Question

The desired daily output for an assembly line is 300 units. This assembly line will operate 425 minutes per day. The following table contains information on this product's task times and precedence relationships: TASK TASK TIME (SECONDS) IMMEDIATE PREDECESSOR A 35 — B 40 A C 35 A D 40 B E 15 C F 75 C G 45 E-F H 30 D-G Balance this line using the largest number of following tasks. Use the longest task time as a secondary criterion. (Leave no cells blank - be certain to enter "0" wherever required.)

Answer 1

We will first draw network diagram as below:

Cycle time = Production time per day/ output per day = 425 minutes per day/ 300 units per day = 1.41 minutes or 85 seconds.

Number of workstations = Sum of total task times/ cycle time = (35+40+40+30+35+15+45+75)/ (85) = 3.7 ~ 4 workstations

Now, we will assign tasks to the workstations following a rule as given- largest number of following tasks and secondary criterion as longest task time. The maximum time available with each workstation is the cycle time (85 seconds).

Beginning with the first workstation, assign each task, one at a time, until the sum of the task times is equal to the workstation cycle time or until no other tasks can be assigned due to sequence or time restrictions. Repeat this step for the remaining workstations until all the tasks have been assigned to a workstation

Task	Number of Following tasks
A	7
C	4
B or E or F	2
D or G	1
H	0

Balance made according to largest number of following tasks as below

Work stations	Task	Task Time	Number of following tasks	Remaining Unassigned Time	Feasible remaining tasks
Station 1	A C	35 35	7 4	85-35=50 50-35=15 IDLE	C None
Station 2	F (with longest time)	75	2	85-75=10 IDLE	None
Station 3	B E	40 15	2 2	85-40=45 45-15=30 IDLE	E
Station 4	G D	45 40	1 1	85-45=40 40-40=0 IDLE	D
Station 5	H	30	0	85-30=55 IDLE

Hence, in actual there is a requirement of 5 workstations.

Line efficiency = Sum of all task times/ (actual number of workstations)* (cycle time)

Line efficiency = (35+40+40+30+35+15+45+75)/ (5*85) = 315/ 425 = 74.12%

Hence, the line efficiency is 74.12%

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