Probability analysis is a powerful tool for decision making in the face of uncertainty, and in my world, at least, there is no shortage of uncertainty. Forecasting sales numbers, demand for certain products, cost assumptions, labor rates, tax impact ó on and on. All of these factors can and do have a major impact on business outcomes, yet in many organizations planning is conducted and decisions are made with little or no attention to the power of this tool.

Growing from the interdisciplinary intersection of mathematics and micro economics, probability analysis has been refined to an incredible degree with the aid of new models and, of course, heavy-duty computing power. Most of us do not have access to this level of analysis, but all of us could benefit from trying to be a bit more rational in the choices we make. Decision trees are a fairly simple way to force us to think about various outcomes and the likelihood of their occurrence. Here is how it works in a nutshell.

Letís say that ďBill,Ē the business owner, is trying to decide whether to purchase a new machine for his manufacturing operation. The new machine costs $100,000, including shipping, installation and training expenses for his people. The new machine is advertised as having twice the production capacity of the old machine it is to replace and to operate at about half the cost on a per unit basis of production (because of reduced labor, reduced material waste, energy consumption costs, and overall quality improvements) as Billís existing machine for making the same widgets. However, Billís business is seasonal, and there is some question about whether the new machine can be available and fully operational in time for his busy season. On top of that uncertainty, Bill is not quite sure how the economy is going to shape up and what level of sales demand he is going to be able to count upon. So, there are two levels of uncertainty to be weighed. One, the timing to make the machine operational; and two, the level of sales Bill can count on. (Note: For simplicity, we will not calculate the margin impact of this analysis, as it is not needed to drive the decision in this case.)

To deal with the first uncertainty ó the timing of installation ó Bill picks three possible outcomes. One, the machine comes in a month early. Two, the machine comes in just in time. And, three, the machine comes in a month late. Based on his research, careful conversations with the supplier and discussions with other companies that have purchased the same machine from the same supplier, Bill assesses the probability of each outcome. In other words, the percentage odds of each of the three occurring. While Bill understands he cannot predict what will happen, he can make informed assumptions. He decides to put a 0.2 (20 percent) probability on the machine coming in early, a 0.6 (60 percent) probability on the machine coming in on time, and a 0.2 (20 percent) probability on the machine arriving a month late. Note that the probabilities must add up to 100 percent, covering all possible outcomes under consideration.

Next, Bill picks three possible sales outcomes. In the little example here, this variable is detached from the machine timing variable as long as the machine comes in early or on time, so he can apply each of the three sales scenarios to the top two machine timing outcomes. The three sales outcomes, expressed in sales dollars, are $50,000, $75,000 and $90,000, respectively. These numbers come from Billís sales and marketing team. Bill then assigns a probability to each. He uses 0.4 for the lowest outcome, feeling a bit nervous about demand. He assigns a 0.5 to the $75,000 outcome, and a 0.1 to the upper outcome, again because he is not very bullish on the upside. However, if the machine comes in late, Bill correctly assumes this will negatively affect his ability to produce, and therefore the sales outcomes will be much lower for this branch, so he uses $25,000, $40,000 and $50,000 as his sales outcomes reflecting the heavy penalty of missing his seasonal production demand. He applies different probabilities ,to these outcomes to reflect the chaos and problems that will occur in peak season if he is not operational: 0.3 for the lowest, 0.5 for the middle and 0.2 for the high numbers.

Now Bill creates his decision tree. In my Nov. 20 column, Iíll explain how the tree works.

Kevin Eichner is president of Ottawa University. He invites your feedback to this column. Email him at leadershipmatters@ottawa.ed