chapter 17
TRANSCRIPT
Quantitative Techniques in
Management
4th Edition
N. D. Vohra
© 2010
Chapter 17
1. Introduction to Simulation2. Process of Simulation3. Monte Carlo Simulation 4. Random Numbers and Their
Generation5. Illustrations
a) Simulation of an Inventory System
b) Simulation of a Queuing System
6. Advantages and Disadvantages of Simulation
Simulation: a descriptive method
To simulate is to replicate a system
Phases of simulation process:Definition of the problem and statement of objectivesConstruction of an appropriate modelExperimentation with the model constructedEvaluation of the results of simulation
Uses random numbers to generate data
Process calls for:Determination of random number intervalsObtaining random numbers and finding the input values corresponding to themCarrying out needed simulation
Is used extensively in areas like capital budgeting; inventory control; queuing analysis; and project management
Example 17.4 data
Objective: to simulate demand for 20 weeks using the following random numbers:
10, 24, 03, 32, 23, 59, 95, 34, 34, 51,08, 48, 66, 97, 03, 96, 46, 74, 77, 44
Hot Water Heater Sales No. of weeks
4 6
5 5
6 9
7 12
8 8
9 7
10 3
Assignment of Random Numbers
DemandNo. of weeks
Prob.Cumulat
ive Prob.
Random Number Interval
4 6 0.12 0.12 00 – 11
5 5 0.10 0.22 12 – 21
6 9 0.18 0.40 22 – 39
7 12 0.24 0.64 40 – 63
8 8 0.16 0.80 64 – 79
9 7 0.14 0.94 80 – 93
10 3 0.06 1.00 94 – 99
Total 50 1.00
WeekRandom Number
Demand
1 10 4
2 24 6
3 03 4
4 32 6
5 23 6
6 59 7
7 95 10
8 34 6
9 34 6
10 51 7
11 08 4
12 48 7
13 66 8
14 97 10
15 03 4
WeekRandom Number
Demand
16 96 10
17 46 7
18 74 8
19 77 8
20 44 7
Total 135
Average Demand = 135/20 = 6.75
Number of times out-of-stock = 3 since demand has exceeded the stock of 8 units during three weeks
Event Probability
No Rain 0.50
1 cm rain 0.25
2 cm rain 0.15
3 cm rain 0.05
4 cm rain 0.03
5 cm rain 0.02
Example 17.8 data
Random Numbers to use:67, 63, 39, 55, 29, 78, 70, 06, 78, 76
Probability Distributions
Event Probability
No Rain 0.75
1 cm rain 0.15
2 cm rain 0.06
3 cm rain 0.04
Rained on Previous day:
No rain on Previous day:
Event ProbabilityCumulative Probability
Random Number Interval
No Rain 0.50 0.50 00 – 49
1 cm rain 0.25 0.75 50 – 74
2 cm rain 0.15 0.90 75 – 89
3 cm rain 0.05 0.95 90 – 94
4 cm rain 0.03 0.98 95 – 97
5 cm rain 0.02 1.00 98 - 99
Table 1
Table 2
Event ProbabilityCumulative Probability
Random Number Interval
No Rain 0.75 0.75 00 – 74
1 cm rain 0.15 0.90 75 – 89
2 cm rain 0.06 0.96 90 – 95
3 cm rain 0.04 1.00 96 - 99
DayRandom Number
RainfallTable
Reference*
1 67 No rain Table 2*
2 63 No rain Table 2
3 39 No rain Table 2
4 55 No rain Table 2
5 29 No rain Table 2
6 78 1 cm Table 2
7 70 1 cm Table 1
8 06 No rain Table 1
9 78 1 cm Table 2
10 76 2 cm Table 1
Total 5 cm
* Given to assume that there was no rain the previous day
Days without rain = 6, Total Rainfall = 5 cm
Mark the wrong statement:
1. To simulate means to imitate a system.
2. Simulation involves developing a model of some real phenomenon and then experimenting on it.
3. Simulation is a powerful mathematical modelling tool.
4. Simulation is very beneficial since results of taking a particular course of action can be estimated prior to its implementation in real world.
Which of the following is not a phase of simulation process?
1. Definition of the problem and statement of objectives.
2. Construction of an appropriate model.
3. Experimentation in real life situations.
4. Performing experiments on the model evolved.
Which of the following is not true about simulation?1. It is a very effective substitute for
hunch and intuition in decision-making.
2. It is an optimising technique.
3. It seeks to determine how the system under consideration would behave in certain conditions.
4. It is effectively used in decision-making situations that cannot be handled with mathematical methods.
Mark the wrong statement: 1. A clear statement of the problem
facilitates the development of an appropriate model.
2. Simulation aims to determine how the system under consideration would behave under certain conditions.
3. The scope and level of detail of simulation should be decided upon carefully.
4. The output of a simulation model is independent of the size of simulation run.
Mark the wrong statement: 1. During the course of a simulation,
the model mimics the important elements of what is being simulated.
2. A simulation model can never be physical.
3. The model for simulation must be so designed that it would enable evaluation of the key decision alternatives.
4. In a mathematical model, mathematical symbols or equations are used to represent system relationships.
Mark the wrong statement:
1. For a deterministic model, a single simulation run is sufficient.
2. Probabilistic simulation is like random sampling whose output is subject to statistical error.
3. Monte Carlo simulation involves modelling a deterministic system.
4. Randomness is a key requirement of Monte Carlo simulation.
Which of the following statements is not true?1. In Monte Carlo simulation, a
problem is solved by simulating the original data with random number generators.
2. A random number generator is a procedure or device to obtain random numbers.
3. In a series of random numbers, different digits appear in a definite, ordered fashion.
4. Random numbers generated by mid-square method are called pseudo-random numbers.
Mark the correct statement.
1. Simulation cannot be used where mathematical methods can be used.
2. Solutions to decision problems by using simulation would be identical to those using mathematical models.
3. Simulation is descriptive in nature.
4. One drawback of using simulation is that it is only applicable where all quantities are deterministic.
Given the following distribution:
For a five-day demand simulation, random numbers are: 89, 32, 01, 12 and 30. What is the average daily demand?
1. 100 units2. 19 units3. 20 units4. none of the above
Demand (Units) 10 15 20 25 30
Probability .05 .25 .30 .28 .12
One can increase the chance that results of simulation are not erroneous by:
1. Changing the input parameters.
2. Using discrete probability distributions and not continuous.
3. Validating the simulation.
4. All of the above.