Three Hills Power Company provides power to a large city. The company is concerned about generator failures because it incurs two added costs when one fails. When a generator breaks down, Three Hills must purchase generator service from a competing company for $368 per hour. At the same time, Three Hills incurs a cost of $120 per labor hour for a repair person to fix the generators. Management wants to assess the two component costs, i.e., the breakdown cost and the labor cost. They have asked you to develop a simulation model which will be used for this assessment. Parameters for your simulation model are: Mean time between failure of these generators is 25.78 hours. Time between failures follows an exponential distribution. The average time to repair the generators is 13.156 hours. Time to service the generators follows an exponential distribution.

Model this scenario using discrete event simulation for 20 failed generators. You are provided uniform random variables between 0 and 1 in the Excel Answer Template. Use Uniform Random Variable (1) to simulate the time between failure (arrival) of a generator, and Uniform Random Variable (2) to simulate the service time. Make the following assumptions:

a. The scenario is modeled as an M/M/1 queue. Times between arrivals are exponentially distributed, while the service time is also exponentially distributed.

b. There is always one and only repair person on duty 24 hours a day, seven days a week. The repair person charges $120 per hour only when servicing the generators. When they are not repairing generators, they are maintaining other equipment and charge this time to another account.

c. When generator X fails it immediately enters the repair system. If no generator is in the system, then generator X is immediately serviced. If generator Y is being serviced at the time generator X fails, then Generator X waits until the maintenance person completes the repairs of generator Y. Then the maintenance person begins servicing Generator X.

d. The probability that all of Three Hills generators are out of commission at any moment in time is zero.

e. There are an infinite number of competing generators to cover all of Three Hills failed generators.

f. All the other assumptions associated with queuing are in effect.

Note: If you are modeling this correctly, the time that your 20th generator fails would be at time T20 = 452.880228 hours, and the time the repair person completed the 20th repair would be at time T20 = 453.833738 hours.

From the simulated data, determine:

a. The total cost of purchasing the competing generator service for the 20 generators

b. The total labor cost to repair the 20 generators

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{40PointsIV} & \multirow{2}{*}{\begin{tabular}{l} MTBA \\ MTTS \end{tabular}} & \multicolumn{2}{|c|}{25.78 hours } & & & & & & & \multirow{2}{*}{ Rate } & & & & \\ \hline & & 13.156 & hours & & & & & & & & Hours & & Cost & \\ \hline & & & & & & & & \multicolumn{2}{|c|}{ Cost of down time: } & 368 & - & a. & & \\ \hline & lambda & 0.0387898 & per hour & & & & & \multicolumn{2}{|c|}{ Cost of labor } & 120 & - & b. & & \\ \hline & mu & 0.0760109 & per hour & & & & & \multicolumn{2}{|l|}{ Total cost } & & & & & \\ \hline & & & & & & & & & & & & & & \\ \hline & & & & & & & & & & & & & & \\ \hline & & \begin{tabular}{l} Generator \\ failure \end{tabular} & \begin{tabular}{c} Uniform \\ random \\ variable \\ (1) \end{tabular} & \begin{tabular}{c} Uniform \\ random \\ variable \\ (2) \end{tabular} & \begin{tabular}{c} Time \\ Between \\ Arrivals \end{tabular} & & \begin{tabular}{l} Time of Arrival \\ of Repair action \end{tabular} & \begin{tabular}{l} Time to \\ begin \\ repair \end{tabular} & & \begin{tabular}{l} Service \\ Time \end{tabular} & \begin{tabular}{l} Time repair \\ is \\ completed \end{tabular} & \begin{tabular}{c} Waiting in \\ queue \end{tabular} & \begin{tabular}{l} Time Waiting \\ in the system \end{tabular} & (1/)LN(U) \\ \hline & & 0 & & & & T0 & & & & & & & & \\ \hline & & 1 & 0.821051 & 0.258531 & & T1 & & & Service T1 & & & & & \\ \hline & & 2 & 0.700157 & 0.569699 & & T2 & & & Service T2 & & & & & \\ \hline & & 3 & 0.445496 & 0.214945 & & T3 & & & Service T3 & & & & & \\ \hline & & 4 & 0.781476 & 0.007871 & & T4 & & & Service T4 & & & & & \\ \hline & & 5 & 0.17864 & 0.32069 & & T5 & & & Service T5 & & & & & \\ \hline & & 6 & 0.189245 & 0.700512 & & T6 & & & Service T6 & & & & & \\ \hline & & 7 & 0.28548 & 0.663273 & & T7 & & & Service T7 & & & & & \\ \hline & & 8 & 0.2009 & 0.867401 & & T8 & & & Service TB & & & & & \\ \hline & & 9 & 0.210758 & 0.107326 & & T9 & & & Service T9 & & & & & \\ \hline & & 10 & 0.032208 & 0.587577 & & T10 & & & Service T10 & & & & & \\ \hline & & 11 & 0.785229 & 0.054258 & & T11 & & & Service T11 & & & & & \\ \hline & & 12 & 0.098977 & 0.16785 & & T12 & & & Service T12 & & & & & \\ \hline & & 13 & 0.495477 & 0.616797 & & T13 & & & Service T13 & & & & & \\ \hline & & 14 & 0.555337 & 0.466255 & & T14 & & & Service T14 & & & & & \\ \hline & & 15 & 0.141834 & 0.746923 & & T15 & & & Service T15 & & & & & \\ \hline & & 16 & 0.109971 & 0.178191 & & T16 & & & Service T16 & & & & & \\ \hline & & 17 & 0.501419 & 0.908462 & & T17 & & & Service T17 & & & & & \\ \hline & & 18 & 0.935698 & 0.677712 & & T18 & & & Service T18 & & & & & \\ \hline & & 19 & 0.793199 & 0.477662 & & T19 & & & Service T19 & & & & & \\ \hline & & 20 & 0.672649 & 0.836125 & & T20 & & & Service T20 & & & & & \\ \hline \end{tabular}