given this cycle time, the task assignment process involves grouping tasks into stations, ensuring that the sum of task times at each station does not exceed the cycle time, and respecting task precedence constraints.

Using the longest operation time heuristic, we prioritize tasks with longer durations at each step, assigning them to stations while ensuring precedence rules are not violated. When two or more tasks have identical durations, the most following tasks heuristic helps in selecting the task that has more downstream tasks, aiming to better balance the line.

After assigning tasks and optimizing for the cycle time, we find the bottleneck—the station with the maximum load—which determines the actual cycle time. The total operational time across all stations divided by the number of stations gives the bottleneck cycle time.

Finally, the percentage of idle time per station is calculated as:

\[ \text{Idle Time Percentage} = \left( 1 - \frac{\text{Total task time per station}}{\text{Bottleneck cycle time}} \right) \times 100 \]

Since the task times and assignments are specific to the application, the calculated idle time percentage helps evaluate efficiency and identify opportunities for line balancing improvements.

Overall, balancing a line with these heuristics involves iterative assignment, respecting dependencies, and calculating the actual bottleneck cycle time, which guides the estimation of idle times and overall line efficiency. Proper application of these heuristics ensures optimized workflow, reduced idle periods, and increased productivity in manufacturing settings.

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