Problem 6.1: Assembly Line With 17 Tasks Is To Be

problem 6 1an Assembly Line With 17 Tasks Is To Be

Analyze an assembly line with 17 tasks where the longest task duration is 2.4 minutes, and the total sum of all tasks is 18 minutes. The line operates for 450 minutes daily. Calculate the minimum and maximum cycle times, the feasible range of daily output, the minimum number of workstations for maximum output, the cycle time required for 125 units per day, and the potential output at cycle times of 9 and 15 minutes.

Given a set of tasks including their durations, precedence relationships, and desired output rates, determine process efficiencies, task assignments, and idle times by applying principles of line balancing, cycle time calculation, and heuristics such as the greatest number of following tasks and positional weights. Use these calculations to optimize productivity and resource utilization.

Sample Paper For Above instruction

In manufacturing systems engineering, efficiently balancing an assembly line is crucial to optimizing productivity and minimizing idle time. This study explores the process of balancing an assembly line consisting of 17 tasks with diverse durations and precedence constraints. By analyzing task durations, total work content, and operational hours, the goal is to compute optimal cycle times, determine the necessary number of workstations, and evaluate potential output rates under different cycle time scenarios.

Task Analysis and Data Summary

The assembly line comprises 17 tasks, with the longest task taking 2.4 minutes, and the total task time summing to 18 minutes. The operation runs for 450 minutes daily, which provides a foundation for calculating theoretical bounds for cycle time and output capacity. These calculations inform decisions such as workstation assignments, process efficiency, and bottleneck identification.

Calculating Cycle Times and Output Ranges

The minimum cycle time can be derived from the best case of maximizing output efficiency, which is the total available time divided by the desired output units. Conversely, the maximum cycle time is constrained by the longest task duration to ensure no task exceeds the cycle time, preventing process bottlenecks. The formulas are as follows:

• Minimum cycle time = Total available time / Maximum number of units (theoretical maximum output)
• Maximum cycle time = Longest task duration = 2.4 minutes

Calculating the minimum cycle time, assuming the total available operational time is 450 minutes:

Minimum cycle time = 450 / 18 ≈ 25.0 minutes. The maximum cycle time is 2.4 minutes, the longest single task.

The potential range of daily output is limited by these bounds. The maximum feasible output occurs at the minimum cycle time, which is approximately 25.0 minutes, yielding about 18 units per day (since 450 / 25 ≈ 18). The minimum output theoretically could be achieved if the cycle time is at its maximum of 2.4 minutes, allowing for approximately 187.5 units (though practical limitations may apply). Therefore, the output range spans from roughly 3 units per day to about 187 units per day.

Determining the Number of Workstations and Cycle Time for a Target Output

To maximize output, we need to establish the minimum number of workstations. This is calculated by dividing the total task time by the desired number of units per day, rounding up to ensure all tasks are assigned. For an output of 18 units, the minimum number of workstations is:

Number of workstations = Total task time / cycle time = 18 / cycle time. Since cycle time is constrained by the max length of 2.4 minutes, and the total work content is 18 minutes, the minimum number of stations is:

Minimum stations = 18 / 2.4 ≈ 8 stations.

When seeking a specific output rate, such as 125 units per day, the cycle time required is:

Cycle time = Total available time / desired number of units = 450 / 125 = 3.6 minutes.

This cycle time ensures the line can produce 125 units daily within the available operational timeframe.

Evaluating Potential Output at Different Cycle Times

Using different cycle times, the potential output can be further examined:

• At a cycle time of 9 minutes, the maximum number of units is approximately 50 (since 450 / 9 ≈ 50).
• At 15 minutes per cycle, about 30 units can be produced (since 450 / 15 ≈ 30).

This analysis underscores the inverse relationship between cycle time and output rate—shorter cycles lead to higher outputs but may increase complexity and operational strain.

Conclusion

Balancing an assembly line involves careful calculations of cycle times, workstation counts, and productivity metrics. This case illustrates how operational timing constraints directly influence output potential and resource utilization. The practices of heuristic task assignment and system analysis, including the longest processing time and greatest number of following tasks heuristics, are instrumental in optimizing line efficiency.

References

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