Abcd

Simulation: Definition • Simulation is a mathematical model of a real system. • The system consists of inputs and outputs and a mathematical expression. • We obtain the outputs by manipulation of the inputs using the mathematical expression.

Simulation Model

Risk Analysis: Example • PortaCom manufactures printers. • These parameters apply:

– Selling price = 249 per unit – Administrative Cost = 400,000 – Advertising cost = 600,000

• Cost of direct labor, cost of parts, and the 1st year demand are probabilistic. • PortaCom wishes to investigate its profitability

Profit Model

Profit = (249 – Direct labor cost per unit – parts cost per unit) (Demand) – 1,000,000

Direct Labor Cost per Unit

Direct Labor Cost per Unit 43 44 45 46 47

Probability 0.1 0.2 0.4 0.2 0.1

Flow Chart for PortaCom Simulation

Model Parameters Selling Price per unit = 249 Administrative Cost = 400,000 Advertising Cost = 600,000

Generate Direct Labor Cost, c1

Next Trial

Generate Parts Cost, c2

Generatate First Year Demand, x

Compute Profit

Random Process Generator • In order to generate values from the probability distributions of each RV, we rely on generating Random Numbers. • When a random number is generated we can associate it with a value from the probability distribution of the RV.

Associating RN to Direct Labor Cost per Unit

Direct Labor Cost per Unit 43 44 45 46 47

Probability Assign this row cost if RN lies within this interval 0.1 0.2 0.4 0.2 0.1 0.0 – 0.0999 0.1 – 0.2999 0.3 – 0.6999 0.7 – 0.8999 0.9 – 0.9999

Associating RN to a Value from a Uniform Distribution

F(x)

1

r

x0 = a + r(b-a)

a x0 b x

Parts cost = 80 + 20r Trial 1 2 3 4 5 6 7 8 9 10 11 RN 0.6836 0.7417 0.9401 0.2894 0.7866 0.4248 0.3342 0.0445 0.9042 0.5910 0.1122 Parts Cost 93.67 94.83 98.80 85.79 95.73 88.50 86.68 80.89 98.08 91.82 82.24

Associating RN to a Value from a Normal Distribution

Demand = N(15,000,4500) Trial 1 2 3 4 5 6 7 8 9 10...