# Probability Theory and Decision Making Essay Example

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• Pages: 5 (1187 words)
• Published: November 27, 2017
• Type: Case Study
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The uses of probability theory with Decision Making are key tools for corporations to made key decisions on new markets and investments. CoffeTime Corporation used Key Tools such as Bayes Theorem and comparisons of probabilities of random and continuous variables in order to access the best approach for the initial phase of the operations for the insurgence of the India Market.

## Management Problem

CoffeeTime Corporation is initializing the first phase of operations within the India market. This initial phase includes a limited product line offered in order to create product awareness. CoffeeTime management needs to identify sales promotion activities and gauge the demand for the CoffeeTime products as well as manage the supply chain of the coffee beans used to produce the products.

As part of this activity CoffeeTime is considering participation in the South Asian Shopping Festival in Mumbai. The festival is a pop

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ular shopping festival and can be used as a vehicle to broaden the customer base by the introduction of the CoffeeTime products. However, the management team of CoffeeTime must determine how best to use this vehicle, including decisions on how to participate, anticipate demand and mange the supply.

## Determination of Participation - Initial Look

To determine how to participate in this festival, CoffeeTime management team utilizes the use of statistical theories. Statistical theories will be used to determining how to maximize profits, maximize exposure and product acknowledgment base while also minimizing cost. The process of decision-making requires choosing the most valuable option, which is the option that has the highest Expected Monetary Value (EMV), a measure of probabilistic value ( www.vanquardsw.com). To do this, the CoffeeTime team management uses probabilities associated with hypothesis based on statistical

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data and theory.

## Sampling

In order to consider participation in the South Asian Shopping Festival in Mumbai, the management team needs to determine the EMV based on the predicted sample size of attendance and use this information to determine if CoffeeTime would set up stalls themselves or franchise them out. In order to predict the attendance for this years' festival, daily attendance for historical festivals were used and probabilities were assigned. This historical sampling is characterized as a probability sampling, which allows the assignment of probability to analyze hypothesis.

Probability Sampling gives each unit in the study population a known, nonzero probability of being selected for inclusion in the sample and uses random selection. Non-Probability Sampling is a sampling in which each unit in the population does not have a nonzero probability of being selected for inclusion in the sample. Probability sampling designs are more likely to produce a sample that is more representative and have less sampling error compared to non- probability sampling designs (www.personal.ksu.edu).

The CoffeeTime management team assigned probabilities of attendance in three categories. These categories were above 100,000, between 50,000 and 100,000 and below 50,000. Based on these probabilities and a higher EVM, the management team recommends setting up the stalls at the festival.

## Determination of Participation - Hypotheses testing

How accurate are the attendance probabilities in which the management team has based their decision. In order to determine the accuracy, hypotheses' testing is invoked. A hypothesis testing has two approaches, the Classical and the Bayesian approach. The CoffeeTime management chose the Bayesian approach, which is not as widely used as the Classical approach, but has become more widely used since the 1950's. The Classical approach represents

an objective view of probability in which the decision-making rests totally on an analysis of available sampling data, which is then used to establish a hypothesis.

Bayesian statistics are an extension of the classical approach. Bayesian also uses sampling data, but extends the data to consider all the other available information such as subjective probability estimates. General experience is used for these subjective estimates rather than on specific collected data. However, a drawback of the Bayesian probability theory is that they are based on subjective data, and therefore all the probabilities appearing in Bayesian probability theory are conditional.

## A Revised Look

During the process of determining participation, the ForeFront Company has come out with a forecast of this years' attendance. The CoffeeTime management team must decide if they want to revise the attendance probabilities based on the new ForeFronts' forecast as well as determine the cost they are willing to pay for the forecast. In order to make this decision, the team needs to understand the accuracy of data from the past.

## Use of Baye's Rule

Bayesian statistics allow for subjective probability estimates in terms of degrees of belief. Specifically Baye's Rule is used to compute the conditional probabilities. The CoffeeTime management team can apply Bayesian statistics to determine the conditional probability that ForeFront's forecast was above the actual number of attendance. This information in turn can be utilized to determine if a new forecast needs to be purchased. Applying this concept to the probabilities and revising the probabilities, the CoffeeTime management team was able to determine not to buy ForeFront's forecast.

## CoffeeTime's Confidence Interval

A confidence interval the specified probability of a parameters occurring within a range of values constructed from

sample data. A standard normal distribution can be used to express the level of confidence if the population follows a normal distribution and as a known standard deviation. If the sample size is extremely large, the corresponding population is more accurately represented. If the standard deviation is known then the confidence interval can be calculated through the z-distribution. The sample data used by the CoffeeTime management team meets these criteria and therefore can be applied to aid in the decisions of the management of supply.

CoffeeTime's branch manager is proposing to treat the demand for a Mocha beans as a continuous random variable. The CoffeeTime management team needs to determine what the service level should be that will maximize profits and focused on the Expected monetary value and the expected opportunity loss. This service level can then be used to calculate the optimal stock level. Using probabilities of stock-out, no stock outs, cost of under-stocking, the cost of over-stocking etc, and a normal distribution for demand, the service level was determined to be 83, with the optimal stock level of 1.413. The corresponding confidence level for the optimum service level is 95%, which indicates the service levels will fall within the middle 95% of the curve, giving the CoffeeTime management team a high level of assurance their data is accurate and therefore a high level of confidence of maximizing profits.

## Conclusion

In conclusion, the CoffeeTime management team has several recommendations, based on the EVM and probabilities they determined. The first is to set up the stalls themselves at the festival. The second is to pass on the purchase of ForeFront's forecast based on the conditional probabilities using Baye's

Theory. The third recommendation is the Service level and stock levels of Mocha that should be maintained at 1,450 to maximize profits. Using these recommendations, the CoffeeTime team feels the initial phase of insurgence of the CoffeeTime products into India will be as expected and successful.

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