Question 1. A workshop has two different workstations (A and B), and each workstation can only handle one part at a time. The workshop normally manufactures two different types of products (P1 and P2). The parts of P1 have an exponential interarrival time distribution with mean 5 (all times are given in minutes). The parts of P1 will first be processed at workstation A, and then workstation B. Parts of P2 have an exponential interarrival time distribution with mean 8. The parts of P2 are only processed on workstation B. The first arrival of both types of parts is at time 0, and both part types are in the same first in first out queue for workstation B, and have the same priority there as each other. The processing time at workstation A follows a triangular distribution with a minimum of 1, mode of 4, and maximum of 8. The processing time at workstation B for both parts follows a uniform distribution between 1 and 4.

Run your simulation for a single replication of one 7-day week (24 hours per day) and observe the average total time in system for P1 and P2 separately, the time-average number of parts in the system of each type separately, and the utilizations of the two workstation.

Question 2. A heating system has two operations. Parts arrive according to an exponential interarrival time distribution with mean 4 (all times are in minutes), with first part's arriving at time 0. Parts enter the first heating machine for initial heating that has a triangular operation time with minimum 1, mode 4, and maximum 6. Once the part completes the initial heating process, it must be allowed to cool down for 10 minutes. During this unattended cooling time, the part is out of the first heating machine so other parts can be heated. And there is no limit on how many parts can be in their 10-minute cooling period at the same time. After cooling down, the parts enter the second heating machine, which is the final heating process. The final heating process has a uniform processing time between 1 and 8. Both heating machine can only handle one part at a time.

Run the simulation for a single replication of 24 hours and observe the average total time in system of parts, the average time in queue for both heating machines.

Question 3. In a shipping company, the items arrive according to an exponential interarrival distribution with mean 1.2 (all times are in minutes), with the first arrival at time 0. The items are first packed by one of four identical packers, with a single queue for all four packers. The packing time is triangular distribution with minimum 2.5, mode 3.5, and maximum 4. Packed boxes are then separated by type. 20% of the boxes are being international, and the rest are for domestic shipping. There is only one shipper for international packages and two shippers for domestic packages. The two domestic shippers share the same queue. The international shipping time is triangular distribution with minimum 2.5, mode 3.5, maximum 5, and the domestic shipping time is triangular distribution with minimum 2, mode 2.5, and maximum 3. The company works three 8-hour shifts, 5 days a week. All the packers and shippers are given a 15-minute break 2 hours into their shift, a 30-minute lunch break 4 hours into their shift, and a second 15-minute break 6 hours into their shift. Use the Wait schedule rule. All the packers and shippers will take their breaks at the same time.

Run the simulation for a single replication of 10 working days to determine the average and maximum number of items in each of the three queues.

Question 4. Using the model from problem 3, change the packer and domestic shipper schedules to stagger the breaks so there are always at least three packers and one domestic shipper working. Start the first 15-minute packer break 1 hour into the shift, the 30-minute lunch break 3 hours into the shift, and the second 15-minute break 6 hours into the shift. Start the first domestic shipper 15-minute break 90 minutes into the shift, the 30-minute lunch break 3.5 hours into the shift, and the second 15-minute break 6 hours into the shift.

Run the simulation for a single replication of 10 working days to determine the average and maximum number of items in each of the three queues.

Question 5. There is a machine shop with three workstations to process two different types of parts. Part type 1 arrives according to an exponential distribution with interarrival time mean 6 (all times are in minutes), and the first arrival is at time 0. Part type 1 is first processed at workstation 1 and the workstation 2. Its processing time at workstation 1 follows a triangular distribution with minimum 2, mode 3, and maximum 5. Its processing time at workstation 2 follows a triangular distribution with minimum 3, mode 5, and maximum 7. Part type 2 arrives according to an exponential distribution with interarrival time mean 8, and the first arrival is at time 0. Part type 2 is first processed at workstation 1 and then workstation 3. Its processing time at workstation 1 follows the same distribution as does part type 1 at workstation 1. Its processing time at workstation 3 follows a triangular distribution with minimum 3, mode 7, and maximum 9. Each workstation can only handle one part at a time with first in first out queue.

Run the simulation for a single replication of 2000 minutes and observe the average and maximum time in system for each part type separately.