This question illustrates the effect of different levels of variability in a serial production system. Use the three station simulation (Three Station_CV.mox) that measures coefficient of variation (COV) in the Examples/Models and Methods folder. For each case use two different policies for releasing raw materials to the system:

Raw Material Release Policies

1. Material is released to the first station with a constant interval between releases of 5 minutes.
2. Material is released to the first station with the interval between releases having an exponential distribution with mean time of 5 minutes..

Processing Time Assumptions

The processing time at each station is governed by a non-central Beta distribution with the parameters alpha = beta = 5. The mean processing time is 4 but the alternatives below have different values COV.

1. The range of the Beta distribution is 0 to 8. COV = 0.447.
2. The range of the Beta distribution is 2 to 6. COV = 0.224.
3. The range of the Beta distribution is 3 to 5. COV = 0.112.

Questions

a. For the 6 combinations of raw material release policies and processing time assumptions, make 10 simulation runs of 1000 minutes each. Measure the average cycle time in each case. Compare the results and rank the runs according to increasing cycle time.

b. For the 6 combinations of raw material release policies and processing time assumptions, use the formulas for non-Poisson queueing networks from Chapter 17 to compute the average cycle time in each case. Compare the results and rank the runs according to increasing cycle time. Compare the results from the simulation of part a. Comment on the accuracy of the approximate analytical formulas.

c. Simulate the system when the release time and all processing times are exponentially distributed. The average time between material release is 5 minutes and the average processing time at each station is 4 minutes. Make 10 simulation runs of 1000 minutes each. Use the formulas for the Jackson network to compute the cycle time and compare the simulated and analytical results. Which results are more accurate?