Suppose a process contains two workstations that operate with no buffer between them. a. Which of the three scenarios will have, on average, the highest flow rate? b. Which of the three scenarios will have, on average, the lowest flow time?

Complete question is in attachment

a) scenario 1 and 3 will have the highest flow rate with 12p/hr

b) scenario 3 will have the lowest flow time of 9 mins

Explanation:

a) let's compute the flow rate ot the 3 scenarios.

We now have:

•For scenario 1:

Processing time of workstation A = 5mins

Processing time of workstation B = 5mins

Therefore, the cycle time of process= max(processing time of A, processing time of B)

=> max(5,5)

=5 mins

flow rate= 1/cycle time

= 1/5 per minute

Convert to hrs we have:

(1*60)/5 = 12per hour

•For scenario 2

Consider the 50℅ probability that processing time of workstation B is 4mins:

Processing time of workstation A = 5mins

Processing time of workstation B = 5mins

Therefore, the cycle time of process= max(processing time of A, processing time of B)

=> max(5,4)

= 5mins

flow rate= 1/cycle time

= 1/5 per minute

Convert to hrs we have:

(1*60)/5 = 12per hour

Let's now consider the 50℅ probability that processing time of workstation B is 6mins

= max(5,6)

=6 mins

flow rate= 1/6 per minute

= (1*60)/6 = 10per hour

Therefore, expected flow rate = 50℅*12+50℅*10= 11hours

•For scenario 3:

Processing time of workstation A = 5mins

Processing time of workstation B =either 3 or 5mins

Therefore, the cycle time of process= max(processing time of A, processing time of B)

=> max(5, 3 or 5)

= 5mins

flow rate= 1/cycle time

= 1/5 per minute

Convert to hrs we have:

(1*60)/5 = 12per hour

Therefore scenario 1 and3 have highest flow rate with 12per hour

b) We find the time rate by adding up the processing time.

•For scenario 1:

Processing time of workstation A = 5mins

Processing time of workstation B= 5mins

Therefore flow time will be= 5+5 = 10mins

For scenario 2:

Processing time of workstation A = 5mins

Processing time of workstation B has 50℅ chance of being 4 mins and anothe 50℅ of being 6mins

Therefore processing time of B will be= 50%*4+50%*6= 5mins

Therefore, flow time = 5+5= 10mins

•For scenario 3:

Processing time of workstation A = 5mins

Processing time of workstation B has 50℅ chance of being 3mins and anothe 50℅ of being 5mins

Therefore processing time of B will be= 50%*3+50%*5= 4mins

Therefore, flow time = 5+4= 9mins

Therefore, scenario 3 has lowest flow time with 9mins

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