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Assignment 4 AD 616 Enterprise Risk Analytics

What to submit?

Please submit (i) a word file explaining in detail your answers to each question (you can use screenshots of the R to explain your answers) AND (ii) an R file with a separate tab for each question. For each question, make sure you develop the model and present the simulation results – the R file should be self-explanatory. The assessment of your work will include both the accuracy and the clarity of your word file and the R file.

1.    A convenience store needs to make a decision of how many packages of California rolls prepare for tomorrow. A package of California rolls cost the store \$2.00 and it sells for \$6.00. Daily demand is normally distributed with a mean of 90 packages of California rolls and a standard deviation of 30 packages of California rolls. If there are leftovers at the end of the day, the store donates them.

a.    Use simulation optimization to find the optimal packages of California rolls that maximizes the store’s profit.

b.    Add a chance constraint to the model (VaR constraint) to make sure that there is a 95% chance that California rolls are available to the customers. Then, use optimization to find the optimal packages of California rolls that maximizes the store’s profit.

2.    Marcy Hotel is a boutique hotel in Boston downtown area. The operations manager, Jenna, needs your help to decide how many rooms (of a particular type) to book for a day. The nightly stay in these rooms is

\$200 and the hotel has 100 of those rooms. The data shows that some customers do not show-up. To protect against no show-ups, Jenna is considering to book more than 100 rooms per night. Although this practice allows Jenna to utilize each room available as much as possible, it comes with a risk. The risk is that if Jenna books more than 100 rooms and if more customers than expected show-up, then some customers will not be able to stay at the hotel even though they made a reservation. To protect those customers, Marcy Hotel is providing a compensation of 120% of the booking price paid by the customer. Also, any no show-up customer Is refunded 30% of the booking price paid by the customer. How many rooms should Jane book in a day to maximize its expected revenue. Answer this question by developing a simulation optimization model. In your model, assume that the number of no-shows is lognormally distributed with a mean of (0.2*number of rooms booked) and standard deviation of (0.05*number of rooms booked).

When modeling the number of no-shows following a lognormal distribution, use the following function “rlnorm2”. Therefore, it should be rlnorm2(n, mean=0.2*number of rooms booked, sd=0.05*number of rooms booked)

rlnorm2 <- function(n, mean, sd){

rlnorm(n, log(mean*(1+sd^2/mean^2)^-0.5), log(1+sd^2/mean^2)^0.5)

## simulation optimization using R programming packages

Simulation optimization is a powerful tool which enables practitioners to explore and optimize complex systems. This can be particularly useful in cases where traditional methods fail to provide meaningful solutions. R programming packages provide a range of features which can be used to facilitate the simulation optimization process.

R packages such as ‘DynOpt’ and ‘deSolve’ offer a range of functions which are designed to assist in the implementation of simulation optimization algorithms. These packages provide functions for fitting models, generating data and running simulations. Additionally, they offer a range of optimization techniques, such as genetic algorithms, particle swarm optimization, and simulated annealing.

The ‘DynOpt’ package is particularly useful for its ability to handle multiple objectives and constraints. It provides functions for computing the objective function and its derivatives, as well as for generating random numbers and permutations. The package also provides a range of plotting functions which can be used to visualize the output of the simulation.

The ‘deSolve’ package is well-suited for dynamic optimization problems. It provides functions for solving ordinary differential equations, as well as for fitting models to data. It also includes a range of optimization algorithms which can be used to solve dynamic optimization problems. By taking advantage of the features provided by these packages, practitioners can easily explore and optimize complex systems using simulation optimization. This can be a powerful tool for understanding and optimizing systems in many different areas.

## Exploring the Benefits of Simulation Optimization for Profit Maximization with R

Simulation optimization is an emerging method for optimizing business decisions in order to maximize profits. It is a powerful tool that combines both simulation and optimization techniques to provide a comprehensive solution for solving complex business problems. This paper will explore the benefits of simulation optimization for profit maximization with the programming language R. Simulation optimization has the potential to improve decision-making by providing an accurate and timely assessment of the performance of a given system or decision.

Through the use of simulated data and optimization techniques, the performance of a system or decision can be evaluated and improved in a variety of ways. This can be done by optimizing the decision parameters or by using different optimization techniques to discover the most profitable decisions. The use of R for simulation optimization can provide several benefits for businesses. First, R is an open-source language that can be easily accessed by anyone. This makes it an ideal choice for businesses who are looking for an efficient, cost-effective way to optimize their decision-making.

Additionally, R has a large library of functions that can be used to perform various optimization tasks. This makes it easy to customize the optimization process and to create specific optimization strategies to suit the needs of the business. In addition to the cost savings associated with using R for optimization, there are several other potential benefits. R is able to provide an intuitive visualization of the optimization process which can help companies better understand their decisions and the effects they will have on their profits.

Additionally, R is able to provide users with detailed reports that can be used to analyze the performance of the optimization process. This can help improve the accuracy of the optimization process and can help businesses make more informed decisions. Overall, simulation optimization is a powerful tool for businesses to maximize their profits.

By using R for simulation optimization, businesses can take advantage of the cost savings and improved decision-making capabilities associated with the language. Furthermore, the ability to visualize the optimization process and to analyze its performance can help businesses make more informed decisions. As such, simulation optimization with R is an invaluable tool for businesses seeking to maximize their profits.

## Implementing Robust Optimization Strategies to Maximize Profits Using R and Simulation Optimization

Robust optimization strategies are essential for businesses to maximize their profit potential. In this article, we will discuss the use of R and simulation optimization to implement robust optimization strategies. R is a powerful and versatile programming language with a wide range of applications. It is widely used in the field of data analysis and predictive modeling. In particular, it is well suited for use in simulation optimization. Simulation optimization is a powerful tool for helping businesses to identify optimal solutions to complex problems. It involves generating a range of hypothetical scenarios and then testing different strategies to optimize the outcome.

Simulation optimization can be used in a variety of business contexts, including financial decision making. For instance, it can help identify the best combination of investments or the most profitable way of pricing a product. It can also help to identify the most cost-effective way of allocating resources. To use R for simulation optimization, businesses must first define the problem they are trying to solve. This should include setting up a mathematical model to describe the problem and the data available to solve it.

Once the model has been defined, R can be used to generate a range of possible scenarios and test them to determine the optimal solution. R also offers a range of packages to support simulation optimization. The “simoptim” package, for instance, is designed to help businesses define and test different scenarios. The “optim” package can be used to identify the most cost-effective and profitable solution to the problem. Finally, the “glmnet” package can be used to develop a predictive model to help businesses make more informed decisions.

By implementing simulation optimization strategies with R, businesses can maximize their profits. Through the identification of optimal solutions, businesses can make more informed decisions, allocate resources more effectively, and develop more robust strategies for the future. This can help them to stay competitive in an ever-changing marketplace.

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