Multiple Decision Points. Difficult to calculate?

When I say a problem is “too difficult to calculate,” it’s often not immediately obvious why. Let me explain with an example. 

Every project involves decision points – moments where choices must be made. In a delivery model, these are represented as decision nodes within a network of possible paths.

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Imagine a project with 20 decision nodes, and each node has 3 independent alternatives. If none of these decision points overlap on the same path through the network, the total number of possible combinations is 3 to the power of 20.

That’s about 3.5 billion different combinations to consider. Even a powerful computer wouldn’t help much. If each option could be evaluated in just 0.1 seconds, it would still take more than 11 years to go through them all, clearly an impractical approach.

This is why projects rely on advanced calculation methods to reduce the number of combinations to something manageable. However, by doing this, they accept the risk of missing the best possible solution. In practice, quickly finding a good enough solution is far more valuable than chasing perfect optimality at all costs.

The key challenge is balancing practicality with optimality. This is where AI adds tremendous value. AI-powered scheduling tools use heuristic optimisation techniques to efficiently explore the solution space and identify near-optimal results without examining every single alternative.

For small schedule fragments (fewer than 30 activities), we can use exact algorithms to find the optimal solution and compare it to the heuristic results. For full project schedules, this isn’t feasible. Instead, we compare outputs from different scheduling systems to assess which has better heuristics.

Systems with stronger heuristics can significantly reduce project duration and increase overall benefits.