Introduction to Simulation

1
Introduction to Simulation
Assistant Professor Dr.Patcharaporn
Neammanee Applied Statistics school, NIDA
2
Agenda

• Inventory problem
• What is simulation?
• Hotel booking problem
• Car insurance problem

3
Software

• Microsoft Excel
• Arena
• MINITAB

4
Inventory problem

• ???????????? 150 ??????????
• ???????? 50 ??????????
• ??????? 300 ??????????
• ??????????? 10,000 ??? ?????????????????????

5
Solution
???????????
?????????????? ?????????? 10,000 ???
6
Additional problem

• ????????
• ????????? 1 ???? 50 ??????????
• ????????? 2 ???? 40 ??????????
• ????????? 3 ???? 30 ??????????
• ????????? 4?????????? 20 ??????????

7
Solution
???????????
8

• ??????????????????????

9
??????????????????
?????????
10
Solution
?????????????????????????????????

• ????????????? 15040
• 190 ???
• ??????????? 300 -190
• 110 ???

• ????????????????????? ?????????? 10,000 ???

11
Probability of items per order
???????????
12
Random-variate generation
13
Examples

• ????????????? 1
• Rand1 0.30432
• ???????????????????????? 1 ??????? 1
• ?????????????????? 100 ???
• ??????? ??????? 100 ???
• ????????????? 2
• Rand2 0. 66387
• ???????????????????????? 2 ??????? 3
• ??????? 100 120x3 460 ???
• ????????????? 3
• Rand3 0.95631
• ???????????????????????? 3 ??????? 5
• ??????? 460 130x5 1,010 ???

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Simulation

• ?????????? Microsoft Excel
• ?????????? 50 ?????

15
Simulation
16
Simulation

• IF(B2ltJ2,G2,IF(B2ltJ3,G3,IF(B2ltJ4,G4,
  IF(B2ltJ5,G5, IF(B2ltJ6,G6,0)))))

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Simulation

• VLOOKUP(C2,G2K6,5,G2G6)

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Simulation output

• X88

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Simulation output
20
Additional problem

• ???????????????????????????????????????
• ??????????? 3 ??????????????????????
• ???? 280 ??????????
• ?????????? 5 ??????????????????????
• ???? 250 ??????????

21
What is simulation?
22
What is simulation?

• Simulation is a computer model that attempts to
  imitate the behavior of a real system or
  activity.

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What is simulation?

• Simulation is the process of designing a
  mathematical or logical model of a real system
  and then conducting computer-based experiments
  with the model to describe, explain, and predict
  the behavior of the real system (Stewart
  Ronald, 1990).

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Types of simulation

• In dynamic simulation models, events occur
  sequentially over time. Specialized software is
  required.
• In static simulation models time is not explicit
  and the analysis can be done in Excel
  spreadsheets.

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Monte carlo simulation

• Monte Carlo method is used for static simulation.
• Computer creates the values of the stochastic
  random variables.
• Distribution and its parameters are specified.
• Samples are repeatedly drawn from each
  distribution.
• For each input variable, look at a histogram to
  verify that we are sampling from the desired
  distribution.
• For each output variable, look at percentiles as
  well as the mean.

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Phases of simulation project

• Phase I (design) identify the problem, set
  objectives, design the model, collect data.
• Phase II (execution) empirical modeling,
  specify the variables, validate the model,
  execute the simulation, prepare reports.
• Phase III (communication) explain the
  findings to decision-makers.

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Hotel booking problem
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Hotel booking problem

• ??????????????????????????????????????????????????
  50 ????
• ????????????????????????????????????????????
• ??????????????????????????????????????????????????
  ??????????????????????????????????????????????????
  ?????

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Objective

• ???????????????????????????
• ??????????????????? 65 ??????????

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Model ???????????????????????????????
31
Collect Data

• ???????????????
• ??????????????????????? ??????????????????????????
  ????????? 0.7
• ????????????????????? ????????????????????????????
  ??????? 0.85
• ???????????????????
• ?????????????????????????? ??????????????? 300
  ????????????????
• ??????????????????????????????????????????????????
  ?(Overbooking) ????????????????????????????? ????
  upgrade ??????? ?????????????????? 200
  ????????????????
• ??????????????????????????????????????? 100
  ????????????????

32
Simulation
33
Simulation

• IF(B2ltF2,1,0)

34
Simulation

• IF(I2ltF6,1,0)

35
Simulation
36
Simulation

• IF(B3gtS1,S3S1-S5(B3-S1),S3B3-S4
  (S1-B3))

37
Simulation output ???????????????????

• ?????????? 100 ?????
• ????????????????????????

38
Simulation output ???????????????????
39
Findings to decision-makers
40
Alternative ???????????????

• ?????? 55 ????
• ?????? 60 ????
• ?????? 65 ????
• ?????? 70 ????
• ?????? 75 ????

41
Result ?????????????????????????????
42
Car Insurance Problem
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Objective

• ????????????????????????? Claim ???????????

44
Model ???????????????? Claim ?????????????
45
Collect Data

• ????????????????????????????????????? Claim
  ??????
• ??????????????????? Claim ??????? Claim
  ?????????????????
• ????????? Claim ????????????????????

46
Raw Data
47
Specify Variable

• ????????????????????????? Claim ??????? 0.316
• ?????????????????????? Claim ?????????????????????
  claim-??????????????????????????????

48
Specify Variable

• ????????? Claim?????????????????????????
• (Normal distribution) ????????????? 9,290
  ???????????????????? 3,740

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Simulation

• IF(B3lt0.316,1,0)

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Simulation

• IF(D30,0,IF(D3lt0.644,1,IF(D3lt0.876,2,IF(D3lt0.966
  ,3,IF(D3lt0.998,4,5)))))

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Simulation

• IF(F30,0,NORMINV(F3,R1,R2))

52
Simulation
53
Simulation output

• ?????????????????????? 300 ???

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Simulation output

• ?????????? 60 ?????

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When do we simulate?

• In general, consider simulation when
• - The system is complex
• - Uncertainty exists in the variables
• - Real experiments are impossible or costly
• - The processes are repetitive

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When do not we simulate?

• we are less inclined to simulate when
• - The system is simple
• - Variables are stable or nonstochastic
• - Real experiments are cheap and nondisruptive
• - The event will only happen once

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Thank you for your attention ? ?

• Patcharaporn Neammanee
• patchara_at_as.nida.ac.th