In many situations it is difficult to construct an analytic or symbolic model of the problem scenario. Sometimes in these situations it is possible to run an extended real-time experiment to study the problem. However, there are situations for which it may be difficult or expensive to run an extended experiment to collect data. The use of random events (e.g., rolling a die or flipping a coin) and the use of computer-generated random numbers gives the modeler another tool to use in investigating complex problem situations.
Study the discussion of Simulation Modeling in the first part of Chapter 7 (Sections 7.1 - 7.3). A copy of a related UMAP module, Monte Carlo: The Use of Random Numbers to Simulate Experiments, will also be available for each group.
Design and carry out a simulation experiment to investigate the problem scenario given in #7, page 236 of your text. You may conduct this experiment in any of the following ways:
Your project report is to follow the usual project report format.
In the Model Formulation section of your report, you should discuss your underlying assumptions about this scenario, and how your experiment accurately models the problem situation.
In the Problem Study section of your report, include the actual data you generated -- tabulated or summarized clearly for your reader. Your reader should be able to look at your data to verify the results you claim to get in your investigations.
In the Model Interpretation section of your report, apply the results of your simulation experiment to the question of your best strategy in this game.
In the Conclusion of your report, reflect on the use of Monte Carlo methods to study problems of this nature. What did you learn about the game, Let's Make a Deal, through your investigations for this project? How robust do you think your solution is in this situation? In general, for what kinds of problems would you consider or recommend simulation as a modeling strategy?