Model formulation ensures that we focus on the following model features: decisions, outcomes, structure, and data. As an example, one must decide how to go about studying for an online college class. We make decisions based on many factors -- work, family, housework, sleep, other classes, and even apathy. Do we schedule how much time we study for each class throughout the week? Complete the work for each class sequentially? Allot a certain amount of time each night for each class? Complete the work for the most difficult class first or last? These are some of the decisions we must make when scheduling our class work.
The outcomes of our decisions are the consequences of our decisions. For example, we decide to complete our classwork during the weekday evenings so that our weekends are free. This might give us time to spend with our families during the weekend, yet leave us unavailable to help our children with their own homework. We might decide to just work on our work when we can, which may lead to procrastination or completing a long assignment on the due date, possibly rushing the quality.
Structure refers to the logic & mathematics that link the elements of our model together. For example, the more homework your child has during the week, the less time you have available to spend on your own homework.
Finally, the data refers to the actual real observations. For example, we may find that week after week, if we don't make a schedule to complete our homework we spend our entire Sunday doing schoolwork. We may find that if we work on our schoolwork for 90 minutes every night that by Friday evening we are done for the week.
Decisions lead to outcomes based on the structure of our model. Data is input into the structure (mathematical formulas / logic) and hopefully lead to the results we're looking for.
Sunday, October 17, 2010
Summarize section 2.3.2 including the influence chart
In section 2.3.2 we take the previous example and expand upon a couple of the end variables -- Quantity Sold & Total Revenue. In our expanded influence chart, we include the decision of how much we would price a unit. As we lower the price we will sell more units, which will affect our Total Revenue. If the lowered cost is less than the increased sales then we will see greater Total Revenue. If, on the other hand, we lower the cost and sales don't makeup for the lower sales, then we'll reduce our Total Revenue. As this issue shows, price will affect both Quantity Sold and Total Revenue.
We also include Elasticity. Elasticity is the third factor noticed above. We need to reduce the price per unit enough to maximize profit, which is the elasticity.
We also include Elasticity. Elasticity is the third factor noticed above. We need to reduce the price per unit enough to maximize profit, which is the elasticity.
Summarize section 2.3.1 including the influence chart
In Section 2.3.1 we look at a simple example of how to determine profitability. In our example, our objective is profit. Profit is directly affected by Total Revenue minus Total Cost. Furthermore, in our example, cost is directly affected by a fixed cost (overhead), and also a variable cost. The variable cost is affected by the quantity sold as well as the per unit cost.
Explain the steps to derive a problem from mess, talk about well/ill and divergent/convergent structured problems. Give your own examples.
The steps in deriving a problem from a mess were already explained previously, in my post on “the six-stage problem solving process. Within this post, I will readdress a couple of important points, and try to add some of my own examples to this process.
First off is the different between divergent and convergent thinking. I’ve already addressed this as well – divergent thinking is more akin to brainstorming, where convergent thinking is more logical, focused on quantification. An example might be, when considering retirement from the military there are many, many issues that muddy the water. Do you have enough money saved up to retire? Will you need a new job? How much money will you have to make in order to continue living in a similar lifestyle? Have you ensured that you will receive all of your benefits? Etc. This would be considered divergent thinking. On the other hand, in focusing on income, you might state that you have $200,000 in savings, and will receive $2500 per month in retirement pay. How long will your money last? What jobs can you get that will add to your retirement pay such that you can live in a reasonable manner?
In regards to well-structured, vs. ill-structured problems, well-structured problems have clear objectives, has obvious assumptions, readily available data, and the logic behind the problem is easy to understand. Ill-structured problems, on the other hand, do not have clear objectives, assumptions, data, and structure.
Explain the Principles/Steps/Symbols in Building Influence Charts
The pinciples utilized in building influence charts include:
1) Start with the outcome measure. In opposition to traditional thinking, when we build an influence chart we start with the end result and work backwards. This is due to the fact that we know what we will achieve. The easiest way to understand how we achieve this is to break down the components one step at a time, starting with the end result (outcome measure).
2) Decompose the outcome measure into a small set of variables that determine it directly. I've already addressed this above. The importance in these variables only being those which affect the outcome measure directly is that we are taking this one step at a time. Variables that indirectly affect the outcome, will most likely directly affect one of the variables as we continue to work backwards through the influence chart.
3) Take each variable in turn and repeat the process of decomposition. Here we basically go back to step 1, however we're doing the decomposition against the variables that directly affect the outcome. We've already decomposed the outcome to those variables; there's no reason to do so again.
4) Identify input data and decisions as they arise. As we decompose our influence charts we will find, along the way, data that is actually an input and can no longer be decomposed. We may also find certain times in which a decision will need to be made. These are graphically depicted with symbols that annotate what they are.
5) Make sure that each variable appears only once. If a variable actually affects more than one other variable, it shouldn't be listed more than once. Instead it should show an arrow pointing to each item that it affects.
6) Highlight special types of elements with consistent symbols. All elements within the influence chart are depicted with symbols. These symbols must be consistent across the influence chart in order for the chart to be understandable.
To support the above principles & steps within building an influence chart you must consistently label the types of data so that when a certain type of symbol is seen, you will know that it's either an input, variable, decision, or objective. The following symbols are used in the book, and seem a valid way forward.
The pinciples utilized in building influence charts include:
1) Start with the outcome measure. In opposition to traditional thinking, when we build an influence chart we start with the end result and work backwards. This is due to the fact that we know what we will achieve. The easiest way to understand how we achieve this is to break down the components one step at a time, starting with the end result (outcome measure).
2) Decompose the outcome measure into a small set of variables that determine it directly. I've already addressed this above. The importance in these variables only being those which affect the outcome measure directly is that we are taking this one step at a time. Variables that indirectly affect the outcome, will most likely directly affect one of the variables as we continue to work backwards through the influence chart.
3) Take each variable in turn and repeat the process of decomposition. Here we basically go back to step 1, however we're doing the decomposition against the variables that directly affect the outcome. We've already decomposed the outcome to those variables; there's no reason to do so again.
4) Identify input data and decisions as they arise. As we decompose our influence charts we will find, along the way, data that is actually an input and can no longer be decomposed. We may also find certain times in which a decision will need to be made. These are graphically depicted with symbols that annotate what they are.
5) Make sure that each variable appears only once. If a variable actually affects more than one other variable, it shouldn't be listed more than once. Instead it should show an arrow pointing to each item that it affects.
6) Highlight special types of elements with consistent symbols. All elements within the influence chart are depicted with symbols. These symbols must be consistent across the influence chart in order for the chart to be understandable.
To support the above principles & steps within building an influence chart you must consistently label the types of data so that when a certain type of symbol is seen, you will know that it's either an input, variable, decision, or objective. The following symbols are used in the book, and seem a valid way forward.
As you can see below, our outcome measure is the objective, and is represented by a hexagon. This is the point at which deconstruction begins.
The objective should be deconstructed into variables, represented by ovals.
These variables will either be further deconstructed into other variables, random/fixed inputs, or a combination of both.
Lastly, there may be a point in which a decision may dictate which inputs to used based off this decision. Decisions are represented by a rectangle.
1) Start with the outcome measure. In opposition to traditional thinking, when we build an influence chart we start with the end result and work backwards. This is due to the fact that we know what we will achieve. The easiest way to understand how we achieve this is to break down the components one step at a time, starting with the end result (outcome measure).
2) Decompose the outcome measure into a small set of variables that determine it directly. I've already addressed this above. The importance in these variables only being those which affect the outcome measure directly is that we are taking this one step at a time. Variables that indirectly affect the outcome, will most likely directly affect one of the variables as we continue to work backwards through the influence chart.
3) Take each variable in turn and repeat the process of decomposition. Here we basically go back to step 1, however we're doing the decomposition against the variables that directly affect the outcome. We've already decomposed the outcome to those variables; there's no reason to do so again.
4) Identify input data and decisions as they arise. As we decompose our influence charts we will find, along the way, data that is actually an input and can no longer be decomposed. We may also find certain times in which a decision will need to be made. These are graphically depicted with symbols that annotate what they are.
5) Make sure that each variable appears only once. If a variable actually affects more than one other variable, it shouldn't be listed more than once. Instead it should show an arrow pointing to each item that it affects.
6) Highlight special types of elements with consistent symbols. All elements within the influence chart are depicted with symbols. These symbols must be consistent across the influence chart in order for the chart to be understandable.
To support the above principles & steps within building an influence chart you must consistently label the types of data so that when a certain type of symbol is seen, you will know that it's either an input, variable, decision, or objective. The following symbols are used in the book, and seem a valid way forward.
The pinciples utilized in building influence charts include:
1) Start with the outcome measure. In opposition to traditional thinking, when we build an influence chart we start with the end result and work backwards. This is due to the fact that we know what we will achieve. The easiest way to understand how we achieve this is to break down the components one step at a time, starting with the end result (outcome measure).
2) Decompose the outcome measure into a small set of variables that determine it directly. I've already addressed this above. The importance in these variables only being those which affect the outcome measure directly is that we are taking this one step at a time. Variables that indirectly affect the outcome, will most likely directly affect one of the variables as we continue to work backwards through the influence chart.
3) Take each variable in turn and repeat the process of decomposition. Here we basically go back to step 1, however we're doing the decomposition against the variables that directly affect the outcome. We've already decomposed the outcome to those variables; there's no reason to do so again.
4) Identify input data and decisions as they arise. As we decompose our influence charts we will find, along the way, data that is actually an input and can no longer be decomposed. We may also find certain times in which a decision will need to be made. These are graphically depicted with symbols that annotate what they are.
5) Make sure that each variable appears only once. If a variable actually affects more than one other variable, it shouldn't be listed more than once. Instead it should show an arrow pointing to each item that it affects.
6) Highlight special types of elements with consistent symbols. All elements within the influence chart are depicted with symbols. These symbols must be consistent across the influence chart in order for the chart to be understandable.
To support the above principles & steps within building an influence chart you must consistently label the types of data so that when a certain type of symbol is seen, you will know that it's either an input, variable, decision, or objective. The following symbols are used in the book, and seem a valid way forward.
As you can see below, our outcome measure is the objective, and is represented by a hexagon. This is the point at which deconstruction begins.
The objective should be deconstructed into variables, represented by ovals.
These variables will either be further deconstructed into other variables, random/fixed inputs, or a combination of both.
Lastly, there may be a point in which a decision may dictate which inputs to used based off this decision. Decisions are represented by a rectangle.
The Six-Stage Problem Solving Process
Within the context of System Modeling, the six-stage problem solving process is used to explore a mess, determine a problem based on our customer's requirements, and then to solve that problem. The problem solving process may, or may not, actually use a formal model for every problem. The stages include both "divergent" and "convergent" styles of thought. In divergent thinking stresses the generation of ideas, where convergent stresses evaluation of ideas to determine the best one.
Stage 1: Exploring the Mess
When we receive a problem to be solved, it will more than likely be "ill-structured", in which the objective, assumptions, data and structure of the problem are all unclear (Powel, S., The Art of Modeling with Spreadsheets, pg 20). In order to explore this ill-structured problems requires primarily divergent thinking, but some convergent thinking as well.
divergent: searching through the mess for some opportunity or problem to solve
convergent: in a broad sense, deciding on what aspect of the mess to pursue
Stage 2: Searching for Information
Again, stage 2 is primarily a divergent process. Within this stage we now start searching for any information regarding the problem we chose in stage 1. We examine the problem from different angles, and in the end we keep that data which is most important.
divergent: gather data, observations from different viewpoints
convergent: separate the most important data
Stage 3: Identifying a Problem
Although we've made references to determining a problem in the first two steps, these steps are really sorting through the mess to determine a problem, but they don't yet address the specifics of that problem (i.e. the problem statement). Stage 3 sees considerably more convergent thinking than the previous two stages. We take the data we've mined in stage 2 and use this to determine example problem statements before eventually chosing one.
divergent: consider several different problem statements
convergent: decide on the one problem statement that we will focus on
Stage 4: Searching for Solutions
Within this stage of the problem solving process, we start to search for solutions to our problem statement. We must use both divergent & convergent thinking along the way. Divergent thought is important in this stage, as we need to consider not just obvious solutions, but possibly solutions we may not have considered before. As well, convergent thought is important as we narrow down the possible solutions to the one or few that are most likely.
divergent: brainstorm, consult experts, possibly form sub-committee to determine many different solutions
convergent: determine the most promising solution(s)
Stage 5: Evaluating the Solutions
Within stage 5 we now must evaluate our possible solutions. If we'd left stage 4 with two or three promising solutions, it's during this stage where we will reduce this to the best solution. This stage uses primarily convergent thinking as we determine the evaluation criteria that is important to our proposed solutions. However, some divergent thinking may be important as well, as we consider relevant data that just might not be obvious.
divergent: determine criteria to be utilized for evaluation of solutions, even if not obvious
convergent: use the most important criteria
Stage 6: Implementing a Solution
Within the last stage of the problem solving process we focus on the actual implementation of our selected solution. This stage primarily utilizes convergent thinking as we include change management. Divergent thinking might include determining what barriers actually exist to implementing our solution.
divergent: sources of resistance/assistance to implementation
convergent: implement the solution
Powell, S & Baker, K, The Art of Modeling with Spreadsheets, pgs 20 - 26
Stage 1: Exploring the Mess
When we receive a problem to be solved, it will more than likely be "ill-structured", in which the objective, assumptions, data and structure of the problem are all unclear (Powel, S., The Art of Modeling with Spreadsheets, pg 20). In order to explore this ill-structured problems requires primarily divergent thinking, but some convergent thinking as well.
divergent: searching through the mess for some opportunity or problem to solve
convergent: in a broad sense, deciding on what aspect of the mess to pursue
Stage 2: Searching for Information
Again, stage 2 is primarily a divergent process. Within this stage we now start searching for any information regarding the problem we chose in stage 1. We examine the problem from different angles, and in the end we keep that data which is most important.
divergent: gather data, observations from different viewpoints
convergent: separate the most important data
Stage 3: Identifying a Problem
Although we've made references to determining a problem in the first two steps, these steps are really sorting through the mess to determine a problem, but they don't yet address the specifics of that problem (i.e. the problem statement). Stage 3 sees considerably more convergent thinking than the previous two stages. We take the data we've mined in stage 2 and use this to determine example problem statements before eventually chosing one.
divergent: consider several different problem statements
convergent: decide on the one problem statement that we will focus on
Stage 4: Searching for Solutions
Within this stage of the problem solving process, we start to search for solutions to our problem statement. We must use both divergent & convergent thinking along the way. Divergent thought is important in this stage, as we need to consider not just obvious solutions, but possibly solutions we may not have considered before. As well, convergent thought is important as we narrow down the possible solutions to the one or few that are most likely.
divergent: brainstorm, consult experts, possibly form sub-committee to determine many different solutions
convergent: determine the most promising solution(s)
Stage 5: Evaluating the Solutions
Within stage 5 we now must evaluate our possible solutions. If we'd left stage 4 with two or three promising solutions, it's during this stage where we will reduce this to the best solution. This stage uses primarily convergent thinking as we determine the evaluation criteria that is important to our proposed solutions. However, some divergent thinking may be important as well, as we consider relevant data that just might not be obvious.
divergent: determine criteria to be utilized for evaluation of solutions, even if not obvious
convergent: use the most important criteria
Stage 6: Implementing a Solution
Within the last stage of the problem solving process we focus on the actual implementation of our selected solution. This stage primarily utilizes convergent thinking as we include change management. Divergent thinking might include determining what barriers actually exist to implementing our solution.
divergent: sources of resistance/assistance to implementation
convergent: implement the solution
Powell, S & Baker, K, The Art of Modeling with Spreadsheets, pgs 20 - 26
Saturday, October 16, 2010
Week 2 assignment
For our assignment this week we've been asked to discuss the 7 topics below. I will create separate blogs for each, and hopefully explain them sucinctly. This will probabaly end up more of the mess we're trying to wade through within the class in order to separate the problems, however I'll do my best!
1. Explain the six-stage problem solving process.
2. Explain the principles/steps/symbols in building influence charts
3. Explain the steps to derive a problem from mess, talk about well/ill and
divergent/comvergent structured problems. Give your own examples.
4. Create an Influence Chart for the Example Invivo Diagnostics from page 21-26.
(You may use Powerpoint or MS Word or othr Drawing tools, or simple draw it on
paper, take a picture with your camera or cell-phone camera, and attach to the blog.)
5. Summarize section 2.3.1 including the influence chart.
6. Summarize section 2.3.2 including the influence chart.
7. Explain the model formulation process: Decision, Outcome, Structure and Data.
Give an example showing the four model formulation steps.
1. Explain the six-stage problem solving process.
2. Explain the principles/steps/symbols in building influence charts
3. Explain the steps to derive a problem from mess, talk about well/ill and
divergent/comvergent structured problems. Give your own examples.
4. Create an Influence Chart for the Example Invivo Diagnostics from page 21-26.
(You may use Powerpoint or MS Word or othr Drawing tools, or simple draw it on
paper, take a picture with your camera or cell-phone camera, and attach to the blog.)
5. Summarize section 2.3.1 including the influence chart.
6. Summarize section 2.3.2 including the influence chart.
7. Explain the model formulation process: Decision, Outcome, Structure and Data.
Give an example showing the four model formulation steps.
System Modeling Theory -- Finding the Problem in the Mess
For my System Modeling Theory class, we've been asked to create a blog to cover some discussion points within our class. This is the first time I've ever even considered a blog, I'm not particularly artsy by nature, so my apologies up front if the design isn't exactly exciting. :)
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