Consider a process that has 3 stations, ordered in sequence: A, B and C. At each
ID: 376861 • Letter: C
Question
Consider a process that has 3 stations, ordered in sequence: A, B and C. At each station, two consecutive tasks are performed one after the other. The time (in seconds per unit) it takes for a single person to perform each task is given in the table below (e.g., task A2 takes 60 seconds per unit):
Station
# of
Workers
Task A1
Task
A2
Task
B1
Task
B2
Task
C1
Task C2
A
1
70
60
-
-
-
-
B
1
-
-
60
60
-
-
C
1
-
-
-
-
15
15
The table also gives the number of workers at each station. What is the capacity of this process (in units per minute)? Remember bottleneck determines the capacity of the process. (The accuracy should be of two digits after the decimal places.)
Please include explanation.
Station
# of
Workers
Task A1
Task
A2
Task
B1
Task
B2
Task
C1
Task C2
A
1
70
60
-
-
-
-
B
1
-
-
60
60
-
-
C
1
-
-
-
-
15
15
Explanation / Answer
As stated in the problem, the capacity of the whole process is equal to the capacity of the bottleneck station. To find this, we need to find the capacity of each individual station.
Capacity of a station in units per minute = Number of workers * (1 / Time in minutes at each station)
But since we have time given in seconds, the formula is rearranged as
Capacity in units per minute = Number of workers * (1/ (time in seconds/60)) = Number of workers * (60 / time in seconds)
Using above formula to calculate individual capacities:
Capacity of station A = 1 * (60 / (70+60)) = 60 / 130 = 0.46 units/minute
Capacity of Station B = 1 * (60 / (60+60)) = 60 / 120 = 0.5 units/minute
Capacity of Station C = 1* (60 / (15+15)) = 60 / 30 = 2 units/minute
The station with the least capacity is the bottleneck.
In this problem, Station A is the bottle neck so the total capacity of the process is 0.46 units per minute
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