Simulation [PDF]

Monte Carlo Simulation

Supplement S10

9 Select numbers randomly from a probability distribution 9 Use these values to observe how a model performs over time 9 Random numbers each have an equal likelihood of being selected at random

模擬 Simulation Operations Management (4版) -- ROBERTA S. RUSSELL & BERNARD W. TAYLOR III (Prentice Hall) To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

0 1 2 3 4 X={0,1,2,3,4}

FREQUENCY OF DEMAND

PROBABILITY OF DEMAND, P(x)

20 40 20 10 10

0.20 0.40 0.20 0.10 0.10

100

1.00

2/14

Roulette Wheel of Demand

Distribution of Demand LAPTOPS DEMANDED PER WEEK, x

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

1/14

0

將轉輪區分r={ 將轉輪區分r={ 0 ,1,… ,1,…,99} 90 x=4 80

x=0 20

x=3

x=2 x=1 60

Table S10.1

Figure S10.1 To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

3/14

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

4/14

1

Generating Demand from Random Numbers DEMAND, x

RANGES OF RANDOM NUMBERS, r

0 1 2 3 4

0-19 2020-59 6060-79 8080-89 9090-99

Random Number Table 39 73 72 75 37

r = 39

65 71 18 12 17

76 23 47 25 79

45 70 33 69 88

45 90 84 17 74

19 65 51 17 63

90 97 67 95 52

69 60 47 21 06

64 12 97 78 34

61 11 19 58 30

Table S10.3

Table S10.2 To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

5/14

6/14

Simulation in Excel

Random Numbers in Excel

Enter this formula in G6 and copy to G7:G20 Enter “=4300*G6” in H6 and copy to H7:H20

Generate random numbers for cells F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20

= RAND()

= AVERAGE (G6:G20)

Exhibit S10.1

Exhibit S10.2 To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

7/14

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

8/14

2

Simulation in Excel

Simulation in Excel This formula entered in G7 and copied to G8:G105 =VLOOKUP (F6,LOOKUP,2) in H6 and copied to H7:H105

=G6*50 entered into cell L6 and copied to L7:L105 Shortages computed by entering =MIN(G6-H6,0) in I6 and copying to I7:I105 Exhibit S10.3

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

Exhibit S10.4

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

9/14

10/14

15 Weeks of Demand

Simulation in Excel WEEK

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

New formula for two laptops ordered per week

r

39 73 72 75 37 02 87 98 10 47 93 21 95 97 69

DEMAND (x (x)

1 2 2 2 1 0 3 4 0 1 4 1 4 4 2 Σ = 31

REVENUE (S)

4,300 8,600 8,600 8,600 4,300 0 12,900 17,200 0 4,300 17,200 4,300 Average demand 17,200 = 31/15 17,200 = 2.07 laptops/week 8,600 $133,300

Table S10.4 Exhibit S10.5

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

11/14

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

12/14

3

Computing Expected Demand

Areas of Simulation Application 9 Waiting Lines/Service 9 Inventory Management 9 Production and Manufacturing Systems 9 Capital Investment and Budgeting 9 Logistics 9 Service Operations 9 Environmental and Resource Analysis

E(x) = (0.20)(0) + (0.40)(1) + (0.20)(2) + (0.10)(3) + (0.10)(4) = 1.5 laptops per week Not particularly close to simulated result of 2.07 laptops Difference is due to small number of periods analyzed To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

13/14

To Accompany Russell and Taylor, Operations Management, 4th Edition, © 2003 Prentice-Hall, Inc. All rights reserved.

14/14

4