In our daily lives, we all experience how difficult making a decision can be. What do I buy for dinner? Which school should I choose? How do I invest my savings? Even the simplest question requires going through a lot of information. However, very often we lack them and we make assumptions trying to figure out the possible future scenarios hoping to avoid bias. When it comes to efficiently analysing information to make unbiased decisions a data-driven approach is surely the best option. But, what about uncertainty? Are we already dealing with it just because we use data?
Are Data enough when it comes to Uncertainty?
Uncertainty permeates every aspect of reality. Very often it is associated with a lack of knowledge that cannot be filled. And yet, even assuming to have an oracle at our disposal, an inherent randomness may be present in the considered system or environment. So, what now?
Well, the first answer is data, of course. Indeed, embracing a data-driven approach allows us to objectively gather and fully exploit the information we dispose of. Data can be leveraged using optimisation tools which allow to improve decisions. As such, the so-called OR (Operation Research) is a fervent academic field which finds large applications in real life, such as:
- Supply Chain Management;
- Transportation Systems;
- Finance and Investment;
- Energy Management;
- …
Despite this, data are only a way to represent what we know about reality… what we do not know, we still do not know. Here, we should make a short digression about the importance of collaboration, data sharing and integration, but we leave it for now 🙂 .
Optimisation Under Uncertainty
Nothing is lost, and we can still try to represent uncertainty somehow. In doing this, data, statistics and probability are our allies.
Why is it important?
But first, let’s try to understand why recognising and accounting for uncertainty is relevant. Assume you are in charge of displacing new ambulance stations in the region under your administration. Hopefully, you will use some optimisation models to locate those new stations in the best possible way to serve citizens and maybe to reduce costs.
Now, the service you grant people is the better the lower the time necessary to reach the building where the emergency occurred. As such, one of the criteria to optimise your model will be the minimisation of the ambulances’ time travel.
Suddenly, a question arose: which times should I consider to optimise my model? How much time do we need to move from any location A to any location B in the region? Clearly, this depends on traffic congestion, which usually follows specific patterns during the day. Also, weather conditions and rare events such as car crashes may influence it. Consequently, any time you pick up is wrong.
Which tools do we have?
Luckily, some years have passed since uncertainty entered the OR discussion, and optimisation models able to represent it have developed.
Stochastic programming is one of them. The idea behind this model is to make assumptions about the future, as we would do when deciding whether to take our umbrella before going out.
Each future possibility is represented by using data. Let’s think of the ambulances example. Since we do not know the amount of road congestion when an emergency occurs, we can assume this to happen in 3 different scenarios:
- High traffic congestion;
- Normal traffic congestion;
- Low traffic congestion.
Then, we would choose a single set of data to represent each scenario. Finally, the stochastic model tries to find a solution which adapts well to every possible future.
Usually, more scenarios allow us to improve the uncertainty representation. On the other hand, this may lead to intense computations requiring much more time and money. As such, there is still a lot of research trying to understand how to reduce scenarios without affecting the quality of uncertainty representation.
Conclusion
In a nutshell, uncertainty is an always present element to face, and data alone is not enough to work with it. However, data with proper tools allow us to account for the stochastic nature of a problem supporting the decision-making process. Generally, stochastic models are more resource-consuming than the others. As such, they should be used when uncertainty can relevantly affect the solution to a problem or the following decision.
