IE232 Operations Research : Stochastic Models

📋 Project Description

Model, simulate, and analyze a real-world system of your choice. The system must be stochastic (involving randomness) and controllable in the sense that the system designer can influence its behavior through decisions or policies. You may work individually or in groups of up to three students.

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Deadlines:

• Proposal due by Nov 3, 2025.
• Final report due by Dec 19, 2025. </aside>

✅ Submission Requirements

Proposal:

• Proposal should include a short paragraph outlining your plan for the project and members of your group (name and student ID).

Final report:

• Two-page report (PDF)

  Your write-up should include:

  • A description of the real-world system.
  • Details of your model(s).
  • Simulation results (with figures included in the report).
  • (Optional) Analysis for determining an optimal policy.

  Two-page limit is not strict. You may add more pages (especially if you are adding mathematical analysis).

• Jupyter Notebook (.ipynb)

  • Python code that reproduces your simulation results. All results must be reproducible with the submitted notebook.
  • If you have good reason to, you may submit other file type with instructions on how to run your code.

Instructions

1. Choose an interesting real-world problem (e.g., elevator, production line, traffic management, customer service, etc.).
2. Model the problem mathematically and make assumptions (e.g., Poisson arrival, exponential service time, etc.). You may choose more realistic distribution if you want.
3. Specify a goal (e.g., maximize revenue minus cost, minimize long-run wait time, minimize queue length, etc.).
   1. For example, in restaurant management, we can define a utility function as revenue per unit time minus cost per unit time, where cost is the wage of the server.
4. Model multiple systems for achieving the goal.
   1. Multiple systems can arise from varying a parameter in the system (e.g. vary the rate of service. vary the queue capacity. vary the number of servers, etc)
   2. Alternatively, create multiple systems using different designs (e.g., number of workers, queue structure, different operations, etc.).
5. Simulate the systems and measure their performance.
6. Choose the best system based on the simulation.
7. (Optional for extra credit) Mathematical analysis.
   1. Determine the best system analytically and verify that it performs best in simulation.
   2. And/or mathematically analyze certain behavior of the system, and show by simulation that what math predicts is consistent with the simulation.

✏️ Grading Criteria

• Proposal (10 points)
  • –1 point per late day.