Simulation

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.

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.

Demand Frequency 15 1 30 2 60 3 120 4 45 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

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

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

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

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.

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

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:

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

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: 0.76 (direct labour cost = $37) Second random number generated: 0.39 (parts cost = 80+20 x 0.39 = $87.8 Normal random number generated: 9062 Total Profit = 250  9062 - (37  9062 + 87.8  9062 +700,000) =2265500 - 1830937.6 =$434562.4 Supply-chain management

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