1. DECISION MODELING WITH MICROSOFT EXCEL Copyright 2001 Prentice Hall Publishers and Ardith E. Baker DISCRETE EVENT SIMULATION SIMULATION Chapter 10 Part 2

2. EXAMPLE 4 – HERVIS CAR RENTAL MODEL REVISITED Based on the previous results, Hervis came up with an idea of pulling some of the car service people off the car lot to staff more rental stations whenever the ______of customers became large. In this way, the staffing of the rental stations would ___________to three or even four clerks whenever a peak in customer ________occurred. To model this __________change in behavior in Extend, we would need a way to alter the value in the Maximum Number in Activity field of the Activity, Multiple block dialog during the _______________.

3. To do this, double-click the Queue, FIFO block to display its dialog window. For explanations, click on the Help button. The ________ output connector reads out the queue _______ throughout the simulation run. The C connector can be used to input a ________ value that overrides the number recorded in the Maximum Number in Activity field.

4. What is needed is a way to _________the L value from the Queue, FIFO block into the desired number of _____________and feed that dynamic number into the C connector of the Activity, Multiple block during the simulation. Extend’s Conversion Table block is similar to Excel’s _________in that it will map the input L values to the output____________.

5. To open the Conversion Table block, click on GENERIC.lix - Math - Conversion Table.

6. Connect the L value output __________of the Queue, FIFO block to the Conversion Table’s _______ connector. Next, connect the Conversion Table’s _________connector to the C value of the Activity, Multiple _______.

7. The text box shows Hervis’ proposed decision rule for increasing the number of rental station clerks.

8. Double-click on the Conversion Table block to open its dialog window. Choose Stepped under the Table is: option. A value of 4 for y out is assigned to values of x in greater than____. This places a ______on the maximum number of rental clerks. Click on the Run Simulation icon. These values (0 - 30 for ____ and 1 - 4 for y out) represent the proposed _________rule.

9. Here is the resulting graph. Remember, results will differ due to the random effects.

10. Now, compare the following results for the Queue, FIFO block: 2 Clerks Up to 4 Clerks during peak periods

11. Compare the following results for the Activity, Multiple block: 2 Clerks Up to 4 Clerks during peak periods

12. To verify these results, we could run the __________many more times. However, it would be difficult to compare each set of_________. Extend’s Queue Stats block, will collect ______ statistics from multiple runs of a simulation model. Using this, we can _______________assess the influence of the model’s inherent ___________on a performance measure. Open this block by going to the Library – Open Library menu and choosing _________from the resulting dialog.

13. Now, open the Queue Stats block and place it anywhere in the Extend model window.

14. Double-click on the Queue Stats block to open its dialog window: To tabulate the results of multiple runs, select the Append new updates and Update at end of simulation options.

15. Now, go to Run – Simulation Setup dialog and change the Number of runs to say,_______. This instructs Extend to make 20 ___________ runs of the model, tabulating the queuing statistics from each run into the ___________ block. Clicking on the Run Simulation _______will now cause the model to automatically run 20 times.

16. After starting the simulation, a ___________and small graph will appear on the bottom of the screen, from which you can _______the progress of the simulations.

17. After the runs are finished, double-click on the Queue Stats block to open the dialog and review the results. These results confirm that _________the number of clerks will not help the model.

18. Clicking on the Confidence Interval button in this dialog will further ___________the results giving 95% confidence intervals.

19. EXAMPLE 5 – FINAL HERVIS CAR RENTAL MODEL Now, return to the original 2 clerk rental station policy.

20. Instead of increasing the number of clerks at the rental station, let’s consider __________only two types of customers: Those who desire smaller compact cars (_____________cars) Those who desire larger, more powerful cars (__________cars) Assume that ________of customers will opt for economy cars and the balance for deluxe cars. The challenge is to decide how many of each type of car to have __________at the beginning of the week to avoid car shortages during the week and ultimately customer_______________.

21. Past data on car rentals shows: Economy car customers rent their car for between ______________days. Deluxe car customers rent their cars typically for two days plus or minus a___________. Since the time interval for economy car rentals is fairly evenly_________, we can approximate the distribution as being___________. For deluxe car renters, a __________distribution for the rental times is a good fit to the data, with a _________________of ½ a day.

22. We will use Extend’s _______________blocks to minimize visual complexity. This will allow us to create models made up of ____________(logical groupings of Extend blocks). To do this, select all of the _________except the Executive and Exit blocks and choose the Make Selection Hierarchical item on the _______menu.

23. A dialog will appear in which you can specify a name for the new__________. Enter the name and click on Make H-Block to create the super-block.

24. You can double-click on the super-block to expand it into a new window and add a label.

25. Now, begin building the expanded _______in place of the original Exit block, so that customers _________out of the Rental Office submodel will enter the rental car lot of the __________model. Delete the ______block in the Extend model and add two new _________: This block uses an _____________to assign a 0 value (to signify an economy car rental) with ____________.7 and a 1 value (deluxe car rental) with probability.3. This block splits the _______of customers to one of two output connectors based upon the value present at its ________connector. Input Random Number block Select DE Output block

26. To insert the Input Random Number block, go to Library – GENERIC.lix – Inputs/Outputs – Input Random Number.

27. Double-click on this icon to open the respective dialog. Choose Empirical Table as the Distribution. Specify the _________which signify whether an economy or deluxe car is rented and the respective_________________. Give the block a _________.

28. To insert the Select DE Output block, go to Library – DE.lix – Routing – Select DE Output.

29. Double-click on this icon to open the respective dialog. The incoming ___________is directed to the top (“a” connector) output if the random number at its Select connector is ____and is directed to the bottom (“___” connector) output if the random number at its Select connector is_____.

30. A Resource Pool is a ___________that indicates how many of a named constrained ___________(e.g., Deluxe cars) are available. Connect the blocks accordingly: Now, introduce a ______________block from the DE.lix library,

31. Double click on the Resource Pool block to open its dialog window. ___________the resource pool of Deluxe Cars to 100, based on the weekly maximum ________for deluxe cars.

32. Insert a special form of a queuing block, a Queue, Resource Pool block (from DE.lix – Queues).

33. The item is then __________and the count in the pool is__________, thus in effect, a deluxe car is assigned to the customer. Note that the Resource Pool block is a ________ accessible variable, tracking the number of deluxe cars on hand in this case, and has no drawn ____________to other bocks. The Queue, Resource Pool block will hold _______(deluxe car customers) until the specified number of Resource Pool units from the __________pool are available (one in this case).

34. Now that a ___________customer has received a deluxe car, we must model the rental _________ until it is returned. We will do this using the Activity, Multiple block and a new Input Random Number block. Specify a ________ distribution with a mean of 2 days (2880 minutes) and standard dev. of.5 days (720 minutes).

35. The __________of the Activity, Multiple block defaults to a ______number, 1000, to assure that no items would be stopped from entering this block.

36. After the rental time random________, the car is returned to the ________car pool to be available for re-renting by the Release Resource Pool block (from the DE.lix – Resources________).

37. Now, model the _________car customers similar to the deluxe car customers. Add another Resource Pool block and set the initial _________to 140.

38. Add another Queue, Resource Pool block to assign economy cars from the pool, if available.

39. Next, add an Activity, Multiple block, Input Random Number block and a Release Resource Pool block to return the economy car to its pool.

40. Finally, insert an Exit (4) block (from DE.lix – Routing menu) to allow both streams of customer types to exit the model.

41. To preserve customer_________, let’s implement a policy of _________an economy car to receive a deluxe car, if possible, in the event no economy cars are available. Open the Queue, Resource Pool block’s dialog window for the economy car. Specify ________under pool name: by clicking on the edit field and entering it in the resulting dialog.

42. Extend will start at the top of the _______list and attempt to assign a _____from the Economy Car pool. If that pool is_____, it will go to the Deluxe Car pool and assign a deluxe car if available. Otherwise, it will hold the ___________until one of either car type becomes available. During the simulation run, ____________car customers assigned a car from one of the two pools will have the name of that pool carried with them as a Car Type _________for later reference.

43. In the Release Resource Pool block, the ________rental car is credited to whatever __________was used earlier and carried by the attribute Car Type. The Input Random Number block shows the random _________ (from 1440 to 2880 minutes) from a _________distribution, for an economy car customer.

44. Now, to complete the model, add Queue Stats (from STATS.lrx), Help (from GENERIC.lix - Inputs/Outputs) and Plotter, Discrete Event (from PLOTTER.lix) blocks.

45. After running the simulation (with initial resource pools of ____economy cars and ___deluxe cars), double click on the Plotter, Discrete Event block to view the graph below:

46. The graph indicates (by the thick line_____) that the initial car pool sizes are grossly __________ for customer demands. The Queue Stats and Activity Stats windows confirm this conclusion. For example, after 20 simulation runs, the 95% _____________interval for the average wait by a deluxe car customer was 140 + 49 minutes.

47. In order to improve on the _______in this model, we need to _______the pool size. Let’s experimentally increase each pool’s initial size by about_____, increasing the Deluxe Cars pool to 115 and the Economy cars pool to 160 and the re-run the_____________.

48. This increase in pool size shows much improvement as illustrated by the average and maximum wait time.

49. In order to reduce the ____________wait time, change the initial resource _____to 170 Economy Cars and 125 Deluxe Cars and re-run the simulation. These results are even better. It seems though, that waiting times may be ____________to small underestimates in the distributions’ parameter ____________and that much more simulation analysis is needed.