Thomas W. Knowles and Associates  


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We are available to help you in many ways.

   1. Help you formulate an optimization model  for your decision problem.
   2. Assist in the choice of the optimization system.
   3. Develop a turn-key decision support system tailored to your problem and to your specifications.
   4. Update old What’s Best! models from an earlier version or migrate them from Lotus 1-2-3 to Excel.
   5. Train your personnel in the formulation of optimization models.
   6. Train your personnel in the use of optimization software.

Our firm has expertise and experience in many areas that can help you develop decision tools.  These include data analysis, forecasting, production planning, inventory control, and spreadsheet modeling.

The spreadsheet has become the ubiquitous tool of the decision maker.  It has powers that most users never discover but that we can unhide for you.  For example, the Decision Tools Suite has many powerful add-ins. PrecisionTree facilitates decision analysis including the construction of decision trees and sensitivity analysis associated with probabilities and payoffs. @RISK is an Excel add-in that facilitates probabilistic simulation.  BestFit selects the probability distributions that best represent your historical data and estimates the probability distribution's parameters. RiskOptimizer combines probabilistic simulation and optimization.

@Risk has many applications. We discuss just one.

Decision makers are often confronted with evaluating major capital investments and frequently use discounted cash flow analyses.  Given the cash flows, calculating the Net Present Value (NPV) is straightforward.  The difficulty is forecasting the cash flows.  Can you really estimate annual sales of a new product?  Can you really estimate the market price, year by year?  How about your costs?  What is the useful life of the capital investment?  These are all subject to uncertainty.  Just using your best estimate for each is unlikely to give an accurate picture of the NPV.  Under some scenarios, the NPV can be negative.  What is the probability that the NPV is negative (indicating that the capital investment is not justified)?  Instead, we can use simulation to estimate the shape of the probability distribution of NPV.

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