CH 12 - Simulation. Questions and Answers

True / False 1. Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures. a. True b. False 2. Simulation is a trial-and-error approach to pro ...

True / False 1. Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures. a. True b. False 2. Simulation is a trial-and-error approach to problem solving. a. True b. False 3. The degree of risk is associated with the probability or magnitude of loss. a. True b. False 4. To use Excel to generate a normally distributed random variable, you must know the mean and standard deviation of the distribution and have a random number between 0 and 1. a. True b. False 5. Trials of a simulation show what would happen when values of the probabilistic input change. a. True b. False 6. Verification is the process of ensuring that the simulation model provides an accurate representation of the real system. a. True b. False 7. Simulation is a method that uses repeated random sampling of values in order to represent uncertainty in a model that represents a real system and computes the values of model outputs. a. True b. False 8. Validation determines that the computer procedure is operating as it is intended to operate. a. True b. False 9. A discrete-event simulation reviews the status of the system periodically, whether or not an event occurs. a. True b. False 10. A static simulation model is used in situations where the state of the system affects how the system changes or evolves over time. a. True b. False 11. The following relationship is valid for any waiting line system: the average number in the waiting line is equal to the total waiting time divided by the total time of simulation. a. True b. False 12. Varying the values of controllable inputs enables simulation models to identify good operating policies and decisions. a. True b. False 13. Using simulation to perform risk analysis is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs. a. True b. False 14. All values of the computer-generated random numbers are equally likely and are uniformly distributed over the interval from 0 to 1. a. True b. False 15. Computer-generated random numbers are not technically random, because they are generated through the use of mathematical formulas. a. True b. False 16. Simulation is an optimization technique. a. True b. False 17. Simulation models that must take into account how the system changes or evolves over time are referred to as dynamic simulation models. a. True b. False 18. Each simulation run provides only a sample of how the real system will operate. a. True b. False 19. One disadvantage of simulation is that it is limited in the variety of probability distributions that can be used in modeling a system. a. True b. False 20. A simulation model provides a convenient experimental laboratory for the real system. a. True b. False 21. Simulation allows the user to specify certain desired results (e.g., profit or service level values), and then the necessary model parameters and operating policies are determined. a. True b. False 22. Simulation models manually generate specific values for the random variables so that the values used reflect what we might observe in practice. a. True b. False 23. Independent trials are those in which the results for one trial have no effect on what happens in subsequent trials. a. True b. False 24. When making a decision in the presence of uncertainty, decision makers should only be interested in the average, or expected, outcome. a. True b. False 25. Simulation analysis requires a model foundation of logical formulas that correctly express the relationships between parameters and decisions to generate outputs of interest. a. True b. False Multiple Choice 26. A simulation model uses the mathematical expressions and logical relationships of the a. real system. b. computer model. c. performance measures. d. estimated inferences. 27. Values for the random variables or uncertain variable inputs to a simulation are a. selected by the decision maker. b. controlled by the decision maker. c. randomly generated from the specified probability distributions. d. calculated by fixed mathematical formulas. 28. A quantity that is difficult to measure with certainty is called a a. risk analysis. b. project determinant. c. probabilistic input. d. profit/loss process. 29. A value for probabilistic input from a discrete probability distribution a. is the value given by the RAND() function. b. is given by matching the probabilistic input with an interval of random numbers. c. is between 0 and 1. d. must be nonnegative. 30. The number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1, then the proper expression for sales is a. 200(r). b. r + 300. c. 300 + 500(r). d. 300 + r(200). 31. When events occur at discrete points in time, a. a simulation clock is required. b. the simulation advances to the next event. c. the model is a discrete-event simulation. d. All of these are correct. 32. If customer 2 has a service time of 1.6, and if customer 3 has an interarrival time of 1.1 and a service time of 2.3, when will customer 3's service be completed? a. 5.0 b. 3.9 c. 3.4 d. There is not enough information to answer. 33. In order to verify a simulation model, a. compare results from several simulation languages. b. be sure that the procedures for calculations are logically correct. c. confirm that the model accurately represents the real system. d. run the model long enough to overcome initial start-up results. 34. Simulation a. does not guarantee optimality. b. is flexible and does not require the assumptions of theoretical models. c. allows testing of the system without affecting the real system. d. All of these are correct. 35. A simulation model in which each trial is used in situations where the state of the system at one point in time does not affect the state of the system at future points in time is called a a. dynamic simulation model. b. static simulation model. c. steady-state simulation model. d. discrete-event simulation model. 36. The process of determining that the computer procedure that performs the simulation calculations is logically correct is called a. implementation. b. validation. c. verification. d. repetition. 37. Using simulation models, we are able to explore the sensitivity of various decisions to some of the model's a. parameters. b. optimizations. c. uncontrollable input. d. None of these are correct. 38. Which of the following statements is NOT true about the advantages of simulations? a. Simulation models are flexible. b. Simulation models can be used to describe systems without requiring the assumptions that are often required by mathematical models. c. Generally, the larger the number of random variables a system has, the less likely that a simulation model will provide the most suitable approach for studying the system. d. Simulation models provide a convenient experimental "laboratory" for a real system. 39. Which of the following statements is true regarding the advantages of using simulations? a. Its methodology can be used to model and learn about the behavior of complex systems. b. Simulations do not guarantee an optimal solution. c. Simulation models can be used to describe systems without requiring the assumptions often required by mathematical models. d. All of these are correct. 40. The word "uniform" in the term "uniform random numbers" means a. all the numbers have the same number of digits. b. if one number is, say, 10 units above the mean, the next number will be 10 units below the mean. c. all the numbers are odd or all are even. d. each number has an equal probability of being drawn. 41. The process of generating probabilistic inputs and computing the value of the output is called a. simulation. b. verification. c. validation. d. implementation. 42. A graphical tool that helps describe the logic of the simulation model is a a. Gantt chart. b. histogram. c. flowchart. d. stem-and-leaf display. 43. A set of values for the random variables is called a a. simulation. b. risk analysis. c. trial. d. None of these are correct. 44. A trial-and-error approach to learning about the range of possible outputs for a model is known as a. what-if analysis. b. worst-case scenario analysis. c. static simulation modeling. d. base-case scenario. Subjective Short Answer 45. For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). Units Sold Number of Times 30 8 40 12 50 15 60 10 70 5 a. Determine the relative frequency for each number of units sold. b. Suppose that the following random numbers were obtained using Excel: 0.12 0.96 0.53 0.80 0.95 0.10 0.40 0.45 0.77 0.29 Use these random numbers to simulate 10 days of sales. 46. The time required to set up lighting for a portrait studio is uniformly distributed between 12 and 20 minutes. Use the following random numbers to generate the setup time for 10 customers. 0.27 0.53 0.06 0.92 0.16 0.74 0.06 0.29 0.82 0.23 47. Estimates of the financial information for a new product include the following information: Units Sold Probability Fixed cost $8,000 600 0.35 Variable cost $6/unit 800 0.45 Revenue $22/unit 1000 0.20 Use the random numbers 0.51, 0.97, 0.58, 0.22, and 0.16 to simulate five trials. What is the net profit for each trial? 48. Seventy-five percent of calls arriving at a help line can be handled by the person who answers the phone, but the remaining 25% of them will need to be referred to someone else. Assume that every call requires one minute of attention by the person who answers the phone (either to answer the question or to figure out how the referral should be handled). Calls that are referred need an additional amount of time, as given in the table below. Time Required Probability 3 minutes 0.25 5 minutes 0.35 10 minutes 0.40 Callers are served on a first-come, first-served basis and are put on hold until the line is free. Use random numbers to simulate what happens to 10 callers. (Use the random numbers in order, from left to right, first row first, as you need them.) What percentage of your callers needs to be referred? Of those who had to be referred, what is the average referral time? 0.82 0.39 0.16 0.79 0.56 0.62 0.13 0.04 0.42 0.81 0.85 0.32 0.64 0.90 0.73 0.02 0.76 0.03 0.86 0.67 49. On a visit to an amusement park, you pass someone who has just ridden a roller coaster and asks you for directions to the First Aid Station. Realizing that traffic at the First Aid Station would be something to study with simulation, you gather some information. Two EMTs staff the station, and patients wait and go to the first one available. People coming there can be divided into two groups: those who need something minor (e.g., Tylenol, a Band-Aid) or those who need more help. Assume those in the first group constitute 25% of the patients and take five minutes to have their problem solved. Those in the second group need an uncertain amount of time, as given by a probability distribution. Develop a flowchart for this simulation problem. 50. Using the spreadsheet below, give the cell address that would have the formula shown. Cell Formula Belongs in Cell =VLOOKUP(B18,$B$10:$C$12,2) =VLOOKUP(D23,$F$11:$G$14,2) =K19*($I$16-I19) =VLOOKUP(H27,$B$10:$C$12,2) =AVERAGE(L18:L27) 51. As the owner of a rent-a-car agency, you have determined the following statistics: Potential Rentals Daily Probability Rental Duration Probability 0 0.10 1 day 0.50 1 0.15 2 day 0.30 2 0.20 3 days 0.15 3 0.30 4 days 0.05 4 0.25 The gross profit is $40 per car per day rented. When there is demand for a car but none is available, there is a goodwill loss of $80 and the rental is lost. Each day a car is unused costs you $5 per car. Your firm initially has four cars. a. Conduct a 10-day simulation of this business using Row #1 below for demand and Row #2 for rental length. Row #1: 63 88 55 46 55 69 13 17 36 81 Row #2: 59 09 57 87 07 92 29 28 64 36 b. If your firm can obtain another car for $200 for 10 days, should you take the extra car? 52. Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows: Freeway 5 Freeway 57 Freeway 55 Freeway 91 Relative Relative Relative Relative Time Frequency Time Frequency Time Frequency Time Frequency 5 0.30 4 0.10 6 0.20 3 0.30 6 0.20 5 0.20 7 0.20 4 0.35 7 0.40 6 0.35 8 0.40 5 0.20 8 0.10 7 0.20 9 0.20 6 0.15 8 0.15 Do a five-day simulation of each of the two combinations of routes using the random numbers below. Based on this simulation, which routes should Susan take if her objective is to minimize her total travel time? Freeway 5 63 88 55 46 55 Freeway 57 59 09 57 87 07 Freeway 55 71 95 83 44 34 Freeway 91 51 79 09 67 15 53. Three airlines compete on the route between New York and Los Angeles. Stanton Marketing has performed an analysis of first class business travelers to determine their airline choice. Stanton has modeled this choice as a Markov process and has determined the following transition probabilities: Next Airline Last Airline A B C A 0.50 0.30 0.20 B 0.30 0.45 0.25 C 0.10 0.35 0.55 a. Show the random number assignments that can be used to simulate the first class business traveler's next airline when her last airline is A, B, and C. b. Assume the traveler used airline C last. Simulate which airline the traveler will be using over her next 25 flights. What percent of her flights are on each of the three airlines? Use the following random numbers, going from left to right, top to bottom. 71 95 83 44 34 49 88 56 05 39 75 12 03 59 29 77 76 57 15 53 37 46 85 24 53