Consider the following four-step process. Assume demand arrives at a rate of 6 j

Question

Consider the following four-step process. Assume demand arrives at a rate of 6 jobs per hour.

Station

Processing Time (minutes)

Number of Workers

A

2.5

1

B

5.0

1

C

3.0

1

D

4.0

1

assume that a job can be processed at Station B and Station
C simultaneously. That is, the activities at these two stations can be executed in parallel.
a. Supporting your answers with “paper-and-pencil” calculations, answer the following questions.
i. What is the utilization of each station? What is the bottleneck?
ii. What is the average flow time?
iii. With sufficient demand, what is the maximum throughput rate achievable by the process?
iv. What is the average throughput rate?
v. What is the average time between items?
vi. What is the average work-in-process?

Station

Processing Time (minutes)

Number of Workers

A

2.5

1

B

5.0

1

C

3.0

1

D

4.0

1

Explanation / Answer

i)

Throughput rate = 6 jobs per hour

So, Cycle time = 60/6 = 10 minutes

Utilization of station A = 2.5/10 = 0.25

Utilization of station B = 5/10 = 0.50

Utilization of station C = 3/10 = 0.30

Utilization of station D = 4/10 = 0.40

Station B is the bottleneck, because it has the maximum processing time.

ii) Average flow time (lead time) = 2.5+MAX(5,3)+4 = 11.5 minutes

iii) Maximum throughput rate achievable by the process = 1/cycle time = (1/5) = 0.2 per minute or 12 jobs per hour

iv) Average throughput rate = demand = 6 jobs per hour

v) Average time between items (Cycle time) = 10 minutes (as determined in part i)

vi) Average work-in-process = Throughput rate * Lead time (using Little's Law)

= 6 jobs per hour * (11.5/60) = 1.15 jobs

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