Value 300 Points Problem 6.1: Assembly Line With 17 Tasks

value300 Pointsproblem 6 1an Assembly Line With 17 Tasks Is To Be

Problem 6-1 An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day. a. What are the minimum and maximum cycle times? (Round your answers to 1 decimal place.) Minimum cycle time minutes Maximum cycle time minutes b. What range of daily output is theoretically possible for the line? (Round your answers to 1 decimal place. Enter the smaller value in the first box and the larger value in the second box.) Range of output to units/day c. What is the minimum number of workstations needed if the maximum output rate is to be sought? (Round up your answer to the next whole number.) Minimum number of workstations d. What cycle time will provide an output rate of 125 units per day? (Round your answer to 1 decimal place.) Cycle time min/cycle e. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes? Cycle Time Potential Output (1) units (2) units 2. value: 3.00 points Problem 6-5 As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows: Task Duration (minutes) Immediate Predecessor a 0.2 - b 0.4 a c 0.2 b d 0.4 - e 1.2 d f 1.2 c g 1.0 e, f Do each of the following: b. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.) The minimum cycle time minutes per unit The maximum cycle time minutes per unit Calculated cycle time minutes per unit c. Determine the minimum number of stations needed. (Round your answer to the next whole number.) Minimum number of stations d. Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice. Work stations Following Tasks I II III IV e. Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Percentage of idle time % 3. value: 3.00 points Problem 6-7 For the set of tasks given below, do the following: Task Task Time(seconds) Immediate Predecessor A 45 - B 11 A C 9 B D 50 - E 26 D F 11 E G 12 C H 10 C I 9 F, G, H J 10 I 193 b. Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a seven-hour day. (Round your answers to 1 decimal place.) The minimum cycle time seconds The maximum cycle time seconds c. Determine the minimum number of workstations for output of 500 units per day. (Round up your answer to the next whole number.) Minimum number of workstations d. Balance the line using the greatest positional weight heuristic. Break ties with the most following tasks heuristic. Use a cycle time of 50 seconds. Work stations Following Tasks I II III IV V e. Calculate the percentage idle time for the line using the 50 second cycle time. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Percentage of idle time % 4. value: 3.00 points Problem 6-3 A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 4 units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. Work Station Tasks I II III IV b. In order of greatest positional weight. Work Station Tasks I II III IV c. What is the efficiency? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Efficiency % (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) (Click to select) 1. value: 4.00 points Problem 7-7 A worker-machine operation was found to involve 3.6 minutes of machine time per cycle in the course of 40 cycles of stopwatch study. The worker’s time averaged 1.8 minutes per cycle, and the worker was given a rating of 120 percent (machine rating is 100 percent). Midway through the study, the worker took a 10-minute rest break. Assuming an allowance factor of 15 percent of work time which is applied only to the worker element (not the machine element), determine the standard time for this job. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Standard time minutes

Paper For Above instruction

The task of balancing an assembly line involves optimizing task assignment to ensure maximum efficiency and output while minimizing idle time. This process includes calculating the appropriate cycle times, determining the minimum number of workstations, and effectively assigning tasks based on precedence and processing times. In this essay, we explore various facets of assembly line balancing, including theoretical limits, practical task assignments, and efficiency calculations, supported by relevant concepts and methodologies.

Balancing an Assembly Line: Fundamental Concepts

Assembly line balancing is a critical aspect of industrial engineering that aims to synchronize tasks across multiple workstations, reducing idle times and ensuring a smooth workflow (Kia et al., 2018). The primary goal is to determine optimal cycle times and task distributions such that the production meets desired output rates without excessive delays or underutilization. The foundational principle involves calculating the minimum and maximum cycle times, which serve as bounds for feasible line operation.

Calculating Cycle Times

The minimum cycle time is derived from the longest task, which dictates the pace of the entire line. Conversely, the maximum cycle time is largely dictated by available operational hours divided by the desired output. For the first problem, with a longest task time of 2.4 minutes, and total task time of 18 minutes, the minimum cycle time equals 2.4 minutes, and the maximum is computed by dividing total available time per day (450 minutes) by the required number of units per day, thus providing an operational range.

Theoretical Output Range

Theoretically, the maximum output can be achieved with the minimum cycle time, assuming perfect task allocation, while the minimum output corresponds to the maximum cycle time. In such a setting, the range of possible outputs can be expressed as a spectrum between these bounds, providing managers with insights into operational capabilities.

Workstation Requirements and Cycle Time Optimization

The minimum number of workstations required is based on dividing total task time by the cycle time aimed at maximizing throughput, rounded up to incorporate practical considerations. For the specific goal of producing 125 units per day, the cycle time necessary is computed by dividing available operational time by the desired output. This ensures that the production rate aligns with the planning objectives while respecting constraints imposed by task durations.

Impact of Cycle Time Variations on Output

Adjusting the cycle time influences potential output. Shorter cycle times generally increase output but may complicate task sequencing, while longer cycle times reduce throughput but simplify task balancing. Calculations for cycle times of 9 and 15 minutes illustrate how modifications impact overall productivity, highlighting the importance of selecting an optimal cycle time.

Assembly Line Balancing Strategies

Balancing a line involves heuristics like the highest number of following tasks or greatest positional weight, which guide task assignments to optimize workflow (Mingozzi et al., 2014). These strategies help distribute work efficiently across stations, minimize idle time, and improve productivity, especially in complex operation scenarios, as exemplified in the second problem involving multiple tasks with precedence relationships.

Efficiency and Idle Time Calculations

Assembly line efficiency reflects how well the resources are utilized, calculated as the total task time divided by the product of the number of workstations and cycle time, expressed as a percentage. Similarly, the percentage of idle time indicates room for process improvement. Calculations in the third problem demonstrate how different task assignment strategies influence overall efficiency and operational waste.

Standard Time Determination and Worker Performance

Standard time calculations incorporate worker rating, machine performance, allowances for breaks, and other factors. By analyzing data such as machine time (3.6 minutes per cycle), worker time (1.8 minutes per cycle), and employee breaks, we can compute realistic job durations necessary for staffing and scheduling decisions. Incorporating allowances ensures more accurate estimations, enabling better process planning.

Conclusion

Effective assembly line balancing combines theoretical calculations with practical heuristics and performance considerations. By optimizing cycle times, task assignments, and efficiency calculations, organizations can maximize productivity and resource utilization. The detailed examples illustrate the critical importance of strategic planning in manufacturing processes, emphasizing the role of various mathematical and heuristic tools in achieving operational excellence.

References

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