Model formulation process

Model formulation is the process of abstracting real world problems and moving those abstracted problems into the model world.  When abstracting real world problems, we leave out all of the details and complexities of the problems because they are simply not important at the initial stages in the process of modeling.  With models, we can make decisions and assumptions without causing any financial harm but in the real world you don’t get to play around with different ideas without costs. The model allows us be creative and to make changes and think outside the box.   In model formulation, you capture the essence of a situation and simplify it.  In the process of module formulation, we are confronted with four features of a model that are critical to the success of that specific outcome we’re seeking.  We must decide the course of action we might take and then measure the consequences of the outcome as a result of the decision we made.  Structure is another feature we are confronted with in the model formulation process.  Per the text, “Structure refers to the logic and the mathematics that link the elements of our model together.”  An example might be the equation Profit =Revenue –Cost (P=R-C).  Finally, in module formulation we are confronted with data.  Data refers to real world raw data which must be observed.  An example of the four model formulation steps are:

Section 2.3.2 summary including the influence chart.

Transferring an income statement into an influence chart can be pretty straight forward if numbers are involved.  The numbers would build upon the influence chart without much thought or creativity from the modeler.  In other words, the variables for the influence chart would already be determined and the modeler would be left with just plugging in the numbers.  Figure 2.4 on page 30 of the text book shows an influence chart in which the relationships are perfect for an influence chart that shows the historical performance of a company but if we needed to make projections for the future then this chart reveals no critical information without numbers.  In its current design, this influence chart could not provide a good model.  In my opinion, this influence chart makes a great overview of a future model and should help the novice and expert come up with all of the necessary questions to build the model needed to determine the outcome one seeks. 

Section 2.3.1 summary including the influence chart

In section 2.3.1 of the text, the author goes into the preliminary steps of building a model.  Prior to building a model, the author suggests that to be successful one much first recognize a problem then end with implementation of a solution.  This initial phase can be tough for the novice modeler because translating a potential vague understanding of a problem into an actual model can be very challenging.  In order to get a visual understanding of the model to be built, an “Influence Chart” should first be drawn out.  The influence chart will be your guide to questions that should be asked when building the model.  We see an example of how the experienced modeler puts together an influence chart.  The modeler takes us step by in his decision making and reasoning for selecting the variables chosen.  We see that the modeler starts with the Objective which is profit and branches out from there by decomposing the profit into total revenue and cost.  The influence chart that I’ve put together starts with the problem of preserving the $100 - $200 Million dollars revenue the company enjoyed from a patented product that the patent would soon expire.  I then ask if the company should consider pushing more of the generic brands and when considering the generics, I pose the concern of spending on research and development for the generics.  In one of the other variables pose the thought of pushing (probably not the best word to use) the drugs in development.  I also noted Regulatory Approval to this thought because there will be questions such as how long, will they, if they don’t, etc.  One other variable is the thought of extending the current patent of this $100 - $200M drug.  There will of course be questions to discus in this area.  What I tried to show in this influence is the overall view of the model to be built and initial questions or concerns which should spark more which in turn builds on the model.

Influence Chart for the Example Invivo Diagnostics

Steps to derive a problem from mess.

Deriving what’s considered a problem to what’s considered a mess is an important distinction to make in the problem solving process of modeling.  Exactly what is a problem and just what is considered a mess?  Well according to the text, a problem is a well-defined situation that is capable of resolution; whereas a mess is a morass of unsettling symptoms, causes, data, pressures, shortfalls, and opportunities.  Because problems don’t come to us fully defined with obvious answers, identifying a problem in a mess will take much creativity to come up with not just any solution but the best solution.  The approach in problem-solving will depend on the problem that’s before you.  During the problem solving process, one should try to distinguish well-structured from ill-structured problems.  In well-structured problems, the objectives of the analysis are clear, the assumptions that must be made are obvious, all the necessary data are readily available and the logical structure behind the analysis is well understood.  Ill-structured problems are just the opposite.  The objective, assumptions, data, and structure of the problem are all unclear.  At any stage in the problem solving process, there are two styles of thinking:  divergent and convergent.  Divergent thinking stresses generating ideas which involves thinking in different directions or searching for a variety of answers to questions that may have many right answers.  Convergent thinking is directed toward achieving a goal, a single solution, answer, or result.  It involves trying to find the one best answer.  In convergent thinking, the emphasis shifts from idea generation to evaluation.

The principles/steps/symbols in building influence charts

In the process of building a model, novice modelers often make the mistake of jumping into designing models with detailed information.   We also have a problem translating an initial vague understanding of a problem into a concrete model.  This is where the influence chart comes into play.  An influence chart is a simple diagram that shows what outcome variables the model will generate and how these outputs are calculated from the necessary inputs.  Influence charts encourage the modeler to focus on major choices, such as what to include and what to exclude from the model, rather than on details that may be unimportant.  The influence chart is not a technical flowchart that must conform perfectly to a rigid set of rules.   Some steps to consider when putting together the influence chart are:

1. Start with the outcome measure.
2. Decompose the outcome measure into a small set of independent variables that determine it directly. 
3. Take each variable in turn and repeat this process of decomposition. 
4. Identify input data and decisions as they arise
5. Make sure that each variable appears only once in the diagram.
6. Highlight special types of elements with consistent symbols. 

When highlighting these special elements, use consistent symbols such as squares to maybe show decisions made or octagons to show your objectives, the triangle can be used to show fixed input parameters and you might use the circle to show a variable.  The idea here is to be consistent with your symbols. 

The six-stage problem solving process.

From the most well structured to the most ill structured, the six-stage problem solving process can be used to solve almost any problem.  The six-stage problem processes are Stage 1: Exploring the Mess, Stage 2: Searching for Information, Stage 3: Indentifying a Problem, Stage 4: Searching for Solutions, Stage 5: Evaluating Solutions and Stage 6: Implementing a Solution.  When using the six-stage problem solving process, one must wear the correct “thinking cap” when beginning the process and also be ready to change caps as the process progresses into the different stages.  There are two different styles of thinking: divergent and convergent.  Divergent thinking stresses generating ideas by thinking in different directions or searching for a variety of answers to questions that may have right answers.  Convergent thinking is directed toward achieving a goal, a single solution, answer, or result in order to find the one best answer.    Early in the process one should wear the divergent “thinking cap” while convergent thinking comes to dominate later on.  At each stage, a modeler should ask him/herself certain questions.  Some of the questions that a modeler should consider at each stage are:

Stage 1:  Exploring the Mess

What problems (or opportunities) do we face?  Where is there a gap between the current situation and the desired one?  What are the stated and unstated goals? 

Stage 2:  Searching for Information

What are the symptoms and causes?  What measures of effectiveness seem appropriate?  What actions are available?

Stage 3: Indentifying a Problem

Which is the most important problem in this equation?  Is this problem like others you have dealt with?  What are the consequences of a broad versus narrow problem statement?

Stage 4:  Searching for Solutions,

What decisions are open to us?  What solutions have been tried in similar situations?  How are the various candidate solutions linked to outcomes of interest?

Stage 5:  Evaluating Solutions and Stage

How does this solution impact each of the criteria?  What factors within our control could improve the outcomes?  What factors outside our control could alter the outcomes?

Stage 6:  Implementing a Solution

What are the barriers to successful implementation?  Where will there be support and motivation, or resistance and conflict?  Are the resources available for successful implementation?

The problem solving process does not end here.  The solution must now be executed or carried forward by a committee.