Question

Problem 6-1 (Static)

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.)







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.)







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.)







d. What cycle time will provide an output rate of 125 units per day? (Round your answer to 1 decimal place.)







e. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes?

Answer 1

The minimum cycle time is 2.4 minutes and the maximum cycle time is 1.06 minutes. The range of daily output is 424.53 to 187.5 units. The minimum number of workstations needed for maximum output is 425.

Step-by-step explanation:

a. Minimum and maximum cycle times:

The minimum cycle time is determined by the longest task, which is 2.4 minutes. Therefore, the minimum cycle time is 2.4 minutes.

The maximum cycle time is determined by the total time for all tasks divided by the number of tasks. In this case, the total time is 18 minutes and there are 17 tasks. So the maximum cycle time is 18 / 17 = 1.06 minutes (rounded to 1 decimal place).

b. Range of daily output:

The range of daily output is determined by the minimum cycle time and the line's operating time. The smaller value is the operating time divided by the maximum cycle time: 450 / 1.06 = 424.53 (rounded to 1 decimal place). The larger value is the operating time divided by the minimum cycle time: 450 / 2.4 = 187.5 (rounded to 1 decimal place).

c. Minimum number of workstations:

To achieve the maximum output rate, we need to divide the total time available (450 minutes) by the maximum cycle time (1.06 minutes). This gives us 450 / 1.06 = 424.53 workstations. Since we cannot have a fraction of a workstation, we need to round up to the next whole number. Therefore, the minimum number of workstations needed is 425.

d. Cycle time for an output rate of 125 units per day:

To find the cycle time for an output rate of 125 units per day, we need to divide the operating time per day (450 minutes) by the desired output rate (125 units). This gives us 450 / 125 = 3.6 minutes (rounded to 1 decimal place).

e. Output potential for cycle times of 9 minutes and 15 minutes:

(1) For a cycle time of 9 minutes, the output potential is the operating time per day divided by the cycle time: 450 / 9 = 50 units.

(2) For a cycle time of 15 minutes, the output potential is the operating time per day divided by the cycle time: 450 / 15 = 30 units

Answer 2

a. The minimum cycle time is 1.8 minutes and the maximum cycle time is 2.4 minutes.

b. The range of daily output is theoretically possible for the line is 22.2 to 30 units per day.

c. The minimum number of workstations needed if the maximum output rate is to be sought is 8.

d. The cycle time that will provide an output rate of 125 units per day is 2.1 minutes.

e. If the cycle time is 9 minutes, the output potential will be 50 units per day. If the cycle time is 15 minutes, the output potential will be 30 units per day.