1. Simulation

2. Five- steps in simulation technique
Setup probability distribution for pertinent variables.
Build cumulative probability distribution for each variable
Establish interval of random numbers for each variable
Generate random numbers
Simulate a series of trials.

3. Example
Encik Fauzi is a car dealer. He has been in this business for quite some time. He knows the importance of keeping all kinds of records pertaining to his business. Specifically, he never forgets to keep record of the number of cars sold everyday. Following Table shows the statistics of the number of cars sold during the previous 300 working days. Conduct a simulation experiment to find out the average demand of cars in the next 10 days.

4. Demand
Frequency 15 1 30 2 60 3
120 4 45 5

5. Demand
Frequency
Probability 15
15/300=0.05 1 30
0.10 2 60
0.20 3
120
0.4 4 45
0.15 5

6. Demand
Frequency
Probability
Cumulative distribution 15
15/300=0.05
0.05 1 30
0.10
0.15 2 60
0.20
0.35 3
120
0.4
0.75 4 45
0.90 5
1.00

7. Demand
Frequency
Probability
Cumulative distribution
Interval of random Nos. 15
15/300=0.05
0.05
01-05 1 30
0.10
0.15
06-15 2 60
0.20
0.35
16-35 3
120
0.4
0.75
36-75 4 45
0.90
76-90 5
1.00
91-100

10. Generated random numbers
Actual Simulation 52 37 82 69 98 96 33 50 88 90 3 4 5 2
Simulated demand
Average demand = 3.6
Expected demand = 2.8

11. Example
Rosly Enterprise has taken a franchise business of selling a number of electronics items. Originally, these products are manufactured by Samsung in Korea. Over the past years, Rosly has seen the fluctuating demand of stereos. From the data, he has found that demand follows normal probability distribution with mean = 200 units and standard deviation = 25 units.
If he cannot sell all the stereos within a specific period, then per unit RM 20 is imposed as holding cost. On the other hand, if demand is more than the stock, then as a goodwill loss, Rosly imposes RM 30 per unit of shortage. Furthermore, Rosly’s profit by selling one unit of stereo = RM 75. In order to maximize profit, help Rosly determining the desired order quantity of stereo.

12. Simulation in Inventory Management
Trial
Simulated demand
Sales
Profit HC SC
Net Profit 1
189
14,175
220
13,955 2
203
200
15,000 90
14,910 3
159
11,925
820
11,105 4
194
14,550
120
14,430 5
223
690
14,310 6
197
14,775 60
14,715 7
243
1290
13,710 8
221
630
14,370 9
212
360
14.640 10
198
14,850 40
14,810
Average = $14,298

13. Simulation in Risk Analysis
Let us assume that the R & D section of a certain printer manufacturing company Portacom has designed a new printer. Now the question is : whether this new project will be implemented or not, i.e., actually the printer will be manufactured or not. The selling price of the printer will be $ 250. The yearly administrative and advertising costs are respectively $ 300,000 and $400,000. The direct labor cost, costs of parts and demand of the printer are not known with certainty. But it is known that the direct labor cost will follow the following discrete distribution:

14. Labor Cost / Unit
Probability
$30
0.1
$32
0.2
$35
0.4
$37
$40
It is also estimated that parts cost will be in the range $80 and $100 and any value is equiprobable.
It is also anticipated that demand will be normally distributed with mean 10,000 units and S.D. = 1500

15. Labor Cost Probability cpd nos.
Int. of random
nos. 30
0.1
0.01  r  0.10 32
0.2
0.3
0.11  r  0.30 35
0.4
0.7
0.31  r  0.70 37
0.9
0.71  r  0.90 40
1.0
0.91  r  1.00
First random number generated: (direct labour cost = $37)
Second random number generated: 0.39 (parts cost = x 0.39 = $87.8
Normal random number generated: 9062
Total Profit = 250  (37   ,000) = =$
Supply-chain management

16. Thank You