2. The production planning and control department (PPCD) at VECO Metal is going

Question

2. The production planning and control department (PPCD) at VECO Metal is going to analyze and improve a production line with two single-machine stations (i.e. A & B). PPCD made the assumption of exponential distribution for both arrival rate and processing time. PPCD also recorded new values for arrival rate and average (effective) processing time for stations A and B as follows Station Arrival rate (parts/day) Processing time (hour) 0.95 0.90 a) Determine if the parts spend more time in station A or B (in average). b) What is the average number of jobs at station A? c) At station B, what happens to CT and WIP if the arrival rate (parts/hour) approaches the value of process rate?

Explanation / Answer

a)

System A

Arrival rate, 1 = 6

Processing rate, 1 = 8/0.95 = 8.42 (assuming 8 hours a day)

Average time in station A = 1/(1 - 1) = 1/(8.42 - 6) = 0.413 day = 3.31 hours

System B

Arrival rate, 2 = 7

Processing rate, 2 = 8/0.90 = 8.9 (assuming 8 hours a day)

Average time in station B = 1/(2 - 2) = 1/(8.9 - 7) = 0.529 day = 4.24 hours

Parts spend more time in station B

b) Average number of jobs at station A = 1/(1 - 1) = 6/(8.42 - 6) = 2.48

c) If arrival rate approaches processing rate, the CT and WIP become very large.

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