Hands-On Prescriptive Analytics

Chapter 8. Simulation Examples

I provide five extensive examples of stochastic simulations in this chapter by building on and extending the material in Chapter 7. I will gradually make the examples more complicated, beginning with a simple coin toss problem and progressing to the hotel investment decision tree problem. More examples and explanations are in Paczkowski (2023).

The leading questions for this chapter are:

• How do you specify a simulation?

• How do you analyze a simulation’s results?

Example 1: Coin Toss

I discussed a simple coin toss experiment in Chapter 4 to introduce frequency-based probabilities. I simply noted that most people are familiar with the basic probability concept from tossing a coin. The assertion is that the probability of a heads-up on a toss of a fair coin is 0.50. I demonstrated where this number comes from in Chapter 4. But this does not mean it is correct in the real world. I also noted that probabilities are interpreted in terms of infinite series giving them a “long-run” interpretation. Of course, we cannot do something (e.g., flipping a coin) an infinite number of times. The question is then: “Can we devise an experiment to determine if, in the long-run (however defined), on the average, the probability is indeed 0.50?” You can do this with a simulation.

I provide a script in Figure 8-1 for simulating a coin toss. I first set some simulation parameters in Lines 4 to 11. A random seed is set at 42 followed by the number of coin tosses in ...