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A) Purpose of Monte Carlo SimulationMonte Carlo Simulation is a computational technique used in complex systems where deterministic results (or precisely known input values) are difficult or impossible to obtain.The main process is to generate random values for each input variable based on your knowledge of their behavior. The formulating would then be replicated over 1000s of instances, each with its own randomly extracted input variables. The resulting 1000s of output values can then be statistically analyzed to provide estimates with the required confidence.Monte Carlo Simulation will therefore resolve the problem analysts get when they are not sure of their estimates.B) Cases where it can be UsedHere are some situations that can be resolved by applying Monte Carlo Simulation:1) When you need to estimate input variables in a formulation. Each estimate will have an error margin. Your output results will therefore have a compounded error, making it difficult for you to be precise and accurate.2) When designing a business process that has an elaborate quantitative formulation. Manually, such objectives as costing, efficiency, reliability and risk cannot easily be calculated to give specific answers. Monte Carlo Simulation can then be used to assist designers get answers that can be quoted within confidence intervals.3) When supporting Data Analysis, Data Science methods or Machine Learning methods that can only be verified using test results based on a large number of scenarios. Applications such as forecasting, optimization, regression, bootstrapping techniques, queuing systems and other system dynamics processes.4) When you have a formulation that requires the use of sensitivity analysis, influence testing and confidence intervals of the outcome and related risk analysis.C) An Example: Planning a ProjectWhen planning projects with a large number of tasks that have imprecise duration and costs, estimation errors will creep into the global duration and cost resulting in a compounded error. Each variation you try will result in a different critical path.MCS allows you to prepare 1000s of scenarios. Each one will represent an "instance" of your project. For each task, you will be able to sample a random value from a probability distribution that best represents the behavior of the duration or the cost of such tasks.The 1000s of scenarios will then result in 1000s of total duration (critical path) or total costs. It can also result in many critical paths and can hence indicate which one is the most likely path your project will take. How does that help? You will be able to express your results with a measured degree of confidence.You might conclude that 90% of your scenarios resulted in a project duration shorter than 34 days. MCS can tell you that there would be a 10% risk the task might have a duration longer than 34 days. If you are more risk averse, you might use a tighter confidence level such 5% of the time, the duration might then be longer than 38 days. Such "confidence" analysis of results can only be reached when we have 1000s of durations or costs, giving you a lot more confidence in your estimates than when entering a single fixed value for the duration or cost of each task.D) But why do we Need a Standardized MCS Process?I learnt so much from many wonderful MCS books and video courses. Such a variety of approaches made it clear that I was wasting time starting each model from scratch. More time was needed to understand how each developer approached their problem and how they developed the simulations. I needed a standardized MCS process that can be used every time I developed a new model. This resulted in the 8-step process we will be using in this course.Such a standardized and segmented process would ease troubleshooting and debugging models. It would also make them more friendly to share. Moreover, you would be able to reuse some of these steps in future models.E) The Practical 8-Step Process for Developing Monte Carlo Simulation ModelsAt the end of this course, you will be able to use the 8 steps having learnt it through a documented Case Model:Step 1: express your problem statement and prepare the information you need in the coming steps. Develop a formulation that is static, that is, it would be based on single fixed estimates of input variables. This would help you validate the formulation early in the process.Step 2: identify the input variables in the model and determine the probability distributions that best represent each variable. In this step, and using the information from step 1, you will also be able to configure each distribution with using its proper parameters: means, rates, standard deviations.Step 3: develop your model using functions that extract random values from each of these distributions. Replace the fixed estimates used in Step 1 with dynamic random values extracted in Step 2. Each of the 1000s of scenarios would be an instant of your formulation containing different values of the input variables. This is the heart of the Monte Carlo model and it would result in 1000s of output results.Steps 4 to 7: develop and interpret the results with 5 analytic methods: frequency tables, combo charts showing the frequency and cumulative frequency percent of your output results, confidence intervals using percentiles, sensitivity and influence analysis.Finally, in Step 8 you will state your findings and answer the questions raised in the problem statement as well as suggest diverse extensions and improvements to the model on hand.F) Related MatterThe course includes many concrete models using the 8-step process. Various distributions will be clarified and used in these models: Uniform, Categorical (Discrete), Normal, Binomial, LogNormal, Geometric, Negative Binomial, Exponential, BetaPERT, etc. These will be explained and documented in detail along with examples and procedures to use them in Monte Carlo Simulation.All lectures will be supported by a variety of resources:· Solved and documented MCS models in Excel (18 all in all)· Dedicated workbooks that animate and describe various probability distributions (10 all in all)· Some blank models that allow you to start from scratch· Templates that can be used by you· Links to Interesting articles and books· Detailed procedures for some elaborate formulations· Related lists

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