Patent Publication Number: US-2010121781-A1

Title: Mechanisms for illustrating the choices in an optimal solution to a set of business choices

Description:
BACKGROUND 
     Organizations have to make decisions about how they invest in information technology (IT). A decision, or a set of supporting decisions, can be considered to be a strategy. 
     The business value of a strategy is modeled as the sum of a set of variables, each with a statistical distribution. The variables may be inter-dependent, or independent. 
     The resulting total business value for an investment strategy can therefore be characterized as a statistical distribution. The mean of this distribution is the expected value of the strategy. 
     Finding the optimal investment strategy is often difficult, because the statistical distribution of each variable is often not known with certainty, or depends on key assumptions or decision factors. It is therefore useful to test assumptions and decision factors by adjusting them and seeing how they alter the expected overall business value. 
     BRIEF SUMMARY OF INVENTION 
     The invention consists of a means of illustrating how each investment in a portfolio of investments is expected to contribute to the total business value of the portfolio, subject to any overall investment budget constraint, while also showing the level of uncertainty around each expected value. This enables the investor to understand the contribution to total value provided by each investment, thereby enabling better decision-making about investments within a portfolio. 
    
    
     
       BRIEF DESCRIPTION OF ILLUSTRATIONS 
       Illustration 1: Depicts how multiple inter-dependent investments sum to provide an optimal overall investment value. This depiction is the essence of the invention: it enables one to see how each individual investment contributes to the total value of a portfolio of investments. It also shows the uncertainty associated with each investment. Finally, it shows that each individual investment is funded at a non-optimal level, even though the portfolio is optimal. 
     
    
    
     DETAILED DESCRIPTION OF INVENTION 
     The purpose of this invention is to enable one to conveniently view how each variable affects the total business value, and to enable the user to receive immediate visual feedback on the change in value as assumptions are adjusted. 
     Each Component Investment Has a Distribution 
     Illustration 1 shows how this works. In this illustration, a small vertically oriented solid line curve is depicted, labeled “1”. The curved line is capped by a shaded dot indicating the point of maximum of its curve, labeled “3”. The solid line curve represents a projected distribution of a random variable. This curve curve is a probability density distribution, with an implied horizontal axis (not shown) that is the probability density and the vertical axis (shown) that is the expected business value. The terms “expected value” and “probability density distribution” are standard terms in the field of statistics. 
     Illustration 1 depicts three investments in a portfolio of investments. Each investment has a curve similar to curve “1”, but the curve is only shown for investment B in order to avoid clutter in the diagram. 
     In addition, each investment has a horizontally oriented curve, representing the probability density of the cost of the investment. This type of curve is exemplified by item “2” in Illustration 1, but the illustration shows this type of curve for each investment. 
     The probability density curves indicate in tangible terms the uncertainties surrounding each investment of the portfolio. These uncertainties can be aggregated mathematically to compute uncertainties for the entire portfolio. That is not shown in the illustration however. 
     Each solid curve in the Illustration therefore represents a random variable that represents the value or cost of a particular investment. However, each of the value variables (V A , V B , and V C  in the illustration) also contributes to overall business value for the investor or organization: the total business value is the sum of these variables. That is, the total business value of a portfolio is the sum of the value of each investment in the portfolio. Similarly, each cost variable (C A , C B , and C C ) contributes to the total investment cost of the portfolio. 
     Choices (strategies) regarding each investment (such as how much to invest) alter the projected distribution of the investment&#39;s value. For each investment in Illustration 1, the dotted line curve (exemplified by curve “4”) shows how the projected expected value for that investment changes over the range of amount to invest (cost) for the investment. Each of these dotted line curves may have a maximum, representing the maximum possible expected value for that investment in isolation. It is not required that it have a maximum, however. 1    1  The reason that a dotted line curve might have a maximum is because unlimited investment usually produces diminishing returns so that cost starts to overwhelm the return. 
     Component Investments are Often Inter-Dependent 
     If the investment value random variables are independent, then the optimal solution for the investor (the organization) is simply the solution that lies on the maximum of each dotted line curve. 2  However, in most investment situations, investments are not independent, because investment funds are limited and so investment in one area takes away from the others, and for investments that are internal to an organization there are often other inter-dependencies as well due to operational constraints. Thus, we are interested in finding the optimal investment amount for each investment, given that the total investment is limited to an overall portfolio investment budget.  2  If any of the dotted line curves has no maximum, then the optimal investment is infinite. 
     Aggregating the Multiple Investments 
     The interdependencies among investment choices can be modeled using many techniques, such as by using random (“stochastic”, or “Monte-Carlo”) simulation or by using “mathematical programming” to algorithmically compute an optimum. Regardless which technique is used, the optimum often involves investment choices that result in a sub-optimal expected value for each separate investment, but that results in an overall maximum for the total of these investments. This is shown in Illustration 1 by the fact that the three green dots are not on the maximum of each dotted line curve. Each dot represents an expected non-optimal value for each of the three investments, but the total of all three is maximized, given the constraints under which the investor (the organization) must operate. (A curve of total value is not shown in the FIGURE, but it could easily be by plotting the change in expected total value versus various investment choices.) 
     The Organization&#39;s Budget 
     The total amount invested by the investor (the organization) is the total of what is invested in each component investment. In illustration 1, this is 
       C A +C B +C C    
     This total must be less than or equal to the total funds available for investment: the organization&#39;s budget for investment. The investment criteria is therefore to maximize the sum of the expected value of each investment, subject to the total amount invested being within the budget. In mathematical terms, this is expressed as: 
     
       
         
           
             
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     where V i  is the value of investment i, and C i  is the cost of investment i. 
     Illustration 1 has the advantage that it shows how the investments stack together to produce a composite investment portfolio for the investor (the organization). 
     How this View Can be Used 
     The type of view described here can be used in very powerful ways to perform “sensitivity analysis” on investment choices. For example:
         1. Key assumptions can be adjusted, the maximization algorithm or simulation re-run, and the illustration updated (perhaps in real time) to show the impact.   2. Investment preferences, such as risk preferences, can be adjusted, and the results updated as in 1 above.   3. Decisions about individual investments can be adjusted to see the impact.   4. The optimal solution might indicate that investment in some components should be zero, indicating that they should be removed from the portfolio. Adjustments to assumptions or decisions might cause this result to change, putting those investments back in the portfolio. These changes can be observed using the type of view depicted by Illustration 1.       

     REFERENCES 
     
         
         
           
             1. Real Options, by Copeland and Antikarov, copyright 2003. 
             2. Value-Driven IT, by Cliff Berg, copyright 2008.