The math problem that would bring the world at wits’ end

Photo by Anna Dziubinska on Unsplash

Not everybody likes math, but the fact is we often face math problems in our everyday lives. From budgeting wages to managing our time, we are surrounded by issues which we could solve by applying a little bit of math. However, there is one math problem which proves to be so difficult to solve that even computers are having a hard time finding the best solution. They are called dynamic resource allocation problems.

The reason for their immense difficulty and almost sheer improbability of being solved is that there are infinitely many situations that need to be considered. Due to an exponentially growing number of possibilities and the constantly changing nature of the parameters, one would be hard-pressed to come up with the right solution as new information becomes available. That is to say, we cannot predict all the possible outcomes therefore, we cannot develop a model or algorithm that would take all scenarios into account and come up with one right answer.

Whether you’re waiting for a taxi or a next-day delivery, the list of dynamic resource allocation problems and their everyday applications is “almost endless” according to Warren Powell, an engineer at Princeton University who has been investigating these problems since the 1980s.

But dynamic resource allocation problems are not just concerned with giving humans what they want, when they want it. They will also be essential for tackling some of the world’s most fundamental and complex issues, including climate change, as they help us allocate our planet’s often scarce and depleted resources in the most efficient ways possible.

In the simplified illustration of trying to cook dinner for one’s family, unexpected events, such as having friends over or family members coming home late, can alter how one must manage to feed everybody. These individual decisions within the system and extraneous factors could affect both demand and supply making it difficult to allocate resources.

Many business processes and operations involve dynamic resource allocation problems. Logistics and supply chain management always work under time constraints among other things. Especially since these processes are caught in the middle, they require real-time updates on information which would help them to find the most efficient route to their destination. But it doesn’t end there. So many other scenarios could happen en route such as road blockages, heavy traffic due to accidents, or other force majeure. Which is why, in the midst of all this chaos, it’s extremely difficult to solve these problems.

Despite the odds, researchers are still trying to find solutions such as making use of deep learning algorithms which would accumulate as much data and information as possible through interaction with the system and come up with solutions to existing problems. It would need a large database and as mentioned, in an ever-changing environment, one must be able to make decisions as soon as the information is available. The one hope we have is that when we develop a solution for these math problems, we would be one step closer to solving system-wide issues which might save humanity and the world as we know it.

By Jeremiah