Executive Decision Support Systems

CentraLytics provides enterprise-grade executive decision support tools. We apply advanced techniques in scenario analysis and simulation to support decisions under uncertainty. Our solutions have been applied to a wide range of problems from risk analysis in oil & gas exploration to critical path analysis in multi-national, professional-services engagement management. We have applied our own custom code base to Global 1000 enterprise determinative models in quantitative finance, global mobility management, accountancy, taxation, and engineering. We have also applied the commercially-available @Risk and Crystal Ball® Monte Carlo software packages when engaged to do so.

No model is complete without scenario analysis. What-if analysis is useful, at least as far as it goes, but it is easy to get lost in the detail and miss valuable insights. The simplest computations, fact patterns, and business rules can involve sufficient complexity when undertaking scenario analysis or sensitivity analysis that the major trends and the logical conclusions they suggest can be lost. Sensitivity analysis suffers from the curse of high-dimensionality. Imagine that there are two inputs that can each take on a meager ten values each. To permute through all the possible scenarios, the model must be calculated 102 (100) times, which is certainly possible. (This is why we have summer interns!) But four inputs with 10 possible values each would require 104 (10,000) iterations to get complete coverage. (This is also possible, and is called "graduate school.")

Consider the simple business rule of adding two integers between one (1) and six (6); that is, a roll of the dice, if you will. Scenario analysis by way of a cursory consideration of possible outcomes would quickly conclude that the range of possible results lies between two (2) and (12), but there is much more to the story. Even though there are thirty-six (36) possible states of the two integers, there are only eleven (11) possible outcomes.

Furthermore, the eleven possible outcomes are not equally probable! Notwithstanding the value of knowing the range of possible outcomes, the distribution of possible outcomes is extremely important knowledge - it tells the betting person where to place his or her wager.

The process to undertake sensitivity analysis on a highly-dimensional system is Monte Carlo simulation. A simulation is the imitation of some real thing - a property, ratio, system state, or process; that is, Monte Carlo simulation is an experiment that is repeated thousands of times. The answer we seek is the distribution of results and the associated probability that a given result will occur.

Monte Carlo starts with the same deterministic mathematical model of a financial or physical process, and allows selected inputs, called assumptions in the trade, to vary throughout their distribution of possible numerical or categorical values. The calculation's results, termed a forecast, are recorded in a tableau for further analysis. The forecast is some result of interest in the model - perhaps a sum, average, standard deviation, or categorical representation that is of interest in the context of the problem being represented mathematically. Change the assumptions' input values, and the resulting forecast changes. Change the assumptions' input values a few thousand times and record the resulting forecasts, and you obtain a distribution of forecasts' states just as with the dice above.

The lesson here is that if even the simplest of business rules - adding two integers, each of which varies in value -- yields a rich probability-weighted distribution of solutions, it is beyond the imagination to envision the distribution of solutions for a complex business risk analysis or engineering analysis with many inputs that can each take any of a defined distribution of values; the high-dimensionality and large number of permutations would quickly saturate and defeat any attempt at scenario analysis. Monte Carlo simulation is required to obtain the distribution of forecasts for informed executive decision support.

Although convenient and expedient, a scenario and what-if analyses have limited utility and extensibility. A model with two inputs and one resultant can straight-forwardly be analyzed with this approach, but in general, a problem of higher dimensionality cannot easily (and we would say meaningfully) be analyzed in this manner; However, a highly-dimensional model can be analyzed straight-forwardly with Monte Carlo simulation by assigning probability distributions to each if the assumptions and observing the distribution of resultant forecasts.

CentraLytics excels at applying Monte Carlo simulation to a wide range of core analyses in business, industry, government, defense, and education.

This article was contributed by Michael A. X. Izatt, who prior to his training and vocations as a statistical physicist and Wall-Street fixed-income quantitative financial mathematician, worked as a croupier on the craps tables of the Las Vegas Strip.