What is prescriptive modeling?
usage of analytical models to analyze data and recommend specific actions in order to achieve desired outcomes.
Give three different prescriptive modeling techniques?
- Linear/ integer programming
- Heuristic optimization
- Simulation optimization
What are the four stages in the common workflow of prescriptive modeling?
reality - Model Optimizaiton Actions / insights
What is a simulation?
representation of real-world system or process to study or understand its behavior.
Simulations are always different from reality, but you need to choose the right assumptions in order to let the model allow you to draw the right conclusions.
Give 4 use cases of simulations?
- Study behavior of systems too complex, expensive or dangerous to study in real-life
- Study evolution of these systems over time
- Test hypothesis and theories
- Make decisions by means of scenario analysis
Give 5 benefits of simulations?
- Able to incorporate many different sources of uncertainty
- Applicable for many complex situations
- Easy what-if analyses
- Able to use visualizations
- Broad software support for many different approaches
Give 5 drawbacks of simulation?
- True optimization is impossible
- Analysis of results is difficult
- Garbage-in-garbage-out
- Large investment costs
- Tends to overestimate results
Give three distinctions in types of simulations?
- Deterministic vs Stochastic
- Static vs dynamic
- Discrete-time vs continuous-time
What is the difference between stochastic and deterministic simulations?
Deterministic: no randomness in system, all information is known in advance and plays out identically
Stochastic: randomness in system, where each run, the simulation does something different
What is the difference between static and dynamic simulations?
Static: time plays no natural role: used to solve problems when analytic models fail
Dynamic: time plays natural role: also counts processes which take time to be executed
What is the difference between discrete-time and continuous time simulations?
Discrete-time: time moves in discrete chunks, in-between is ignored
Continuous-time: system dynamics modeled continuously over time
What are two important types of simulations?
- Monte Carlo simulations
- Discrete-event simulations
Give two characteristics of monte carlo simulations?
Stochastic, static
Used for calculating difficult to calculate expressions
Give two characteristics of discrete-eveent simulations?
Stochastic, dynamic, discrete-time
Used to evaluate system dynamics over time
What are inferential statistics?
Methods used to make inferences about population based upon some set of statistics we do on the sample. Random sample tends to exhibit same properties as population from which it is drawn
how do you make Monte Carlo simulations 10 times more accurate?
To make your Monte Carlo simulation 10 times more accurate, you need to run 100 times more items.
Give two properties of Monte Carlo simulations?
- Confidence increases with number of repetitions
- Confidence decreases with observed variance
What is the law of large numbers?
if the number of observations is infinite, than the mean of the population = the sample mean
What is the central limit theorem?
for sufficiently large n, the population mean is approximately normally distributed with the sample mean as mean and the sample’s std. deviation.
What are three use cases for monte carlo simulations?
- Numerical integration
- Random number generation
- Stochastic optimization
How do decisions have to be made in stochastic scenarios?
In stochastic scenario’s, decisions have to be made before all factors that impact the outcome are known. We model this unknown factor as a random variable.
How do single stage and two-stage stochastic optimization happen?
- Single stage stochastic optimization:
Decision epoch 0 Random influence Outcomes - Two-stage stochastic optimization
Decision epoch 0 Random influence Decision epoch 1 Random influence Outcome
What are the three steps of a Monte Carlo simulation?
- Construct a model connecting inputs to outputs
- Run simulation
Generate multiple values of the random input
For each input, compute and record the output - Evaluate outputs
Distribution of the output
Plot histogram
Average, standard deviation etc.
Generate confidence intervals
