Simulation – Module F | Test Bank – 10th Global Edition

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Operations Management, 10e, Global Edition (Heizer/Render)

Module F Simulation

1) Simulation has numerous applications in modern business, but few of these are in the area of operations.

Diff: 1

Topic: What is simulation?

Objective: no LO

2) All forms of simulation are based on probability or chance.

Diff: 1

Topic: What is simulation?

Objective: no LO

3) The idea behind simulation is threefold: (1) to imitate a real-world situation mathematically, (2) then to study its properties and operating characteristics, and (3) finally to draw conclusions and make action decisions based on the results of the simulation.

Diff: 1

Topic: What is simulation?

Objective: no LO

4) Simulation is usually capable of producing a more appropriate answer to a complex problem than can be obtained from a mathematical model.

Diff: 2

Topic: What is simulation?

Objective: no LO

5) Virtually all large-scale simulations take place on computers, but small simulations can be conducted by hand.

Diff: 1

Topic: What is simulation?

AACSB: Use of IT

Objective: no LO

6) One effective use of simulation is to study problems for which the mathematical models of operations management are not realistic enough.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

7) Simulation allows managers to test the effects of major policy decisions on real-life systems without disturbing the real system.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

8) Simulation provides optimal solutions to problems.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

9) Like mathematical and analytical models, simulation is restricted to using the standard probability distributions.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

10) Simulation models are inexpensive to design and use.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

11) Simulation models, because they are based on the generation of random numbers, fail to give the same solution in repeated use to any particular problem.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

12) By starting random number intervals at 01, not 00, the top of each range is the cumulative probability.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

13) A simulation model is designed to arrive at a single specific numerical answer to a given problem.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

14) A simulation is "Monte Carlo" when the elements of a system being simulated exhibit chance in their behavior.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

15) Random number intervals are based on cumulative probability distributions.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

16) Simulation is the attempt to duplicate the features, appearance, and characteristics of a real system, usually by means of a computerized model.

Diff: 1

Topic: What is simulation?

Objective: no LO

17) Results of simulation experiments with large numbers of trials or long experimental runs will generally be better than those with fewer trials or shorter experimental runs.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

18) Some reasons for the use of simulation in queuing are that the four standard queuing models do not allow for LIFO (or LIFS) discipline, for multi-phase waiting lines, or for unusual arrival and service distributions.

Diff: 1

Topic: Simulation of a queuing problem

Objective: LO-Module F-3

19) In most real-world inventory problems, lead time and demand vary in ways that make simulation a necessity because mathematical modeling is extremely difficult.

Diff: 1

Topic: Simulation and inventory analysis

Objective: LO-Module F-4

20) One reason for using simulation rather than an analytical model in an inventory problem is that the simulation is able to handle probabilistic demand and lead times.

Diff: 2

Topic: Simulation and inventory analysis

Objective: LO-Module F-4

21) The Las Vegas method is a simulation technique that uses random elements when chance exists in their behavior.

Diff: 1

Topic: Monte Carlo simulations

Objective: LO-Module F-2

22) Simulation can use any probability distribution that the user defines.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

23) Which of the following statements regarding simulation is true?

A) Simulation can be physical or mathematical.

B) Simulation has numerous areas of application in operations.

C) Simulation attempts to duplicate a real system.

D) Monte Carlo simulation is a chance-based mathematical model of a real system.

E) All of these are true.

Diff: 2

Topic: What is simulation?

Objective: no LO

24) Which of the following is not an application of simulation in the area of operations?

A) personnel scheduling

B) truck dispatching

C) plant (or facility) layout

D) inventory management using EOQ principles

E) inventory planning and control

Diff: 2

Topic: What is simulation?

Objective: no LO

25) The seven steps in the use of simulation include all but which of the following?

A) define the problem

B) construct a mathematical model

C) introduce important variable associated with the problem

D) find the optimal solution

E) run the experiment

Diff: 2

Topic: What is simulation?

Objective: no LO

26) Which of the following is not an idea behind simulation?

A) to imitate a real-world situation mathematically

B) study the properties and operating characteristics

C) draw conclusions and make decisions based on the results

D) both A and B

E) A, B, and C are all ideas behind simulation,

Diff: 2

Topic: What is simulation?

Objective: no LO

27) Which of the following is not a disadvantage to simulation?

A) Time compression

B) Expensive, can take months to develop

C) Trial and error approach

D) All input must be user generated

E) All of these are disadvantages to simulation

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

28) Which of the following are advantages to simulation?

I. Time compression

II. What-if questions are possible

III. Flexibility

IV. Trial and Error approach

V. Input must be user generated

A) I, III, V

B) I, II, V

C) II, III, IV, V

D) I, II, IV, V

E) I, II, III

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

29) Which of the following is true regarding simulation?

A) Small problems can be done by hand.

B) Most simulations are computerized.

C) Real-world complications can be included in simulation models.

D) Simulation is most suitable where standard analytical models are too complex.

E) All of the above are true.

Diff: 2

Topic: Advantages and disadvantages of simulation

AACSB: Use of IT

Objective: LO-Module F-1

30) Which of the following is true regarding simulation?

A) If an analytical model can't solve a problem, neither can a simulation.

B) Simulation can only be done by computer.

C) Monte Carlo simulation requires the use of random numbers.

D) Simulation models are inexpensive.

E) All of the above are true.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

31) Which of the following is true regarding the use of simulation?

A) It is always very easy to build a simulation model.

B) It is very inexpensive to use a simulation model.

C) It always yields optimum solutions.

D) It allows time-compression in testing major policy decisions.

E) Few constraints, if any, have to be considered.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

32) Simulation is used for several reasons, including

A) MODEL development is a fast process

B) it is inexpensive

C) the models are usually simple

D) it can handle large and complex real-world problems

E) it always generates optimal solutions

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

33) One of the advantages of simulation is that

A) it is much less expensive than a mathematical solution

B) it always generates a more accurate solution than a mathematical solution

C) the policy changes may be tried out without disturbing the real-life system

D) model development is less time consuming than for mathematical models

E) model solutions are transferable to a wide variety of problems

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

34) One of the disadvantages of simulation is that it

A) does not allow for very complex problem solutions

B) is not very flexible

C) is a trial-and-error approach that may produce different solutions in different runs

D) is very limited in the type of probability distribution that can be used

E) interferes with the production systems while the program is being run

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

35) The effects of OM policies over many months or years can be obtained by computer simulation in a short time. This phenomenon is referred to as

A) time suppression

B) time suspension

C) time compression

D) time inversion

E) time conversion

Diff: 2

Topic: Advantages and disadvantages of simulation

AACSB: Use of IT

Objective: LO-Module F-1

36) One of the disadvantages of simulation is that it

A) does not allow for very complex problem solutions

B) is not very flexible

C) may be very expensive and time-consuming to develop

D) is very limited in the type of probability distribution that can be used

E) interferes with the production systems while the program is being run

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

37) One of the disadvantages of simulation is that it

A) does not allow for very complex problem solutions

B) produces solutions and inferences that are not usually transferable to other problems

C) cannot study the interactive effects of individual components or variables

D) is very limited in the type of probability distribution that can be used

E) interferes with the production systems while the program is being run

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

38) One of the advantages of simulation is that

A) it is much less expensive than a mathematical solution

B) it always generates a more accurate solution than a mathematical solution

C) it can study the interactive effects of individual components or variables

D) model development is less time consuming than for mathematical models

E) model solutions are transferable to a wide variety of problems

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

39) One of the advantages of simulation is that

A) real-world complications can be included that most OM models cannot permit

B) it always generates a more accurate solution than a mathematical solution

C) it is a trial-and-error approach that may produce different solutions in repeated runs

D) model development is less time consuming than for mathematical models

E) model solutions are transferable to a wide variety of problems

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

40) "Time compression" and the ability to pose "what-if" questions are elements of

A) Monte Carlo analysis

B) the disadvantages of simulation

C) physical simulations but not mathematical simulations

D) the advantages of simulation

E) the broad threefold idea of simulation

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

41) Setting up a probability distribution, building a cumulative probability distribution, and generating random numbers are

A) necessary when the underlying probability distribution is normal

B) three of the five steps in Monte Carlo analysis

C) elements of physical simulation but not mathematical simulation

D) the three steps involved in simulating a queuing problem

E) advantages of simulation

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

42) Which of the following is not a step in running a Monte Carlo simulation?

A) setting up a probability distribution for important variables

B) building a cumulative probability distribution for each variable

C) establishing an interval of random numbers for each variable

D) generating random numbers

E) All of the above are steps in running a Monte Carlo simulation.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

43) From a portion of a probability distribution, you read that P(demand = 0) is 0.05 and P(demand = 1) is 0.10. The cumulative probability for demand 1 would be

A) 0.05

B) 0.075

C) 0.10

D) 0.15

E) cannot be determined

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

44) From a portion of a probability distribution, you read that P(demand = 1) is 0.05, P(demand = 2) is 0.15, and P(demand = 3) is .20. The cumulative probability for demand 3 would be

A) 0.133

B) 0.200

C) 0.400

D) 0.600

E) cannot be determined from the information given

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

45) From a portion of a probability distribution, you read that P(demand = 0) is 0.05, P(demand = 1) is 0.10, and P(demand = 2) is 0.20. The two-digit random number intervals for this distribution beginning with 01 are

A) 01 through 05, 01 through 10, and 01 through 20

B) 00 through 04, 05 through 14, and 15 through 34

C) 01 through 05, 06 through 15, and 16 through 35

D) 00 through 04, 00 through 09, and 00 through 19

E) 01 through 06, 07 through 16, and 17 through 36

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

46) From a portion of a probability distribution, you read that P(demand = 0) is 0.25, and P(demand = 1) is 0.30. The random number intervals for this distribution beginning with 01 are

A) 01 through 25, and 26 through 30

B) 01 through 25, and 01 through 30

C) 01 through 25, and 26 through 55

D) 00 through 25, and 26 through 55

E) 00 through 25, and 26 through 30

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

47) A distribution of service times at a waiting line indicates that service takes 6 minutes 30 percent of the time, 7 minutes 40 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. In preparing this distribution for Monte Carlo analysis, the service time 8 minutes would be represented by the random number range

A) 20 through 40

B) 21 through 40

C) 70 through 90

D) 71 through 90

E) none of these

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

48) A distribution of service times at a waiting line shows that service takes 6 minutes 30 percent of the time, 7 minutes 40 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first two random numbers drawn are 53 and 74. The simulated service times are __________ minutes, then __________ minutes.

A) 6; 7

B) 7; 7

C) 7; 8

D) 8; 9

E) Cannot determine, because no service time probability is that large.

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

49) A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. In preparing this distribution for Monte Carlo analysis, the service time 13 minutes would be represented by the random number range

A) 00 through 29

B) 01 through 30

C) 30 through 99

D) 31 through 00

E) None of these; 13 minutes is not a possible outcome.

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

50) A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first four random numbers drawn are 07, 60, 77, and 49. The average service time of this simulation is

A) 12 minutes

B) 13 minutes

C) 13.5 minutes

D) 14 minutes

E) none of these

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

51) A distribution of lead times in an inventory problem indicates that lead time was 1 day 20 percent of the time, 2 days 30 percent of the time, 3 days 30 percent of the time, and. 4 days 20 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first four random numbers drawn are 06, 63, 57, and 02. The average lead time of this simulation is

A) 1.75 days

B) 2 days

C) 3 days

D) 3.5 days

E) none of these

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

52) What is the cumulative probability distribution of the following variable?

A) 1

B) .5

C) 10

D) .2

E) none of the above

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

53) The number of tires sold at a car garage varies randomly between 0 and 4 each hour. What set of random numbers (on the 1-100 scale would tire sales of 2 be assigned?

A) 01 through 20

B) 21 through 40

C) 41 through 60

D) 61 through 80

E) 81 through 100

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

54) There are four possible outcomes for a Monte Carlo simulation variable (A, B, C, and D). The random numbers 02, 22, 53, and 74 correspond to the variables __________ respectively if each possible outcome has an equivalent chance of occurring.

A) A A C C

B) B B D D

C) A B C D

D) D C B A

E) none of the above

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

55) Monte Carlo simulations applied to queuing problems have what advantage?

A) simpler

B) Arrival distribution does not need to be a Poisson distribution.

C) Unloading rates can vary randomly.

D) B and C

E) A, B, and C

Diff: 2

Topic: Simulation of a queuing problem

Objective: LO-Module F-3

56) Which of the following restrictions applies to queuing models but not Monte Carlo simulations?

A) Poisson distribution of arrivals

B) constant or exponential service times

C) average length of line

D) A and B

E) A, B, and C

Diff: 2

Topic: Simulation of a queuing problem

Objective: LO-Module F-3

57) Which of the following is a necessity for common EOQ methodology but not simulations

A) constant lead time

B) variable demand

C) variable holding costs

D) A and B

E) A, B and C

Diff: 2

Topic: Simulation and inventory analysis

Objective: LO-Module F-4

58) __________ is the attempt to duplicate the features, appearance, and characteristics of a real system, usually by means of a computerized model.

Diff: 1

Topic: What is simulation?

AACSB: Use of IT

Objective: no LO

59) The __________ method is a simulation technique that uses random elements when chance exists in their behavior.

Diff: 2

Topic: What is simulation?

Objective: no LO

60) A(n) __________ is the accumulation of individual probabilities of a distribution.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

61) A(n) __________ is a series of digits that have been selected by a totally random process.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

62) The effects of OM policies over many months or years can be obtained by computer simulation in a short time. This phenomenon is referred to as __________ .

Diff: 2

Topic: Advantages and disadvantages of simulation

AACSB: Use of IT

Objective: LO-Module F-1

63) The numbers used to represent each possible value or outcome in a computer simulation are referred to as __________ .

Diff: 2

Topic: Monte Carlo simulations

AACSB: Use of IT

Objective: LO-Module F-2

64) Would you simulate a problem for which there is an exact mathematical model already?

Diff: 2

Topic: Advantages and disadvantages of simulation

AACSB: Reflective Thinking

Objective: LO-Module F-1

65) Define simulation.

Diff: 1

Topic: What is simulation?

AACSB: Use of IT

Objective: no LO

66) Identify five applications of simulation.

Diff: 1

Topic: What is simulation?

Objective: no LO

67) State the three-fold idea behind simulation.

Diff: 2

Topic: What is simulation?

Objective: no LO

68) Identify the seven steps involved in using simulation.

2. Introduce the important variables.

3. Construct the numerical model.

4. Set up possible courses of action.

5. Run the experiment.

6. Consider the results (perhaps modifying the model).

7. Decide what course of action to take.

Diff: 1

Topic: What is simulation?

Objective: no LO

69) What is the Monte Carlo method?

Diff: 1

Topic: Monte Carlo simulations

Objective: LO-Module F-2

70) Identify, in order, the five steps required to implement the Monte Carlo simulation technique.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

71) Explain how Monte Carlo simulation uses random numbers.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

72) What are the advantages and disadvantages of simulation models?

• Simulation is relatively straightforward and flexible.

• It can be used to analyze large and complex real-world situations that cannot be solved by closed-form operations management models.

• Simulation allows for inclusion of real-world complications that most OM models cannot permit.

• "Time compression" is possible with simulation.

• Simulation allows "What if __?" type questions.

• Simulations do not interfere with the real-world system under study.

• Simulation allows us to study the interactive effect of individual components or variables in order to determine which ones are important.

Disadvantages:

• Good simulation models are very expensive.

• Simulation does not generate optimal solutions.

• Managers must generate all the conditions and constraints for the solutions that they want to examine.

• Each simulation model is unique. Its solutions and inferences are not usually transferable to other problems.

Diff: 2

Topic: Advantages and disadvantages of simulation

Objective: LO-Module F-1

73) Provide a small example illustrating how random numbers are used in Monte Carlo simulation.

Diff: 2

Topic: Monte Carlo simulations

AACSB: Reflective Thinking

Objective: LO-Module F-2

74) A waiting-line problem that cannot be modeled by standard distributions has been simulated. The table below shows the result of a Monte Carlo simulation. (Assume that the simulation began at 8:00 a.m. and there is only one server.) Why do you think this problem does not fit the standard distribution for waiting lines? Explain briefly how a Monte Carlo simulation might work where analytical models cannot.

Diff: 3

Topic: Monte Carlo simulations

AACSB: Reflective Thinking

Objective: LO-Module F-2

75) Explain what is meant by "simulation is not limited to using the standard probability distributions."

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

76) Explain what is meant by the concept of "time compression" in simulation modeling.

Diff: 2

Topic: Advantages and disadvantages of simulation

AACSB: Use of IT

Objective: LO-Module F-1

77) Explain the difference between random numbers and random number intervals.

Diff: 2

Topic: Monte Carlo simulations

Objective: LO-Module F-2

78) A waiting-line problem that cannot be modeled by standard distributions has been simulated. The table below shows the result of a Monte Carlo simulation. (Assume that the simulation began at 8:00 a.m. and there is only one server.

a. What is the average waiting time in line?

b. What is the average time in the system?

Diff: 2

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

79) A distribution of service times at a waiting line shows that service takes 6 minutes 40 percent of the time, 7 minutes 30 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. Prepare the probability distribution, the cumulative probability distribution, and the random number intervals for this problem.

Diff: 1

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

80) A warehouse manager needs to simulate the demand placed on a product that does not fit standard models. The concept being measured is "demand during lead time," where both lead time and daily demand are variable. The historical record for this product suggests the following probability distribution. Convert this distribution into random number intervals.

Diff: 2

Topic: Simulation and inventory analysis

AACSB: Analytic Skills

Objective: LO-Module F-4

81) A distribution of service times at a waiting line shows that service takes 6 minutes 40 percent of the time, 7 minutes 30 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. Prepare the probability distribution, the cumulative probability distribution, and the random number intervals for this problem. The first five random numbers are 37, 69, 53, 80, and 60. What is the average service time of this simulation run?

The average service time is 1*6 + 3*7 + 1*8 = 35 / 5 = 7 minutes.

Diff: 2

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

82) A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. Prepare the probability distribution, the cumulative probability distribution, and the random number intervals for this problem.

Diff: 1

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

83) A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. Prepare the probability distribution, the cumulative probability distribution, and the random number intervals for this problem. The first six random numbers were 99, 29, 27, 75, 89, and 78. What is the average service time for this simulation run?

The average service time is 2*12 + 4*14 = 80 / 6 = 13.33 minutes.

Diff: 1

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

84) Historical records on a certain product indicate the following behavior for demand. The data represent the 288 days that the business was open during 2000. Convert these data into random number intervals.

Diff: 2

Topic: Simulation and inventory analysis

AACSB: Analytic Skills

Objective: LO-Module F-4

85) A small store is trying to determine if its current checkout system is adequate. Currently, there is only one cashier, so it is a single-channel, single-phase system. The store has collected information on the interarrival time, and service time distributions. They are represented in the tables below. Use the following two-digit random numbers given below to simulate 10 customers through the checkout system. What is the average time in line, and average time in system? (Set first arrival time to the interarrival time generated by first random number.

Random numbers for interarrival times: 07, 60, 77, 49, 76, 95, 51, 16, 14, 85

Random numbers of service times: 57, 17, 36, 72, 85, 31, 44, 30, 26, 09

Average time in line = 0/10 = 0.0 minutes; Average time in system = 18/10 = 1.8

minutes.

Diff: 2

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

86) Sam's hardware store has an order policy of ordering 12 gallons of a specific primer whenever 7 gallons are on hand (unless there's already an ordered delivery due). The store would like to see how well their policy works. Assume that beginning inventory in period 1 is 10 units, that orders are placed at the end of the week to be received one week later. (In other words, if an order is placed at the end of week one, it is available at the beginning of week 3.) Assume that if inventory is not on hand, it will result in a lost sale. The weekly demand distribution obtained from past sales is found in the table below. Also, use the random numbers that are provided and simulate 10 weeks worth of sales. How many sales are lost?

Random numbers for sales: 37, 60, 79, 21, 85, 71, 48, 39, 31, 35

Over the 10 weeks only 1 gallon of sales is lost.

Diff: 2

Topic: Simulation and inventory analysis

AACSB: Analytic Skills

Objective: LO-Module F-4

87) The lunch counter at a small restaurant has difficulty handling the lunch business. Currently, there is only one cashier in a single-channel, single-phase system. The restaurant has collected information on the interarrival time, and service time distributions from past lunch hours. They are represented in the tables below. Use the following two-digit random numbers given below to simulate 10 customers through the checkout system. What is the average time in line, and average time in system? (Set first arrival time to the interarrival time generated by first random number.

Random numbers for interarrival times: 32, 73, 41, 38, 73, 01, 09, 64, 34, 44

Random numbers of service times: 84, 55, 25, 71, 34, 57, 50, 44, 95, 64

Average time in line = 11/10 = 1.1 minutes; Average time in system = 39/10 = 3.9 minutes.

Diff: 2

Topic: Simulation of a queuing problem

AACSB: Analytic Skills

Objective: LO-Module F-3

88) Julie's Diamond Boutique is very concerned with its order policies related to one-carat diamond solitaires. Their current policy is to order 10 diamonds whenever their inventory reaches 6 diamonds (unless there is already an ordered delivery due). Currently there are 8 diamonds on hand. Orders are placed at the end of the month and take one month to arrive (e.g., if an order is placed at the end of month 1, it will be available at the beginning of month 3). The following distribution of monthly sales has been developed using historical sales. If Julie's does not have a diamond on hand, it will result in a lost sale. Use the following random numbers to determine the number of lost sales of one-carat solitaires at Julie's over 12 months.

Random numbers for sales: 10, 24, 03, 32, 23, 59, 95, 34, 34, 51, 08, 48

Over the 12 months 2 sales are lost.

Diff: 2

Topic: Simulation and inventory analysis

AACSB: Analytic Skills

Objective: LO-Module F-4

89) Complete the following table in preparation for a Monte Carlo simulation.

Diff: 1

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

90) Suppose the following random numbers (1, 34, 22, 78, 56, 98, 00, 82) were selected during a Monte Carlo simulation that was based on the chart below. What was the average demand per period for the simulation? What is the expected demand?

Tires sold sum is given by 0+2+1+3+2+4+4+4=20 over 8 periods. Thus the average demand was 20/8 = 2.5 tires.

The expected demand is simply the EV, or .1(0)+.15(1)+.4(2)+.15(3)+.2(4) = 2.2 tires per period.

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

91) Create a distribution of random numbers that would result in average demand per period for a Monte Carlo simulation that is equivalent to the expected demand per period using the data given by the chart below.

This problem will most likely confuse many students, however its aim is to test their true understanding and ability to work both ways. The smallest common denominator for the probabilities is .05 so 20 separate random numbers must be generated for the simple solution where each possible demand has probability/.05 random numbers representing it within the set. For example, one set would be

(0, 0, 11, 11, 11, 26, 26, 26, 26, 26, 26, 26, 26, 66, 66, 66, 81, 81, 81, 81)

Students may also create sets that draw unevenly from various demand rows, such as drawing only from 0 and 4. The expected demand is 2.4, so students would solve a relation of the form X*0+Y*4/(X+Y)=2.4 thus X=2Y/3 so when Y=3 then X=2. Therefore another possible set of random numbers would be (00, 00, 00, 01, 01)

Diff: 3

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

92) Complete the following table in preparation for a Monte Carlo simulation.

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2

93) Complete the following table in preparation for a Monte Carlo simulation. The expected demand is 3.52.

Students should have only moderate difficulty filling in the table, save for the demand column. To do this they must set up the equation for the expected demand and solve for the missing component.

.13(2)+.27(3)+.35(4)+.15(X)=3.52 so X=7

Diff: 2

Topic: Monte Carlo simulations

AACSB: Analytic Skills

Objective: LO-Module F-2