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The math problem that could bring the world to a halt

Blog: Decision Management Community

Dynamic resource allocation problems arise from a range of different real-world scenarios and each one has its own specific issues. “Dynamic resource allocation problems deal with changing inputs and environments, which are highly dynamic and difficult to estimate and predict, as the future load is not statistically dependent on the current load. One change triggers another change, and if you want to control the system with accurate decisions, one must consider the future status of the system.Link

The trouble is that most existing methods rely on historical data to make predictions. This method doesn’t scale very well for such systems and can’t cope with even the smallest changes. If a change does occur, they go back to square one and start working out a solution all over again. Such problems quickly become computationally intractable, even for a fairly small number of people and resources – whether that’s a meal or an MRI scanner. For example,  a large hospital is trying to treat and feed all the patients coming through its doors. The medicines they require, which themselves have a limited shelf life, and the equipment needed for diagnosis and treatment will change constantly as different patients arrive. Limited resources like MRI scanners, doctors and nurses need to be allocated too. To address this, and prevent costs from soaring out of control, the hospital management might deploy mathematical models to help coordinate all these things.

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.

You will struggle to find an industry that doesn’t faces the challenges of managing a dynamic resource allocation problem in one form or another. Electricity prices, yield of parts in a supply chain, travel times, equipment failures, and the behaviour of people are all issues I have had to deal with. This problem is so rich that there are at least 15 distinct research communities working on this problem from different perspectives.

If we don’t start to address dynamic resource allocation problems now, we won’t just struggle to get dinner on the table – the entire world could grind to a halt. Read more

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