A random number is a generated value used to represent one possible outcome from a specified probability distribution or numerical interval. In Monte Carlo simulation, random numbers convert modeled uncertainty into simulated scenarios: each value is mapped to an outcome according to cumulative probabilities. section 9.2
A practical simulation workflow uses random numbers to:
- Translate a discrete probability distribution into cumulative-probability intervals. section 9.2
- Assign two-digit values from 00 through 99 to possible outcomes in proportion to their probabilities. section 9.3.3
- Generate reproducible samples with a fixed seed, using sampling without replacement for smaller runs or with replacement for larger runs. section 9.3.4
- Run repeated trials by mapping each generated value to an outcome and analyzing the resulting distribution. section 9.3.5
Absenteeism staffing simulation
A call-center model assigns random digits to values of k under a Poisson distribution. Digit 73 maps to k = 3, indicating three additional associates for that trial rather than the rate-based expectation of two. Across 10 trials, the simulated outcomes have a mean of 2.4 additional staff, helping balance understaffing risk against overstaffing cost. section 9.3.5 section 9.3.3
>>> random_digits = [f'{i:02}' for i in range(0, 100)] #1
>>> random_digits_ranges = [] #2
>>> current_index = 0 #3
>>> total_digits = len(random_digits) #4
>>> for i, row in poisson_table.iterrows(): #5
>>> count = max(1, int(row['Probability (%)'])) #6
>>> end_index = (current_index + count - 1) % total_digits #7
>>> if current_index <= end_index: #8
>>> start = random_digits[current_index] #9
>>> end = random_digits[end_index] #10
>>> random_digits_ranges.append(f’{start}-‘ \
>>> f’{end}’) #11
>>> else: #12
>>> start = random_digits[current_index] #13
>>> end = random_digits[end_index] #14
>>> random_digits_ranges.append(f’{start}-99, ‘ \
>>> f’00-{end}') #15
>>> current_index = \
>>> (end_index + 1) % total_digits #16
>>> poisson_table['Random Digits'] = \
>>>. random_digits_ranges #17
>>> print(poisson_table) #18
k Probability (%) Cumulative Probability (%) Random Digits
0 0 13.53 13.53 00-12
1 1 27.07 40.60 13-39
2 2 27.07 67.67 40-66
3 3 18.04 85.71 67-84
4 4 9.02 94.73 85-93
5 5 3.61 98.34 94-96
6 6 1.20 99.55 97-97
7 7 0.34 99.89 98-98
8 8 0.09 99.98 99-99
Inspect Python code that allocates two-digit ranges to discrete outcomes according to probability percentages, including ranges that wrap from 99 to 00. section 9.3.3
>>> np.random.seed(1) #1
>>> random_digits = \
>>> np.random.choice(100, 10, replace = False) #2
>>> formatted_digits = \
>>> [f'{digit:02}' for digit in random_digits] #3
Inspect NumPy code that seeds the generator, samples ten values, and formats them as two-digit strings. section 9.3.4
Table 9.1 Random numbers aligned to k values
|
Random number
|
k value
|
|---|---|
|
80
84
33
81
93
17
36
|
3
3
1
3
4
1
1
|
|
82
69
65
Sum
Mean
|
3
3
2
24
2.4
|
Inspect the trial table aligning generated random numbers with k values and calculating the total and mean staffing requirement. section 9.3.5
