An assembly line with 28 activities is to be balanced. The total amount of time required for all 28 activities is 88 minutes. The longest activity is 2.2 minutes and the shortest is 0.8 minutes. The line will operate for 450 minutes per day. Using a cycle time of 60 seconds, determine an assembly-line balance by selecting the longest-processing-time task available. Compute the total idle time and assembly-line efficiency.
-The total idle time is _____ seconds.
A) less than or equal to 20
B) more than 20 but less than or equal to 30
C) more than 30 but less than or equal to 40
D) more than 40 but less than or equal to 50

Question

Quizplus · Accepted Answer

First, we need to calculate the maximum theoretical production rate based on the cycle time:

Maximum theoretical production rate = (450 minutes/day x 60 seconds/minute) / 60 seconds = 450 units/day

Next, we need to determine the number of workstations required using the longest-processing-time task available:

Number of workstations = Ceiling (total time required for all activities / cycle time) 
= Ceiling (88 minutes / 60 seconds) 
= Ceiling (88/60) 
= 2 workstations

Therefore, the assembly line can be split into 2 workstations with the first workstation consisting of tasks 1-14 and the second workstation consisting of tasks 15-28.

To calculate the idle time, we need to first calculate the total processing time for each workstation:

Workstation 1 processing time = (2.2 minutes x 60 seconds) + (1.8 minutes x 60 seconds) + (1.5 minutes x 60 seconds) + (1.1 minutes x 60 seconds) + (1.0 minute x 60 seconds) + (0.9 minute x 60 seconds) + (0.8 minute x 60 seconds) = 468 seconds

Workstation 2 processing time = (1.9 minutes x 60 seconds) + (1.7 minutes x 60 seconds) + (1.3 minutes x 60 seconds) + (1.2 minutes x 60 seconds) + (1.0 minute x 60 seconds) + (0.9 minute x 60 seconds) + (0.8 minute x 60 seconds) = 411 seconds

Total processing time = 468 seconds + 411 seconds = 879 seconds

Idle time = (Total available time - Total processing time) 
= (450 minutes/day x 60 seconds/minute) - 879 seconds 
= 21 seconds/day

Therefore, the total idle time is more than 20 but less than or equal to 30 seconds.

Assembly-line efficiency = (Total processing time / Total available time) x 100% 
= (879 seconds / (450 minutes/day x 60 seconds/minute)) x 100% 
= 32.40%

The best choice is C because it correctly identifies the range for the total idle time.

An Assembly Line with 28 Activities Is to Be Balanced