Model Formulation Process

The model formulation process takes a real life situation and creates a representation of it in order to gain insight or solve a problem. The formulation process involves the elements: decisions, outcomes, structure and data. Decisions are the actions that may solve the problem. Outcomes are the results of decisions. Structure involves the process of actually building the model to arrive at a solution. Data deals with the information related to the model. The elements structure and data may involve the use of numbers.

To illustrate consider a company facing a remodeling project. The problem facing the company is to complete the project in as little time possible utilizing a fixed budget. The decision of the model would be amount of money needed to complete the project. This acts as the decision because it determines the success of the model. The outcome in this model is the amount of time taken to complete the project. Structure would encompass the planning of the remodeling. For example what tasks should be completed on each day, how much each task will cost and so forth. Lastly data will encompass research into the remodeling. Research may include answering questions such as: Has this type of project been done before? If so, how much time did it take? Can it be completed in less time? How much would construction and materials costs? What are the labor fees for getting the project done? As a result of this questioning data will result in calculations as well as observations.

Summary of Section 2.3.2

Section 2.3.2 deals with two influence charts of one individual tax income statement. The first chart diagrams the tax income statement in a present day view. The diagram is not a model because it cannot be used to determine outcomes long-term. For example the variable Sales is fixed. Because this variable is fixed it cannot be manipulated to work for future numbers. Cost of Goods is also a fixed variable that similar to Sales must be manipulated to have any use beyond the present numbers. Therefore the problem arises and a need for another influence chart emerges. The problem is to create a chart that would allow predictions for later dates. This model is presented in Figure 2.5. Figure 2.5 contains that changes needed to the previous influence chart. These changes are primarily making Sales Revenue and Cost of Goods regular variables (not fixed variables). As a result each variable is broken down into the fixed variables that influence them. Price influences Sales Revenue and is a fixed variable. Units Cost (a fixed variable) influences Cost of Goods. Lastly the variable Quantity Sold is added to the chart with the variables Initial Sales and Sales Growth influencing it.

Summary of Section 2.3.1

Section 2.3.1 reviews a basic example of constructing an influence chart. The problem for the chart needed (the question it must answer) is to find what the price of a product needs to be in order to gain the maximum profit possible. The first step in the influence chart involves determining the main factor that will indicate the effectiveness of the model. In this chart Profit is the outcome and is marked by a hexagon. Next the Profit outcome is broken down into the two variables that create it. These two variables are Total Revenue and Total Cost. Both variables are identified with a circle. The two variables are then examined to see if they may be broken down even further. In this case Total Cost is broken down into Variable Cost and Fixed Cost. Fixed Costs is identified as a fixed variable denoted by the triangle. Due to the fact that a variable does not influence its value fixed cost never changes. Variable cost is broken down further into quantity Sold and Unit cost. Unit cost is also a fixed variable since the cost of a unit is set and not subject to change with any influencing factors. Unit cost is also represented by the triangle.

Price is a variable of total revenue and is ultimately the decision that needs to be made within the entire chart. Price is then placed inside the square to indicate it as a decision. Lastly elasticity and price are fixed variables of quantity sold. These two factors in combination determine quantity sold.

Influence Chart for Invivo Diagnostics

 

The pharmaceutical company Invivo Diagnostics faces the loss of the product patent for its #1 selling drug. This drug has been responsible for bringing in between $100 and $200 million of the company's revenue. After brainstorming and working through the six-stage problem solving process the team has decided on the problem in which to concentrate on. The problem is to find a drug that will compensate for the loss of sales after its #1 selling product has lost its patent.

Starting with the outcome of the model, the sales revenue from the new product sales and the existing #1 product  sales will determine the effectiveness of the model. In other words the sales revenue will determine if the model answers the problem. In order for this to occur the new product sales must compensate for the loss in revenue. The influence chart for Invivo Diagnostics reveals that the new product sales is the decision. As stated above, the new product sales serve as the means of evaluating whether or not the model achieved its intended goal. The new product sales are determined by the price of the product, the number of units produced and the cost of each unit. The existing product sales (denoted by the label  #1 Product) are determined by the market effects of the drug losing its patent. This is a random variable. The variable is random because it is unknown how the market will respond after the patent has expired. Sales for this drug may go up or down.

Defining a Mess

Usually when referring to a mess there is no description that can explain this condition. The general feeling one gets when hearing the word mess is disorder. Before any problem solving process begins there is a mess that has prompted this need. Why is the situation called a mess? A mess results from several reasons such as time restraints, failures, lack of communication, lack of facts or information, etc. The elements creating the mess are not necessarily always a result of negative causes. Nevertheless a mess is still a mess and must be treated as such. It is by identifying a problem that control over the mess is obtained.

The problem resulting from the mess can either be well structured or ill structured. A well structured problem involves a solution that is definite. No other solution will yield the desired result. An ill structured problem on the other hand can have several solutions. Of these solutions there may be more than one effective approach. An example of a well structured problem is an algebraic expression in which only one answer will make the formula work. An ill structured problem example is finding the best fundraising option for an organization.

Divergent and convergent thinking are what generate the problem. Divergent thinking encourages an imaginative process in which any and everything may result in the correct approach and right answer. Therefore this process involves more innovative and outside of the box thinking. Convergent thinking on the other hand calls for more situation specific thought and analysis. As an example of convergent and divergent thinking consider the problem of determining the best way to promote a store's upcoming sale in the most cost effective way. Divergent thinking would come up with every way possible way of advertising. Convergent thinking would narrow this list down by asking questions with regard to resources and budget.

Influence Chart

An influence chart is composed with the following symbols:

Outcome- the outcome represents the determining factor or effectiveness of the model. It is by observing the outcome that the model is rated as a success or the need for reconstruction. It is represented by a hexagon.

Variable- Variables are individual elements that combine to create an outcome or another variable in an influence chart. Variables are represented by a circle.

Fixed Input Parameter- Variables that are non-changeable are identified as a fixed input parameter. They are represented by a triangle.

Random Input Variable- These variables cannot be calculated or guessed and have uncertain values. They are represented by double circles.

Decision- The decision is the variable that will provide the solution to the problem. It is represented by a square.

An influence chart is guided by principles depicting the use of each symbol. Approaching an influence chart begins with finding the outcome which is the factor that will indicate the effectiveness of the model. For example if a company will monitor sales to rate the effectiveness of a model then sales is the outcome. The next principle involves breaking down the outcome into variables. After each variable is determined this set of variables should also be broken down. Inputs are marked through this process as well as decisions as they are discovered. Inputs are wither fixed or random. To illustrate the difference consider a company trying sell a product to the highest offer. The offer is a random variable because it is not known.  No variables are repeated throughout constructing the chart. Lastly the symbols used must be applied consistently and uniformly. This means that each factor (outcome, variables, fixed variables, etc.) in the chart should have a specific symbol.

Six-Stage Problem Solving Process

The six stage problem solving process is a tool used in modeling. The aim of this process is to come up with a solution to a problem which usually results in a model of some kind. Divergent and convergent thinking are utilized in the six-stage process. Divergent thinking focuses on exploring possibilities and an imaginative approach. Convergent thinking however is directed more toward specific resolutions. Each stage is observed from a divergent and convergent lens.

The six stage process is executed with the following steps.:

1. Exploring the Mess
The mess is the situation that prompted the action. The situation is called a mess because it is in raw form and no specific problem to address has been identified at this point.

2. Searching for Information
At this stage facts are gathered. The facts obtained can range from numerous sources including numerical data to interviews or case studies.

3. Identifying a Problem
During this step a list of problems are formulated and the best one fit for the scenario is chosen to continue in the the problem solving process.

4. Searching for Solutions
Several solutions to the problem are considered. This process involves generating possible modes of action and critiquing them.

5. Evaluating Solutions
Here the best possible answer or solution to the problem is decided upon. Therefore all solutions generated in the previous stage must be eliminated to one.

6. Implementing a Solution
At the last stage of the process, the model is now ready for execution. The results of the solution are examined and this process can last over time.