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How Optsee® Works
Optsee® uses a logical step-by-step process to build decision models that objectively rank your choices based on your values and strategies. Optsee® gives you a clear picture of your alternatives using Monte-Carlo prioritizations, optimizations, and multi-dimensional charts. The Optsee Prioritizer™ provides you with highly insightful statistical rankings of all your choices by evaluating them in up to 100,000 different decision models. The Optsee Optimizer™ can easily optimize your portfolios against up to six independent constraints so you can quickly find optimized solutions from millions or billions of possibilities. Optsee® uses sophisticated algorithms to create your decision models and perform prioritizations and optimizations, but the user interface has been designed so that you can focus on your decision, not the math. Optsee® does it for you.
Below is a fast overview using a simple non-business decision to illustrate how Optsee® works:
• Attractiveness Means Satisfaction or Value
• Attractiveness Curves
• Building a Simple Decision Model and Portfolio
• How "Overall Attractiveness" is Calculated
• Visualize Your Data Using Bubble Charts
• Ask "What If?" Using Sensitivity Charts
• Get a Statistical Analyses With the Optsee Prioritizer™
• Running a Fixed-Order Prioritization
• Running a Random-Order Prioritization
Attractiveness means satisfaction or value
Optsee works by prioritizing your choices based on the overall attractiveness value (or utility) of each choice based on your inputs. In economics, utility is a measure of the satisfaction or value gained from the consumption of a "package" of goods or services. The concept of attractiveness is a measure of happiness or satisfaction. Optsee® prioritizes your choices according to the overall attractiveness of each choice, based on its attribute values, and the relative importance that you assign to each individual attribute.
For example, when you purchase a car, you compare each car's "package" of individual attributes (the combination of price, appearance, reliability, etc.) with those of other cars. You make your selection based on which car has the highest overall attractiveness for you. The relative importance of individual attributes is usually different for different consumers. For some consumers, horsepower is more important than gas mileage; for others, the opposite is true. Decision-makers select choices that have the "package" of attributes that gives them the highest overall attractiveness or value.
Optsee models your attractiveness by generating attractiveness curves for each attribute in the decision model. A attractiveness curve assigns an attribute's worst outcome to have 0 units of attractiveness (no satisfaction) and the best outcome to have 100 units of attractiveness (completely satisfied). Enter the Best and Worst outcomes for your decision model attributes and Optsee can generate the curve automatically. This curve can be adjusted with a mouse click to reflect increasing and diminishing attractiveness returns; see Adjusting the Attractiveness Curve for more information.
Example: Figure 1 illustrates a attractiveness curve showing Attractiveness versus Potential Revenue for new development projects. In this case, projects that have potential revenues of $10 million score 0 attractiveness units and projects that have potential revenues of $50 million score 100 attractiveness units. Since the attractiveness curve is a straight line (a neutral attractiveness curve), projects that have a revenue potential of $30 million score 50 attractiveness units (the mid-point between $10 and $50 million).
Figure 1: Straight-line (Neutral) Attractiveness Curve
If each choice had only one attractiveness curve associated with it, decision-making would be easy - you'd simply pick the choice with the highest attractiveness value. But choices usually have more than one attractiveness curve. Furthermore, decisions involving choices with multiple attribute attractiveness values become even more complex because the relative importance of one attribute to another can change, based on strategy and circumstance.
For purposes of illustration, we're going to create a simple decision model for choosing a restaurant. Each restaurant has a common set of attributes to use for comparison, such as location, cost, atmosphere, quality of food, etc. The choice we make depends on which restaurant has the most attractiveness (overall attractiveness) based on our current needs. If we are choosing a restaurant for a nice long dinner, then atmosphere and quality of food would be more important than if we wanted a quick lunch before an important meeting - where travel time may be given higher attractiveness weight. The attributes for the restaurants would not change, but the importance of the attributes change relative to meeting our attractiveness requirements.
Similarly, in business decisions, the relative importance of different attributes will be different for different decision-makers, business strategies, and circumstances. Budget planners prioritize attributes differently based on the strategic goals and needs of the company or division. New product designers prioritize attributes differently based on the market segment whose attractiveness appeal they are trying to maximize. Financial portfolio planners prioritize attributes differently based on long or short term investment strategies
You prioritize your attributes in Optsee by assigning them with numerical weights. Attributes with higher weights are more important than attributes with lower weights. Optsee uses your assigned weights with your attractiveness curves to evaluate and rank your choices.
Building a simple decision model and portfolio
Now, let's look at how this all comes together by using a simple restaurant example as discussed above. The desired decision outcome is to select the best restaurant for a nice dinner with an old friend. We'll choose from 5 choices. Of course, you wouldn't use Optsee to make this decision, but this is a useful example to understand how Optsee works, and how it can be applied to your business decisions.
Figure 2 shows an Optsee Decision Model form with four attributes chosen to determine which restaurant to go to for the desired outcome: Atmosphere, Food Quality, Approximate Cost, and Travel Time.
Figure 2: A Decision Model for Restaurants (Click here for a larger view.)
On the Decision Model form, the attributes are automatically ranked in the first column (Best Outcome), based on the assigned weights in the last column (Weight). In this model, the "Atmosphere" attribute has the largest weight and highest rank, whereas the "Travel Time" attribute has the smallest weight and lowest rank. The magnitude of the weights indicates that Atmosphere is twice as important as Cost (1,000÷500=2), and more than three times as important as Travel Time (1,000÷300=3.33). Thus, the relative importance between the different attributes can be calculated by dividing the larger attribute weight by the smaller attribute weight.
The atmosphere and food quality attributes are given a subjective outcome value in the range of 1 to 10, where 10 represents the best atmosphere or food quality and 1 represents the worst. Approximate cost and travel time attributes are both quantified in real units (dollars and minutes, respectively). The Attractiveness Curves for all of these attributes are Neutral indicating a straight-line linear relationship between the attribute value and attractiveness. (See Adjusting the Attractiveness Curve for more information on "Diminishing" and "Increasing" Attractiveness curves.)
Let's assume that we've narrowed our selection to five restaurants from which to choose. Here is how those restaurants are displayed in an Optsee Portfolio form table (Figure 3):
Figure 3: A Portfolio of 5 Restaurant Choices (Click here for a larger view.)
Each restaurant was automatically ranked according to its Overall Attractiveness as it was added to the portfolio. The italicized font indicates that the portfolio table has been sorted according to the overall attractiveness, thus the restaurants are listed in order of diminishing attractiveness. In this decision model and portfolio, Japanese Lotus is the most attractive restaurant and the Blue Crab Grill is the least attractive.
How "overall attractiveness" is calculated
The following is a general explanation of how the Overall Attractiveness for each individual choice is calculated:
1) The individual attractiveness for each choice attribute value is calculated according to the Attractiveness Curve function. These are the individual attractiveness values.
2) The individual attractiveness values are adjusted in proportion to their relative weight or importance. These are the individual weighted attractiveness values.
3) The weighted individual attractiveness values are summed together to yield the combined attractiveness or "Overall Attractiveness".
To see a numerical example that explains how the Overall Attractiveness of the Italiana! restaurant was calculated, click here.
Visualize your data using bubble charts
In addition to using the Decision Model and Portfolio forms to analyze your models, you can also use Optsee's Bubble Charts. Bubble charts are a type of X-Y (scatter) chart that are used to plot three sets of data simultaneously. Each data point has X and Y values that correspond to the location of the bubble center, and the size (area or radius) of the bubble represents the third value. In Optsee, the user can use both the bubble pattern and color to distinguish one choice representation from another. For example, the bubble chart in Figure 4 displays the Overall Attractiveness on the Y-axis, Atmosphere on the X-axis, and Cost is represented by the bubble size. In this figure, you can easily see why Japanese Lotus is the most attractive restaurant, being positioned in the middle of the selection relative to both Atmosphere and Cost.
Figure 4: Atmosphere and Cost Bubble Chart (Click here for a larger view.)
Bubble charts can provide important insights into the distribution of your choices within the decision model parameters, which are not readily apparent from just studying the portfolio, particularly when you have several dozen or more choices. Bubble charts are extremely useful for understanding and communicating all aspects of the decision. The Optsee bubble charting tool is fully integrated within the application. It is easy to use and has a variety of features for viewing, comparing, annotating, and exporting your charts.
Ask "what if?" using sensitivity charts
Another useful tool for decision management is sensitivity analysis. Sensitivity analysis allows you to answer many "what if?" questions about your decision model, and to understand quickly which attributes have the most impact on your choices. The Optsee Sensitivity Analysis feature models the impact of a change in an attribute value as well as the impact of changing an attribute's weight in the decision model.
Let's look at testing the sensitivity of the Cost attribute. The goal of an attribute sensitivity test is to model what happens when one attribute changes while all the other attributes stay constant. Figure 5 shows the Sensitivity Analysis Chart for the Cost attribute. This chart illustrates the change in overall attractiveness for each choice as the cost changes. The bubble positions show the current costs in the portfolio. Note how the attractiveness goes up as the cost goes down.
Figure 5: Cost Sensitivity Chart (Click here for a larger view.)
The Cost Sensitivity Chart shows that for the Gardenville Inn (Point A) to be equal in Overall Attractiveness to the Japanese Lotus (83), it would have to lower its cost from $60 to $43.30 (Point B). The chart also shows that Le Bon Chateu, Italiana! and the Blue Crab Grill could never be equal to the Japanese Lotus in Overall Attractiveness even if their costs fell to $30. Thus, these three restaurants are insensitive to cost relative to the Japanese Lotus.
Now let's look at testing the sensitivity of the Cost attribute to changes in weight (Figure 6). This chart illustrates how the Overall Attractiveness of all the choices changes as the Cost attribute weight changes and all the other weights remain constant. The bubbles in this chart are shown at their current weight value in the decision model (500), and the X-axis maximum and minimum weights are equal to the highest (Atmosphere) and lowest (Travel Time) weights in the decision model.
Figure 6: Cost Weight Sensitivity Chart (Click here for a larger view.)
The Cost Weight Sensitivity Chart shows that Japanese Lotus is insensitive to the changes in the cost weight because it remains the most attractive choice regardless of the Cost weight. If the Cost weight were moved up to over 655 (Point A), Italiana! becomes more attractive than the Gardenville Inn. The Blue Crab Grill and Le Bon Chateau are close in attractiveness at the current weight value , but they separate markedly (Point C) as the Cost weight increases, due primarily to the high cost of Le Bon Chateau. If the Cost weight were moved below 395 (Point B), Le Bon Chateau becomes more attractive than the Blue Crab Grill. When you look at a Weight Sensitivity Chart, the choices with values closest to the best and worst outcomes will generally have steeper slopes than choices that have values closer to the middle of the attractiveness curve.
Get a statistical analyses with the Optsee Prioritizer™
Now that we've seen how to use Optsee to study a single decision model where the user sets fixed attribute weights, let's look at one of Optsee's most powerful features: the ability to create thousands of models in a single click, and study the resulting choice rankings based on a statistical analysis of those models. Optsee generates up to 100,000 models using a Monte Carlo simulation, and then displays the results in specialized charts and tables.
The Monte Carlo simulation methodology was named for Monte Carlo, Monaco; a city that is famous for its casinos and games of chance such as roulette wheels, dice, cards, and slot machines. Games of chance exhibit random behavior within the context of the game equipment and rules. For example, a shuffled deck of cards will contain 52 cards, but the card order is random. An Optsee Monte Carlo simulation involves creating thousands of random decision models within a set of defined parameters, testing your portfolio in each model, and then calculating the average rank, standard deviation, and cumulative percentage ranking for each choice in your portfolio.
In the Restaurant Decision Model, the 4 attributes had fixed rank and weight values (Table 1). Weight sensitivity testing allows you to vary a single attribute weight while holding the other attributes constant. A Monte Carlo simulation allows you to vary all of the attribute weights at once in either a fixed sequential or random rank order. A fixed sequential rank order generates random weights that maintain the same rank order as the decision model (for example, in the Restaurant decision model, Atmosphere would always have the highest rank, Food Quality the next highest, Approximate Cost the third highest, and Travel Time the lowest). A random rank order randomly varies both the weights and the rank order. This allows you to explore the entire decision model space.
Table 1: Atmosphere Weight and Rank
Let's look at a creating a Monte Carlo Prioritization test chart. Figure 7 shows the Prioritization Chart form used to set-up a prioritization test.
Figure 7: Prioritization Set-up Form
The Save and Open as radio buttons allow you to select which chart opens after the prioritization. The Attribute Order radio button allows you to generate the random decision models in either fixed sequential order (attributes are always in the same rank order as the parent decision model) or in a random order (attribute rank order is also randomly varied). The Number of Tests drop-down menu allows you to set the number of models that you want to generate in the prioritization (from 1000 to 100,000). The Weight Range drop-down menu allows you to set the range between the highest and lowest weight (from 1000 to 10,000). A setting of 1,000 means that the largest possible weight is 1,000 and the smallest is 1.
Running a fixed-order prioritization
During the prioritization, a portfolio is tested in each of the random decision models, and the choices are ranked sequentially based on the Overall Attractiveness values. After running the prioritization, the Optsee Prioritizer Summary List Form is displayed (Figure 8). This form displays the results in a list form including the average rank, standard deviation, highest rank, lowest rank, and cumulative percentage rank. The cumulative percentage rank is discussed in more detail below.
Figure 8: 5000 Model Fixed Order Summary Statistics (Click here for a larger view.)
Clicking the Statistics button displays the Statistics Chart form (Figure 9)
Figure 9: 5000 Model Prioritization Statistics Chart: Average and Standard Deviation (Click here for a larger view.)
The default view displays the average choice rank as a circle, and the standard deviation as "error bars". The choices are ordered and numbered in absolute rank order from left to right along the X-axis, which corresponds to the legend number.
You can see this chart in a view that displays the maximum and minimum individual values (Figure 10). In this view, the bars represent the highest and lowest individual rank that the choices achieved. Notice that the Japanese Lotus and the Gardenville Inn are clearly the number one and two choices, respectively. The averages, standard deviations, and max-min ranges are very similar.
Figure 10: 5000 Model Prioritization Statistics Chart: Average, Standard Deviation, Maximum and Minimum (Click here for a larger view.)
Next, let's look at the Cumulative Percentage Chart (Figure 11). This chart displays the cumulative percent of the number of decision models that a choice was ranked at a particular rank or higher. For example, Japanese Lotus was ranked first in 70% of the models (Point A), second or higher in 83% (Point B), and third or higher in 100% of the models (Point C). The Gardenville Inn was ranked first in 22% of the models (Point D), and second or higher in 98% of the models (Point E).
Figure 11: 5000 Model Prioritization Cumulative Percentage Line Chart (Click here for a larger view.)
To simplify this data, we can look at a bar chart that shows the normalized area-under-the-curve (AUC) for each of these choices (Figure 11a). This is the data from column 7 of the list form (Figure 8). Note here that the Japanese Lotus and Gardenville Inn have virtually the same ranking, and the remaining three restaurants are significantly less attractive.
Figure 11a: 5000 Model Prioritization Cumulative Percentage Bar Chart (Click here for a larger view.)
The results of this prioritization show that the top two choices, Japanese Lotus and Gardenville Inn, respectively, would both be good choices based on the decision model's attribute order. The Japanese Lotus has a slight edge because it was the top choice in 65% of the models versus the Gardenville Inn which was the top choice in 22% of the models. But, they are about the same statistically. Next, we'll run a random order prioritization to see if a clear top choice emerges.
Running a random-order prioritization
It is also worthwhile to run a prioritization in which the attribute rank order is varied to see how the choices rank without maintaining the original decision model rank order, that is, both the attribute rank order and the attribute weights are varied randomly. Often, in this type of prioritization, the differences in the choices will not be as clear because the different models will equally emphasize the attribute strengths and weaknesses in each choice. Therefore, the differences in average choice ranks becomes smaller, the standard deviations become larger, and the spread between the maximum and minimum increases. Nevertheless, choices that have relatively high overall attractiveness in the individual attributes can emerge from this type of prioritization.
Figure 12 shows the Statistics chart for 5000 models generated using a random rank order for the Restaurants Portfolio.
Figure 12: 5000 Model Random Order Prioritization Statistics Chart: Average and Standard Deviation (Click here for a larger view.)
Compared with the sequential order Statistics Chart (Figure 9), the order of attractiveness using the average choice rank has changed for every restaurant except for the Japanese Lotus. You can also see that the standard deviations and the spreads between the maximum and minimum have become larger for most of the choices. It would appear from this chart that the Japanese Lotus is the best selection.
Expanding the lines to display the maximum and minimum values for each choice, you can see that the random order prioritization showed that all of the choices except the Japanese Lotus had a larger spread between the maximum and minimum values (Figure 13) compared to the fixed order prioritization (Figure 10).
Figure 13: 5000 Model Prioritization Statistics Chart: Average, Standard Deviation, Maximum and Minimum (Click here for a larger view.)
Examining the Cumulative Percentage chart (Figure 14) shows how the cumulative percentage lines have "flattened out" compared with the fixed order prioritization (Figure 11).
Figure 14: 5000 Model Random Order Prioritization Cumulative Percentage Line Chart (Click here for a larger view.)
The Japanese Lotus was ranked first in 70% of the models (Point A), and ranked third or higher in 100% of the models (Point B). No other model was ranked first in more than 25% of the models. The Gardenville Inn and Italiana! were ranked fourth or higher in 100% of the models (Point C). You can also see that the cumulative percentage for the Japanese Lotus is significantly higher than the Italiana! (100 vs 84.6) as shown in the bar chart (Figure14a) and summary list form (Figure 15). This is a much greater difference between the first and second choices than in the fixed order prioritization (100 vs 96.8). Thus, this prioritization confirms the Japanese Lotus as the preferred choice given this set of attributes and attractiveness curves.
Figure 14a: 5000 Model Random Order Prioritization Cumulative Percentage Bar Chart (Click here for a larger view.)
Figure 15: 5000 Model Random Order Summary List Form (Click here for a larger view.)
As was mentioned earlier, you probably wouldn't use Optsee to determine where to go to dinner, however, the purpose of this example is to illustrate how Optsee works so that you can understand how to apply it to complex and important business decisions.
The Optsee Optimizer™ would not be used for a small model like this, but for information on how the Optsee Optimizer™ works, see the Optsee Optimizer™.