8.6 Exercises

Exercise 8.1 Consider the STEM Career Fair Mixer of Example 7.7. Change the model so that the implementation uses the DistancesModel class to represent the travel distances. Use the moveTo() function to model the movement of the students within the STEM Career Fair. Compare your results to the implementation in Chapter 7.


Exercise 8.2 Consider the implementation of the tandem queue with constrained movement in Section 8.2.3. Change the model so that the implementation uses the following movable resource allocation rules.

  • MovableResourceAllocateInOrderListedRule
  • FurthestMovableResourceAllocationRule
  • LeastUtilizedMovableResourceAllocationRule
  • RandomMovableResourceAllocationRule (with stream 4)

Compare your results with those of Section 8.2.3. Which rule do you recommend and why?


Exercise 8.3 Consider the implementation of the Test and Repair Shop of Section 8.3. Change the model so that the implementation uses the following movable resource allocation rules.

  • MovableResourceAllocateInOrderListedRule
  • FurthestMovableResourceAllocationRule
  • LeastUtilizedMovableResourceAllocationRule
  • RandomMovableResourceAllocationRule (with stream 4)

Compare your results to the results of Section 8.3. Which rule do you recommend and why?


Exercise 8.4 Reconsider Exercise 7.2. Assume that there is a pool of 3 workers that perform the transport between the stations. Assume that the transport time is triangularly distributed with parameters (2, 4, 6) all in minutes. Make an assessment for the company for the appropriate number of workers to have in the transport worker pool.


Exercise 8.5 Consider the implementation of the Test and Repair Shop of Section 8.3. Re-analyze this situation and recommend an appropriate number of transport workers.


Exercise 8.6 Reconsider Exercise 8.4. The distances between the four stations (in feet) are given in the following table. After the parts finish the processing at the last station of their sequence they are transported to an exit station, where they begin their shipping process.

Station A B C D Exit
A 50 60 80 90
B 55 25 55 75
C 60 20 70 30
D 80 60 65 35
Exit 100 80 35 40

There are 2 fork trucks in the system. The velocity of the fork trucks varies within the facility due to various random congestion effects. Assume that the fork truck’s velocity between the stations is triangularly distributed with parameters (3, 4, 5) miles per hour. Simulate the system for 30000 minutes and discuss the potential bottlenecks in the system.


Exercise 8.6 Reconsider the Test and Repair example from Section 8.3 In this problem, the workers have a home base that they return to whenever there are no more waiting requests rather than idling at their last drop off point. The home base is located at the center of the shop. The distances from each station to the home base are given in as follows.

Station Diagnostics Test 1 Test 2 Test 3 Repair Home base
Diagnostics 40 70 90 100 20
Test 1 43 10 60 80 20
Test 2 70 15 65 20 15
Test 3 90 80 60 25 15
Repair 110 85 25 30 25
Home base 20 20 15 15 25

Rerun the model using the same run parameters as the chapter example and report the average number of requests waiting for transport. Give an assessment of the risk associated with meeting the contract specifications based on this new design.


Exercise 8.7 (This problem is based on an example on page 223 of (Pegden, Shannon, and Sadowski 1995). Used with permission) Reconsider Exercise 7.11. Assume that all parts are transferred by using two fork trucks that travel at an average speed of 150 feet per minute. The distances (in feet) between the stations are provided in the table below.

Enter Workstation Paint New Paint Pack Exit
Enter 325 445 445 565 815
Workstation 120 130 240 490
Paint 250 120 370
New Paint 130 380
Pack 250
Exit

The distances are symmetric. Both the drop-off and pickup points at a station are at the same physical location. Once the truck reaches the pickup/drop-off station, it requires a load/unload time of two minutes.

Analyze this system to determine any potential bottleneck operations. Report on the average flow times of the parts as a whole and individually. Also obtain statistics representing the average number of parts waiting for allocation of a transporter and the number of busy transporters. Run the model for 600,000 minutes with a 50,000 minute warm up period.


Exercise 8.8 Three independent conveyors deliver 1 foot parts to a warehouse. Once inside the warehouse, the conveyors merge onto one main conveyor to take the parts to shipping. Parts arriving on conveyor 1 follow a Poisson process with a rate of 6 parts per minute. Parts arriving on conveyor 2 follow a Poisson process with a rate of 10 parts per minute. Finally, parts arriving on conveyor 3 have an inter-arrival time uniformly distributed between (0.1 and 0.2) minutes. Conveyors 1 and 2 are accumulating conveyors and are 15 and 20 feet long respectively. They both run at a velocity of 12 feet per minute. Conveyor 3 is an accumulating conveyor and is 10 feet long. It runs at a velocity of 20 feet per minute. The main conveyor is 25 feet long and is an accumulating conveyor operating at a speed of 25 feet per minute. Consider the parts as being disposed after they reach the end of the main conveyor. Simulate this system for 480 minutes and estimate the accessing times and the average number of parts waiting for the conveyors.


Exercise 8.9 Consider the scenario discussed in Section 8.4.4 concerning recirculating conveyors regarding the test and repair system. Assume that each test station only has room for two parts (the part being processed and one waiting). Implement the conveyor system such that parts that arrive to a full testing station recirculate until they can eventually get processed. Run the model for the same model settings as used in the textbook example. What is the effect of recirculating on the conveyor utilization? How does the finite buffers and recirculating conveyor affect the total system time for the parts?


Exercise 8.10 Consider the scenario discussed in Section 8.4.4 concerning two conveyors with one conveyor merging into the middle of the second conveyor. Entities arrive at the midpoint station from both entry points (A and B). Those arriving from Station A continue on their conveyor. Those arriving from Station B exit the merge belt conveyor and access the main belt conveyor. Type A entities arrive to station A according to a Poisson process with a rate of 1 arrival every 2 minutes. Similarly, Type B entities arrive according to a Poisson process with a rate of 1 arrival every 2 minutes to station B.

The main belt conveyor has two segments each of length 5 feet. The first segment goes from station A to the middle (merge point) and the second segment goes from the merge point to the exit station. The merging conveyor has one segment of length 10 feet, which goes from station B to the merge point. Both conveyors have velocity of 1 foot per minute with cell size of 1 and the maximum cells occupied as one. Both conveyors are also accumulating.

Develop a KSL model for this situation using base time units of minutes. Report the results for system time and throughput for the parts based on 480 minutes of operation.


Exercise 8.11 Consider the scenario discussed in Section 8.4.4 concerning a diverging conveyor. Entities arrive at the arrival station according to a Poisson process with a rate of 1 part every 12 minutes. The parts are conveyed on the main conveyor to a sorting area. The length of the main conveyor is 20 feet. The main conveyor has a velocity of 1 foot per minute and uses a cell size of 1. Assume the maximum cell size is also one.

At the sorting area, the parts are shunted to either of two processing areas: area 1 and area 2. Thus, there is a conveyor from the sorting area to the first processing area. Call this conveyor the line 1 conveyor. There is also a conveyor from the sorting area to the second processing area. Call this conveyor the line 2 conveyor. Both conveyors have one segment of 20 feet and use velocity of 1 foot per minute and single unit cell sizes with maximum cell size of 1.

The logic at the sorting area is simple. Each arriving part is shunted to area 1 or 2 in an alternating fashion. The first arriving part goes to area 1. At the sorting area there is a small delay of 3 seconds as the part is scanned and then sent to the appropriate area.

Develop a KSL model for this situation using base time units of minutes. Report the results for system time and throughput for the parts based on 120 minutes of operation.


G References

Pegden, C. D., R. E. Shannon, and R. P. Sadowski. 1995. Introduction to Simulation Using SIMAN. 2nd ed. McGraw-Hill.