Probability Concepts & Applications (1) Describe the rationale for utilizing probability concepts. Is there more than one type of probability? If so, describe the different types of probability.

One uses probability mathematics in order to assess the probability of a particular occurrence or the results of a particular action; For instance, whether or not one should go into a certain market or invest in a certain product -- what are the chances or possibilities of the product succeeding.

There are five major approaches of assigning probability: Classical Approach, Relative Frequency Approach, Subjective Approach, Anchoring, and the Delphi Technique

Classical Approach -- this is used when each of the possibilities have an equally likely chance of occurring. The theorem is: P (X) = Number of favorable outcomes / Total number of possible outcomes

Relative Frequency Approach -- calculation is based on past historical / experimental experience. Theorem: P (X) = Number of times an event occurred / Total number of opportunities for the event to occur.

3. Subjective Approach -- calculation is based on one's personal / subjective experience

4. Anchoring -- one assigns the value based on past experience and adjusts it according to current experience.

5. The Delphi Technique -- a series of questionnaires that accumulate reiterated data as it gets passed around the group. This eliminates bandwagon effect of majority opinion (Statistical Thinking for Managerial Decisions ).

(2) Briefly discuss probability distributions. What is a normal distribution? Please provide a written example of how 'understanding distribution' can be an asset for any business project.

Probability distributions assign a certain probability to each of the possible outcomes of a random experiment. A normal; distribution is one that symmetrical and bell-shaped. It is the most frequently used distribution and used when the sample size is grater than 30.

The distribution curve can help management in three key ways: 1) identify the probability of a certain (called z) value, 2) identify the critical z value for a given probability, and 3) identify the probability of a defined range. An example of this may be the case when management wants to identify employees who have atypical high or low scores, namely who score in the upper and lower 3% when compared to the norm (average employee). A distribution curve would be used to map this.

Decision Analyses

Select an organization you have worked for or any organization of interest and discuss how decision analysis could be used to solve a business problem. Describe a decision tree and discuss how such a tool can be utilized to improve decision making.

Decision analysis provides a person with many methods and tools for clearly delineating the way through the problem, defining it, and working out what to do. Chevron, for instance, won the Decision Analysis Society Practice Award in 2010 for using decision analysis in all major decisions. In a video detailing Chevron's use of decision analysis, Chevron Vice Chairman George Kirkland notes that "decision analysis is a part of how Chevron does business for a simple, but powerful, reason: it works." (http://www.youtube.com/watch?v=JRCxZA6ay3M). Two of their objectives for using it would be targeting locations for spreading their business and targeting consumers for marketing initiatives.

Decision tree _ this is an illustration that uses branches to illustrate the various possible outcomes of a certain action / circumstance, assigning probability values to each outcome. Resource costs, and utility can also be plotted. Decision trees help the user decide which strategy will more likely help him reach his goal.

Regression Models

(1) What benefit does a variable provide when developing and examining models?

(2) Explain the purpose of simple linear regression and scatter diagrams. Please provide a simple linear regression model and define each variable used.

(3) Describe multiple regression analysis and discuss potential uses for this model

Regression analysis uses a dependent variable and explanatory variables and explains / predicts the association between each based on their interactions. As an example: sales volume of a certain item would be the dependent variable. It depends on the explanatory variables if amount spent on advertising (z) and number of people you employ (y). You want to see how much sales volume will likely be predicted depending on amounts of z and y. This is where a regression model comes in and where variables are used in plotting association. When there is only one explanatory variable and where the plot is a straight line, this is called simple linear regression. A scatter diagram is likewise used for plotting relationships between dependent and independent variables. One variable is

Plotted on the horizontal axis and the other is plotted on the vertical axis. The pattern of their intersecting points can show relationship patterns. The...

(SCATTER DIAGRAM)
An example of a simple linear model and its application in management is adapted from the following website http://www.stat.wmich.edu/s216/simpreg/package.html

The scenario: the management of a chain of package delivery stores wants to predict the weekly sales for individual stores based on the number of customers who made purchases. He randomly selects 20 stores and predicts their weekly sales (dependent viable (i.e. Y)) based on number of customers (independent variable (i.e. X)). X is placed on the horizontal; Y is the vertical.

Below is a figure that shows the scatter diagram. A line drawn through the dots connecting them would, according to given calculations, reveal how much of an association if any exists and strength or weakness of this association. (From the pattern, there does seem to be an obvious increasing relationship. As the number of Customers increases, Sales increase.) (Simple Linear Regression; online)

Multiple regression analysis is when the dependent variable (for instance sales) is predicted on more than one variable e.g. On amount of customers, location for store, character of employees, character of manager etc. It is more complex than simple linear, but also more valuable since it takes into account various variables (and business situations are comprised of various possible determining factors).

Forecasting

Discuss the different types of forecasts to include time-series, causal, and qualitative models. When might a researcher or project manager utilize exponential smoothing? What benefit does a Delphi technique provide when working with qualitative-based decision making?

In forecasting one makes judgments about events whose actual outcomes still remain to be observed. There are various different types of forecasts. Three of these are time-series, causal, and qualitative models

Time-series, - This uses past data (for experiments or experience) for estimating future outcomes

Causal, - This includes data of a relevant factor in order to assess possible outcome. For instance, data of weather conditions may be used in order to predict ice-cream sales.

Qualitative models -- These are subjective based on the experience / say-so of consumers or of managers etc. Examples of such methods may be the Delphi model, observation, focus groups, questionnaires etc.

The Delphi Technique is a series of questionnaires that accumulate reiterated data as it gets passed around the group. This eliminates bandwagon effect of majority opinion.

Exponential smoothing is a technique that is applied to time series data (i.e. A series of accumulated data made form repeated observations) in order to arrive at a certain forecast. This technique is usually applied to financial market and economic data but can be applied to any string of data.

Inventory Control Models

(1) Discuss the importance of inventory control with respect to supply and demand.

(2) What benefit can tools such as ABC analysis and just-in-time controls provide for an organization?

(3) How can an enterprise resource planning system assist a firm with improving its business operations?

Inventory control models enable the manager to know the amount of demand that is existent, the level of resources he has in his inventory to meet that demand, and how much he would need to purchase. These models help him budget and help prevent wastage of money. An inventory management system in short helps the manager to control and balance the flow of incoming and outgoing merchandise.

The ABC analysis is useful for dividing one's business into priorities according to A, B, C (strongest, moderate least strong priorities). This is useful for goals or for any aspect of the business in order to help one determine how to achieve objectives.

Just-in-time controls are models that are designed to help management to produce sufficient products that will meet customers' demands and meet them in time in an effective, lean manner so that the most limited amount of inventory is involved.

Enterprise resource planning (ERP) system: ERP uses software to integrate all aspects of the internal and external systems of the organization and make sure that are functioning well together. This includes the functions of finance/accounting, manufacturing, sales and service, customer relationship management, etc. The objective of ERP is to ensure optimum communication between all departments / levels of the business and to achieve optimum communication between internal and external spheres (i.e. with stakeholders).

ERP typically uses a database as its repository of information and as its control base.

Introduction to Linear Programming

Discuss the requirements of a linear programming (LP) model. Provide an example of an LP model and define each variable used. What are the key steps that need to be considered when formulating an LP…