The WIND The WIND 
WTI develops an Excel add-in to aid in making decisions. Alicia Smith Consulting and Training (ASCAT) teaches a course called "Solutions! A Systematic Approach to Problem Solving" . In this course real commercial problems are presented to a team of students and solutions are then generated and presented to management. The software described below was developed for this course.
The art of making and defending decisions is probably the most important skill a manager must possess. How often have you been presented with a problem that has conflicting criteria and a multitude of possible solutions? Examples that come to mind include employee promotion, employee ratings, or the purchase of a new computer. We will discuss in detail the problem of deciding on an investment strategy for retirement. Many decisions are made by default because we fail to take actions.
One method of organizing the Decision-Making process is to arrange the strategies/criteria in a rectangular array. If one can assign numerical values to the various criteria for each strategy, then a ranking of the criteria is possible and a comparison across criteria is also possible.
A simple example follows: Suppose that you want to plan your retirement investment strategy. Obviously your goal is to have the most money at the time of retirement. However, strategies that maximize the expected value of your portfolio generally have high risk. Let us assume that four strategies are presented: A, B, C, and ABC/3. The latter strategy means investing 1/3 of your money in each of the three opportunities. The criteria are EAR (expected annual return) and Risk. If we were to be cautious we might well weight Risk 3/2 of EAR. The decision matrix for this problem might look like this:
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EAR |
Risk + - |
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Weights = |
2 |
3 |
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A |
6% |
0% |
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B |
10% |
8% |
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C |
15% |
13% |
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ABC/3 |
10.3% |
7% |
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Best = |
High |
Low |
Notice that the EAR column is marked High (since high returns are good) while the Risk column is marked low (since low risk is good). By risk we mean that the actual earnings could fluctuate by as much as plus or minus the percentage indicated in the Risk column.
We transform the above matrix into a weighted rankings matrix by ranking the individual criteria against the strategies and then multiplying the ranks by the weights. For example, the EAR column has
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Strategies |
Rank |
Weighted Ranks |
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A |
4 |
8 |
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B |
3 |
6 |
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C |
1 |
2 |
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ABC/3 |
2 |
4 |
These ranks are entered into the weighted rankings matrix below. The "Risk +-" column is computed similarly (except that high risk is less desirable)
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EAR |
Risk +- |
Total |
Rank |
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Weighted Scores |
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A |
8 |
3 |
11 |
2 |
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B |
6 |
9 |
15 |
4 |
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C |
2 |
12 |
14 |
3 |
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ABC/3 |
4 |
6 |
10 |
1 |
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Best = |
Low |
Low |
Low |
Low |
The Decision Matrix is scored by adding the weighted ranks across the rows. Low scores are best. We record this in the "Total" column and rank these scores in the "Rank" column.
Thus the preferred investment strategy (of the four listed) is to invest equally into A, B, and C, i.e. choose strategy ABC/3.
Alicia Smith has been a professional facilitator and trainer for over 12 years. "I genuinely care that the people who are in that room have a positive experience and gain work habits that they can take directly into their jobs and perform better with enhanced skill sets," says Alicia. "I really believe that learning can be fun and interesting. I'm there to make sure that the knowledge sinks in and the way to do that differs with every group I teach. Our Solutions! course gives participants a six step, proven method to solve problems. It is a means to develop innovative solutions and then formally evaluate those solutions against the characteristics of your specific problem. Working with the professionals of WTI was a pleasure. They understood my requirements and quickly developed the Decision Matrix Excel add-in which helped to differentiate and strengthen this course." For more information on ASCAT see the web page http://members.aol.com/goalicia/
The second quarter has been very busy here at WTI. We have developed several Excel add-ins. One we have discussed already is the Decision Matrix software. Another application area is in the area of heterogeneous sampling theory, where we have developed an add-in for the computation and graphical display of the Variogram. Variograms are used to find hidden periodicities, determine proper sampling frequency, and assess the use of compositing. Engineers at Shell Oil Company are currently using this software. On a third front we have developed an Excel add-in that implements Carl de Boor's spline package. We have found Excel to be an excellent development environment for exploratory computations.
This example describes a control that drives a pendulum from a starting position to a prescribed final position. The position of the pendulum is specified as an angle Q that is between -p and p. When Q = 0 the pendulum is positioned at 6 o'clock and when Q = ± p it is positioned at 12 o'clock. We use Q = 0 as the starting position. The desired final position is determined by the value of the variable Setpoint. We use Setpoint Q = p /2 which means that we want to drive the pendulum from its 6 o'clock position to 3 o'clock.
The closed loop control U has the form
U = A sin(Q - S) + B Q ' + (g/l)sin(S)
The two parameters, A and B, determine the energy used to drive the pendulum to the final position. The control U has three terms. The first two involve the feedback information and the third term balances the effect of gravity at the set point. The optimization problem is to determine settings for the A and B that drive the pendulum to its final position within a prescribed time and a prescribed tolerance using the least amount of energy (as measured by the integral of U^2). We use a time period of 10 seconds and a tolerance of ± 0.01 for the tolerance of the final pendulum position. Analytically the equations for this system are:
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MQ '' = -(g/l)sin(Q ) + U |
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Pendulum Control Equations |
We initially set A = -2 and B = -7. A simulation run with these settings moves the pendulum to 3 o'clock and the cost (energy used) is 27.1. The plot produced by this simulation run shows the path of the angle of the pendulum from 0 to p /2 (Figure 1). The parameter settings caused the pendulum to overshoot the target and thus use more energy than necessary.
An optimization run with OptimizePRO returns A = -2.61 and B = -1 with a corresponding cost = 8.1. The plot in Figure 2 shows that the pendulum takes a smooth path to its final position, does not overshoot the target, and uses less energy (cost = 8.1).
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Figure 2. |
The pendulum diagram, which is part of the OptimizePRO demo, is available from our free download area: VisSim/OptimizePRO.
According to the Wall Street Journal, the price of memory for PCs has been falling for 7 straight years. The following graph illustrates this point by depicting the average price for 8 megabytes of memory from 1990 to 1996. Note that the price has fallen by a factor of nearly 4 over this period.
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Price for 8 megabytes |
Tom Aird attended IFAC (International Federation of Automatic Control) 96 which was held in San Francisco, June 30 - July 5.
Tom joined Visual Solutions in their exhibit to give demos and explain VisSim / OptimizePRO to many of the 1200 conference attendees.
ON SITE CONSULTING We find that many of our clients have an explicit need to upgrade or add optimization to their products, but they do not have the time to invest in coming up to speed on the new technologies. At WTI we recognize this need and offer a site visit and consultation on your specific software needs. The cost for this service is $500 a day, plus expenses.
GUARANTEE We are so convinced in the quality of this service and our products in general that if you are not completely satisfied, we offer a 90 day money-back guarantee.
This is a quarterly newsletter of Windward Technologies, Inc. Please let us know what your interests are and what sort of articles you would like to see. Please contact us if you would like to have your name added to our newsletter mailing list or if you would like to contribute an article to the newsletter!
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Phone: |
281-564-6523 |
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Fax: |
281-564-6921 |
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Mail: |
Windward Technologies, Inc. |
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12039 Mulholland |
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Meadows, TX 77477 |
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E-mail: |
Regards,
Tom Aird
TomAird@aol.com and
Phil Smith
PWSmith@aol.com
Figure 1. 
