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Robust Optimization Case Solution & Answer

LINEAR PROGRAMMING

Linear programming is a technique used in mathematical modeling. While coding a linear program, we set our objective either to be minimized or maximized subjected to thegiven set of constraints.(Britannica, 2016)

It is oneof the simplest ways for doing optimization. It assists in solving some very complicated problems of optimization after making few abridging assumptions. Being an analyst, we are bound to encounter implications and problems to be resolved by using linear programming.

MODELING UNCERTAINTY

Statisticians construct statistical models for some diversified purposes, but classically indulge efforts to explain variables in present data in the form of some fundamental structure. These models are seldom a perfect explanation of the variables under observation;therefore reflexion of model uncertainty is a critical chunk of statistics.

For many reasons, model uncertainty has been the most thought-provoking area of statistics. Firstly, there are many probable models under contemplation that may be devastating. For Example, consider an ordinary linear regression, where we try to explain our data by relating it linearly to likely covariation. Assume that we have around 60 probable covariates, but we are not sure that which variable we should involve, or which should we omit in our regression model. Then there will be 260 regression models, that is even too big to compute.

The secondary key trial is the “big data”. It has been a major issue since last 5 years that the number of descriptive variables could exceed the amount of data in hand.

Many more challenges come in the way in the trial of implementing strategies to deal with the uncertainty model, making it more interesting in research problems of statistics.(Berger, 2018)

METHODS TO MODEL UNCERTAINTY

There are several methods to model uncertainty including:

  • Values generation from known probability distributions

Variables that cannot be predicted with certainty are called random variables. For any stationary random process, if there is not any serial correlation between the order then we can characterize random process by using single distribution. The variables from the present data are used to define probability distribution or to estimate the parameters.(Ecommons, 2017)

  • Monte-Carlo Simulation

For each task, a random value is opted in Monte Carlo Simulation, based on the range of estimates. This model makes its all calculations based on our selected random variable.This process goes on along with the continuous recording of the results. A classical Monte Carlo Simulation calculates the model as many times, using different randomly selected variable every time. At the end of the simulations, we have a data set of the results derived from the simulation based on our randomly selected variables. These results show the variety of different possible outcomes of the results.(RiskAmp, 2018)

  • Chance constrained model

Chance constrained model is the formulation to solve the optimization problem. It ensures the likelihood to meet a certain limit which is above the certain point. In short, it limits the practicable region to make the confidence level of the solution higher.However, this approach to model uncertainty is hard but is one of the robust approaches…………

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