Question 3a and b

Question 3 A manufacturing company employs a maintenance crew to repair its machines as needed. Management now wants a simulation study done to analyse what the size of the crew should be, where the crew sizes are 2, 3, and 4. The time required by the crew to repair a machine has a uniform distribution over the interval from 0 and twice the mean, where the mean depends on the crew size. The mean is 4 hours with two crew members, 3 hours for three crew members, and 2 hours with four crew members. The time between breakdowns of some machine has of 5 hours. When a machine breaks down and so requires repair, management wants its average waiting time before repair begins to be no more than 3 hours. Management also wants the crew size to be no larger than I an exponential distribution with a mearn necessary to achieve this. (a) Consider the case of a crew of size 2. That means that the corresponding repair time has the uniform distribution between 0 and 8 hours. Assume that the following numbers represent times between breakdowns (in minutes) 100; 120; 90: 230: 20: 60: 280:220: 110:20; 270; 220; 140:90: 50; 260:240 Assume also that the following numbers represent repair times (in minutes) 80; 170; 130:370: 300: 120; 420;80; 190: 250: 120: 180:310: 460; 30; 170 Simulate this system by hand for 20 hours. (That is stop the simulation process when the simulation time is 20 hours or 1800 minutes.) Indicate the number of machines that have completed their delay in the queue and compute the time- average number of machimes in the repair queue and other relevant performance measure of this queuing system. (b) Use the Mathematica code in the study guide (on pages 35-37) to simulate 10000 breakdowns and their repair for each of the three crew sizes. Comment on the perfor mance of each case. Note that to generate a random number from the uniform distri- bution Ula, b, use the Mathematica code: abRandom; Then to you should re- place InterArrivalTimesMeanInterArrivalTime Log [Random 1 with InterArrivalTimes-abRandom: (where a 0 and b 8) for the crew with two members. Also take NumberDelaysRequired 10000; Question 4 Question 3 A manufacturing company employs a maintenance crew to repair its machines as needed. Management now wants a simulation study done to analyse what the size of the crew should be, where the crew sizes are 2, 3, and 4. The time required by the crew to repair a machine has a uniform distribution over the interval from 0 and twice the mean, where the mean depends on the crew size. The mean is 4 hours with two crew members, 3 hours for three crew members, and 2 hours with four crew members. The time between breakdowns of some machine has of 5 hours. When a machine breaks down and so requires repair, management wants its average waiting time before repair begins to be no more than 3 hours. Management also wants the crew size to be no larger than I an exponential distribution with a mearn necessary to achieve this. (a) Consider the case of a crew of size 2. That means that the corresponding repair time has the uniform distribution between 0 and 8 hours. Assume that the following numbers represent times between breakdowns (in minutes) 100; 120; 90: 230: 20: 60: 280:220: 110:20; 270; 220; 140:90: 50; 260:240 Assume also that the following numbers represent repair times (in minutes) 80; 170; 130:370: 300: 120; 420;80; 190: 250: 120: 180:310: 460; 30; 170 Simulate this system by hand for 20 hours. (That is stop the simulation process when the simulation time is 20 hours or 1800 minutes.) Indicate the number of machines that have completed their delay in the queue and compute the time- average number of machimes in the repair queue and other relevant performance measure of this queuing system. (b) Use the Mathematica code in the study guide (on pages 35-37) to simulate 10000 breakdowns and their repair for each of the three crew sizes. Comment on the perfor mance of each case. Note that to generate a random number from the uniform distri- bution Ula, b, use the Mathematica code: abRandom; Then to you should re- place InterArrivalTimesMeanInterArrivalTime Log [Random 1 with InterArrivalTimes-abRandom: (where a 0 and b 8) for the crew with two members. Also take NumberDelaysRequired 10000; Question 4