- Cumulative Probability Distribution
In this step determine the cumulative distribution of each variable selected. Cumulative probability is the sum of numbers in the probability column added to the previous cumulative probability.
- Setting Random Numbers
Monte Carlo Simulation have established cumulative probability distribution for each variable. It requires generation of a sequence of random numbers. Random numbers of a series of digits say one digit, two digits etc. e.g. if we are interested in one digit number there are only ten such numbers. And if we want to generated number, then chance of that number should be 1/10. These random numbers are called pseudo random numbers. Random number are generated using the digital computers these days. Using the cumulative probability distribution computed, we can set intervals of random numbers for each item.
- Generating Random Numbers
Random numbers may be generated in several ways. If problem is large it involves thousands of simulation trials. If the simulation is small the number may be selected that has 100 lots randomly from the random table. We can select the numbers from anywhere in the table. These random numbers are selected in such a way that every no. Has an equal probability. If selection from 5 digit random number table these numbers may be chosen from any fashion. Selecting the columns or rows or diagonals, we can select our numbers as first two digits or last two digits or middle one out of the five digits.
Example :
Pastry emporium is a bakery shop who keeps stock of a popular brand of pastries. Previous experience indicates the daily demand as given here .
|
Daily Demand : |
0 | 10 | 20 | 30 | 40 | 50 |
|
Probability : |
.01 |
.20 | .15 | .50 | .12 |
.02 |
Consider the following sequence of random numbers.
R. No. 48, 78, 19, 51, 56, 77, 15, 14, 68, 09
Using this sequence, simulated the demand for the next 10 days. Find out the stock situation if the owner of the bakery decides to make 30 pastries every day. Also estimate the daily average demand for the pastries on the basis of simulated data.
Solution
According to the given distribution of demand, the random number coding for various demand levels is shown in the table below:
Random Number Coding
|
Demand |
Probability | Cum. Prob. | Random Number Interval |
| 0 | 0.01 | 0.01 |
00 |
|
10 |
0.20 | 0.21 | 01-20 |
| 20 | 0.15 | 0.36 |
21-35 |
|
30 |
0.50 | 0.86 | 36-85 |
| 40 | 0.12 | 0.98 |
85-97 |
|
50 |
0.02 | 1.00 |
98-99 |
The simulated demand for the pastries for the next 10 days is given below. Also given is the stock situation for various days in accordance with the bakery decision of making 30 cakes per day.
Determination of Demand and Stock Levels
|
1 |
48 | 30 | – |
|
2 |
78 | 30 | – |
| 3 | 19 | 10 |
20 |
|
4 |
51 | 30 | 20 |
| 5 | 56 | 30 |
20 |
|
6 |
77 | 30 | 20 |
| 7 | 15 | 10 |
40 |
|
8 |
14 | 10 | 60 |
| 9 | 68 | 30 |
60 |
|
10 |
09 | 10 |
80 |
Expected Demand = 220/10 = 22 units per day.