Problem 6 4a: Producer Of Inkjet Printers Is Planning To Add

Problem 6 4a Producer Of Inkjet Printers Is Planning To Add A New Line

Problem 6-4 A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible. Task Length (minutes) Immediate Predecessor:

  • a 0.2 -
  • b 0.4 a
  • c 0.3 -
  • d 1.3 b, c
  • e 0.1 -
  • f 0.8 e
  • g 0.3 d, f
  • h 1.2 g

Do each of the following:

  1. Assign tasks to stations in order of greatest number of following tasks. Use greatest positional weight as a tiebreaker rule.
  2. Determine the percentage of idle time. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
  3. Compute the rate of output in printers per day that could be expected for this line assuming a 420-minute working day. (Round your answer to the nearest whole number.)

Paper For Above instruction

Balancing an assembly line in manufacturing, especially for complex processes such as printer production, requires careful analysis of task times, precedence relationships, and efficient station assignments. The goal is to minimize cycle time while maximizing productivity. This analysis focuses on assigning tasks to workstations based on their precedence and the overall line efficiency, calculating the idle time percentage, and determining daily output rates under varying cycle times.

Task Analysis and Sequencing

The initial step involves understanding the tasks, their durations, and the dependencies. Tasks a, c, and e are independent; tasks b, d, f, g, and h depend on preceding tasks, forming a sequence that must be respected to ensure proper assembly flow. The task times vary from 0.1 to 1.3 minutes, which indicates the different workloads each task imposes on the stations. The tasks with longer durations, like d (1.3 minutes) and h (1.2 minutes), tend to be critical in determining the cycle time because they set lower bounds on the total process time per cycle.

Assigning Tasks to Stations

The task allocation is based on ordering tasks by the number of following tasks to optimize workflow efficiency. Using the rule of assigning tasks with the greatest number of successors first and employing the greatest positional weight as a tiebreaker helps streamline task sequencing and minimize idle time. The following assignments are made accordingly:

  • Station 1: a, c, e
  • Station 2: b, f
  • Station 3: d, g, h

This arrangement allows each station to process tasks in sequence while respecting precedence. For example, task d can only be processed after b and c are completed, and similarly, task g must follow d and f.

Calculation of Idle Time

The total work content per cycle is the sum of task times assigned to each station. For the above distribution:

  • Station 1: a (0.2) + c (0.3) + e (0.1) = 0.6 minutes
  • Station 2: b (0.4) + f (0.8) = 1.2 minutes
  • Station 3: d (1.3) + g (0.3) + h (1.2) = 2.8 minutes

The cycle time is determined by the station with the maximum workload, which is 2.8 minutes here. The total processing time across stations is 0.6 + 1.2 + 2.8 = 4.6 minutes. The total idle time is computed as the difference between total available processing time (sum of station cycle times times number of stations) and total work content, relative to the total available time, to derive the idle percentage. The exact calculations help identify inefficiencies and room for process improvements.

Output Rate Calculation

Assuming a 420-minute workday, the number of cycles that can be completed per day at the given cycle time (2.8 minutes) is approximately:

Number of cycles = 420 / 2.8 ≈ 150 cycles

Given that each cycle produces one printer, the daily output is approximately 150 printers per day.

Efficiency and Optimization Considerations

To improve productivity, reducing the cycle time to match the longest task (here, 2.8 minutes) is ideal. Shorter cycle times may require replicating tasks or additional stations, which increases complexity and costs. However, identifying the shortest feasible cycle time that allows only two workstations is a critical step in process optimization.

Conclusion

Effective assembly line balancing relies on understanding task dependencies, times, and sequence optimization. By assigning tasks based on the number of following tasks and balancing workload across stations, companies can reduce idle time, increase throughput, and improve overall efficiency. These principles are vital for manufacturing contexts where minimizing cycle time significantly impacts productivity and profitability.

References

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  • Vollmann, T. E., Berry, W. L., Whybark, D. C., & Jacobs, F. R. (2012). Manufacturing Planning and Control for Supply Chain Management. McGraw-Hill Education.
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  • Ulrich, K. T., & Eppinger, S. D. (2015). Product Design and Development. McGraw-Hill Education.

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