Probability concepts and decision analysis in business

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 s most frequently used for proving or disproving cause-and-effect relationships. (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).

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 problem?

Linear programming (LP or linear optimization) is a model used for determining a way to achieve the best outcome for example achieving lowest costs according to a set of linear relationships. A widely used example is the problem of minimizing the cost of a selection of foods that meets all the recommended daily nutrient guidelines. (Gurobi. nd)

The LP model would have variables that capture the amount of each food to buy, a linear objectives that minimizes the total cost of buying all these foods, and a linear constraint for each nutrient so that the total food together supply that nutrient.

The LP would thus be described thusly:

Objective:

minimize cTx

Constraints:

A x = b (linear constraints)

l ? x ? u (bound constraints)

The vector (x) refers to the decision variables, (c) is the linear objective function, the equation Ax = b represents the linear constraints on (x), whilst variables l and u define the lower and upper bounds on x. (Vanderbilt, 2010)

Marketing Research

1. What benefit would be gained by utilizing linear programming (LP) for marketing research?

2. Discuss and provide a basic example of how LP can be used for marketing and/or consumer research.

Linear programming is used in an infinite amount of ways in the commercial / marketing world. It touches virtually every aspect from production scheduling to web advertising optimization to clothing manufacturing and affects almost every single commercial industry. This is so too because many practical problems in operations research can be expressed as linear programming problems

Aslan (2011) used the LP model in his research on his company in order to minimize total costs of the following variables: inventory levels, overtime, subcontracting and Backordering levels and machine and warehouse capacity. The study also considered the problem of scheduling a set of parts with sequence-dependent setup times. The firm in question wanted to decrease the costs to enlarge their inventory without decreasing the quality of its products, and they wanted to do this along the lines of Toyota's lean management style, namely with minim wastage. It used constraints in order to define its limits also realizing that as the company expands the "Sensitivity analysis can be used to change the values and see what the results are" (P11). LP was therefore most useful for this research, although Aslan (2011) affirmed that other models, such as simulation, could be used too. (Aslan, I (2011)

Network Models

Discuss the benefits provided by network modeling. Describe how the shortest-route and maximal-flow techniques can be utilized. Please provide an example of one of these techniques.

Network modeling provides a more flexible way of viewing objects and their relationships. They can often be placed in the form of a graph or in boxes with arrows linking one to another freeing them from the constraints of, for instance a hierarchical order.

The hierarchical database model allows one parent recorded to have many children, but the network modeling on the other hand allows existence of many parents' records with many child records. It also allows a more natural modeling of relationships between entities and this is its chief preference to the more limited and limiting hierarchical database model.

Two techniques of network modeling re the shortest-route and maximal-flow techniques where the maximal-flow determines the maximum flow through a network whilst the shortest route technique does just that finding the shortest path through a network.

The maximum flow, for instance, can be used to determine the maximum number of vehicles (cars, trucks, etc.) that can go through a network of roads from one location to another.

(1) Discuss how project management techniques can be used to improve the completion of projects. With this in mind, discuss the role of start and finish times with respect to project completion time.

(2) Explain the role of software in project management

Project management techniques enable people to specify exactly parts of the project that need to be accomplished as well as desired outcomes, possible problems and whom aspects of project should be delegated to. Needed resources are also specified, an s well as evaluation of current resources and all people that are needed for the job. Deadlines are implemented, benchmarks are formulated, a way of evaluating (project evaluation or performance appraisal) is implemented and a time carved in for review. By delineating each and every step of the project in this way and by pacing it as well as having inbuilt criteria for evaluation, the project is more likely to be effectively completed and on time.

Software enables workers AND TEAM to plot these plans out using Excel for instance to record amount of current and needed resources as well as names of delegates and details of their various responsibilities as well as dates of deadlines; other software allows appraisal opportunities and tracks project development. Finally, (although not conclusively) other projects have inbuilt capacities for review of project and for seeing blocks that need to be modified.

Waiting Lines

(1) Discuss the benefits provided by network modeling. Describe how the shortest-route and maximal-flow techniques can be utilized. Please provide an example of one of these techniques.

Network modeling provides a more flexible way of viewing objects and their relationships. They can often be placed in the form of a graph or in boxes with arrows linking one to another freeing them from the constraints of, for instance a hierarchical order.

The hierarchical database model allows one parent record to have many children, but the network modeling on the other hand allows existence of many parents' records with many child records. It also allows a more natural modeling of relationships between entities and this is its chief preference to the more limited and limiting hierarchical database model.

Two techniques of network modeling re the shortest-route and maximal-flow techniques where the maximal-flow determines the maximum flow through a network whilst the shortest route technique does just that finding the shortest path through a network.

The maximum flow, for instance, can be used to determine the maximum number of vehicles (cars, trucks, etc.) that can go through a network of roads from one location to another.

Queuing Theory

(1) Discuss the advantages and disadvantages of queuing theory for an organization in the service industry.

Queuing theory is the mathematical study of waiting lines, or queues. A model is constructed so that queue lengths and waiting times can be predicted. The idea has a huge amount of applications for numerous fields that include telecommunications, traffic engineering, computing and the design of factories, shops, offices and hospitals.

The benefits are of course that lean management is better fulfilled here with less resources and expense as well as labor wasted. Less time too is absorbed and the business has more content customers.

On the other hand, real-world situations are often more messy than mathematical models and models may sometimes fail to meet he unpredictability and complexity of real-life. Other models meantime have been devised to deal with these problems and/or to consider possibility of slack / error.

(2) What benefits are provided by the constant service time model?

This presents a single Queue leading to a single Service Facility which, in turn, handles each customer in the exact same amount of time. It is therefore shorter, more convenient and less messy as well as leading to less possibility for conflict. It is also extremely organized. (QUEUING THEORY DISCUSSION)

Benefits of Simulation

Discuss the many costs that businesses face today. Is it always practical to test new ideas via a 'real life' study - with participants, facilities, etc. If not, how can a simulation be utilized to test ideas while keeping costs manageable? If a simulation is used, what steps are needed in order to have a successful model?

Businesses face huge costs today with the larger and more complex the business, the greater the costs. Contemporary business needs money not only for employees and for basic resources as well as for support and for wooing and maintaining customers, but also for technology and for technological security. Marketing has its own costs, and then there are the costs of HR, a s well as legal expenses and auditing. This is just the skimming of costs that contemporary business face.

For this reason, amongst others, it may be impractical to test new ideas via a 'real life' study - with participants, facilities, etc. since many variables are involved and the outcome may not necessarily extend to all factors of the business or to all possible eventualities. Simulation on the other hand provides possible explanations too for decisions and enables the manager to trace cause-to-effect situations.

Modeling is often used with simulations where certain possibilities are recreated as a 'game' and thereby explored. The models should not be complex. Simulation is done with certain variables that are carefully defined and controlled -- since the possibility of situations is almost infinite. The hard constraints of time and space -- that are a problem with qualitative experiments -- a re controlled in the case of modeling and simulations. This too lowers the cost of the models. (Barnett, online)

Simulation Model Research

Use the internet to conduct research on popular simulation modeling software applications. Find two applications to compare by examining the costs, features, and training requirements.

"Applied AutoMod is a graphical simulation software that provides true-to-scale 3-D simulation of manufacturing and distribution operations from any angle. AutoMod detects bottlenecks and anticipate problems in existing or simulated factory environments, builds accurate and detailed simulation models that can run at accelerated speeds, enables analysis and optimization of system performance through experimentation and "what-if" scenarios, and verifies systems will work as planned. An AutoMod development license starts at $18,900, which includes any two of the specialized automation modules (e.g., conveyers, AS/RS, etc.). "(Simulation Software List http://www.design-rate.com/simulation_software.htm)

"ExtendSim CP & #8230; Use ExtendSim CP to model the behavior of any process where time or values are recalculated at each periodic step. The package includes a Value library of components for performing continuous modeling tasks. For custom applications, the internal development environment allows you to create fully integrated, custom components to fit any need. Standalone license $995, Maintenance $199."

(Simulation Software List http://www.design-rate.com/simulation_software.htm)

Review & Reflection

*Review and reflect on what you learned in the past 8 weeks. What is the most practical and easily applied lesson you learned?

What was the hardest to grasp? Why? What else do you need to know about Quantitative Analysis?

Final Project

Using what you have researched and studied throughout Modules 1-7, write a report addressing a quantitative analysis (QA) project. Here, you are asked to select a business of interest and develop QA best practices that can be developed and implemented to increase revenues and/or to decrease costs. Please provide at least three mathematical examples supporting your recommendations

McDonald's Corporation is one of the best known global brands. Starting with 2004, McDonald's witnesses a turn around and has become very profitable again, despite a high turnover of CEOs.

McDonald's leadership decided to continue to grow, using many new strategies, such as refurbishing locations, customizing service in each country and geographic area, enhancing R&D and product development, as well as marketing and packaging, extending service, offering healthy choices, and so on. These functions of management can best be categorized into four units -- Planning, Organizing, Leading, and Controlling.

Three quantitative analysis that can be used to increase revenues are the following:

1. Probability applications to see whether a certain location would be profitable for McDonald to move to or whether a certain food item would have a probability of succeeding.

2. Simulation modeling -- before going into the expense of actually refurbishing place from the start, McDonald can create a model or simulation of their proposed plan and test it vicariously

3. Queuing theory -- McDonald may well want to cut down on its ques. There are various queuing models that it can apply in order to test ways for doing so.