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# Farr Pharmaceutical average waiting time, queue length

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5. You are in charge of a major new product development project for your company. Instead of presenting the details of your analysis, you aggregate all three elements of this product into a simple PERT network to present to senior management as shown below. You would like to introduce simulation as a project management tool for your company and you feel that this product has enough visibility to persuade senior management of its utility. Using Crystal Ball, develop a plot of project duration as a function of probability of completion (please cut and paste the spreadsheet along with the cumulative frequency view).

Where

A = Requirements gathering (uniformly distributed varying between 3 and 5 week)
B = Develop prototype and test market (normally distributed with a mean of 5 weeks and a standard deviation of 3)
C = Manufacture and distribute new product (uniformly distributed varying between 5 and 8 week)
D = Advertising, trade shows, market to distributors, etc. (fixed at 11 weeks)

6. As a new manager of manufacturing of specialty devices for Farr Pharmaceutical Devices, you need to improve turnaround time. You currently are operating one manufacturing line. You did a queuing analysis on the operation, but found the mathematical solution did not accurately model the real world system; therefore, you decide to manually simulate the operation. You analyzed last year's data and arrived at the following distribution of arrival intervals and service times:

Distribution of Arrival Intervals

Arrival Interval (days) Number of
Occurrences Probability P(x) Cumulative Probability Random Number Range
1.0 4
2.0 6
3.0 3
4.0 7

Manufacturing times are uniformly distributed and vary between 1 and 3 days.

= 1+2r

Use the table below to manually simulate (hint - do NOT round your numbers to integer values) the process of your specialty manufacturing operation.

Job # r1 Inter-arrival time Total Clock Time Start Manu Time Wait Time Queue Length After Entry r2 Manu Time Depart Clock Time in System
1 --- --- 0 0.00 0.00 0 0.93
2 0.06 0.72
3 0.47 0.83
4 0.3 0.35
5 0.97 0.17
6 0.96 0.82
7 0.22 0.63
8 0.16 0.68
9 0.52 0.95
10 0.98 0.07

Determine the average waiting time, average queue length, and average time in the system.