Operations Research

  1. Stochastic Processes and Markov Chains
    1. Introduction to Stochastic Processes
      1. Classification of Stochastic Processes
        1. Discrete vs. Continuous Time
          1. Discrete vs. Continuous State Space
          2. Markov Chains
            1. Markov Property
              1. State Space and Transition Probabilities
                1. Transition Probability Matrix
                  1. Chapman-Kolmogorov Equations
                    1. N-Step Transition Probabilities
                    2. Classification of States
                      1. Accessible and Communicating States
                        1. Recurrent and Transient States
                          1. Periodic and Aperiodic States
                            1. Irreducible Chains
                            2. Long-Run Behavior
                              1. Steady-State Probabilities
                                1. Limiting Distributions
                                  1. Ergodic Theorems
                                  2. Absorbing Markov Chains
                                    1. Absorbing States
                                      1. Fundamental Matrix
                                        1. Absorption Probabilities
                                          1. Expected Time to Absorption
                                          2. Applications of Markov Chains
                                            1. Reliability Analysis
                                              1. Inventory Systems
                                                1. Queueing Systems
                                                  1. Brand Switching Models

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                                                8. Dynamic Programming

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                                                10. Queueing Theory