# Variability, Randomness, And Uncertainty in Operations

This elaborates on the topics of randomness versus uncertainty that I briefly touched on in a prior post. Always skittish about using dreaded words like “probability” or “randomness,” writers on manufacturing or service operations, even Deming, prefer to use “variability” or “variation” for the way both demand and performance change over time, but it doesn’t mean the same thing. For example, a hotel room that goes for \$100/night in November through March and \$200/night from April to October has a price that is variable but not random. The rates are published, and you know them ahead of time.

By contrast, to a passenger, the airfare from San Francisco to Chicago is not only variable but random. The airlines change tens of thousands of fares every day in ways you discover when you book a flight. Based on having flown this route four times in the past 12 months, however, you expect the fare to be in the range of \$400 to \$800, with \$600 as the most likely. The information you have is not complete enough for you to know what the price will be but it does enable you to have a confidence interval for it.

# Probability For Professionals

In a previous post, I pointed out that manufacturing professionals’ eyes glaze over when they hear the word “probability.” Even outside manufacturing, most professionals’ idea of probability is that, if you throw a die, you have one chance in six of getting an ace.  2000 years ago, Claudius wrote a book on how to win at dice but the field of inquiry has broadened since, producing results that affect business, technology, science, politics, and everyday life.

In the age of big data, all professionals would benefit from digging deeper and becoming, at least, savvy recipients of probabilistic arguments prepared by others. The analysts themselves need a deeper understanding than their audience. With the software available today in the broad categories of data science or machine learning, however, they don’t need to master 1,000 pages of math in order to apply probability theory, any more than you need to understand the mechanics of gearboxes to drive a car.

It wasn’t the case in earlier decades, when you needed to learn the math and implement it in your own code. Not only is it now unnecessary, but many new tools have been added to the kit. You still need to learn what the math doesn’t tell you: which tools to apply, when and how, in order to solve your actual problems. It’s no longer about computing, but about figuring out what to compute and acting on the results.

Following are a few examples that illustrate these ideas, and pointers on concepts I have personally found most enlightening on this subject. There is more to come, if there is popular demand.