A segment-level model now guides billions in Dutch dike investment

Summary

• Dutch dike rings can contain up to ten segments with different soils, histories and structures, while the weakest segment can determine the safety of the whole ring.

• The research combines mixed-integer nonlinear programming with robust optimisation to decide when and how much to invest in each segment under different future scenarios.

• The method was translated into software used by Deltares and the Dutch government in work underpinning national safety standards under the Dutch Water Act.

Why can treating a dike ring as one structure lead to the wrong decision?

A dike ring may look like one defence system on a map, but in practice it is often a collection of distinct segments. One stretch may follow a river, another may sit on different soil, and another may include a sluice or floodgate. They can differ in age, construction cost and flood risk.

Earlier cost-benefit models treated an entire ring as a uniform structure. That simplification made the mathematics manageable, but it could also lead planners to raise parts of a ring that did not need investment while missing the segment that most constrained safety.

The decision is therefore not simply how high a dike should be. It is which segment to invest in, by how much, and at what point in time.

Why is this a prescriptive analytics problem?

Prescriptive analytics is designed for decisions where several choices interact, and resources are limited. Here, the model must balance expected flood damage against construction costs while accounting for the fact that one weak segment can shape the risk of the full ring.

The problem also unfolds over decades. A decision that looks efficient today can become expensive if conditions change, so the research needs to identify investment paths that remain useful across more than one plausible future.

How did the team approach the problem?

Researchers from Tilburg University, Delft University of Technology and the CPB Netherlands Bureau for Economic Policy Analysis developed a mixed-integer nonlinear programming model that represents each dike segment separately. The model can combine continuous choices, such as how many centimetres to raise a dike, with yes-or-no choices about whether an investment should happen at all.

Directly solving the full problem became too slow for dike rings with more than six segments. The team therefore developed an iterative algorithm that starts with a feasible investment plan and improves it step by step. They also compared each strategy across several possible futures, looking at how much worse a decision could turn out compared with the best choice in hindsight. This approach, known as regret-based robust optimisation, reduces the risk of committing to a plan that works well under one forecast but performs poorly when conditions change.

What was the impact when the model was applied?

Tests with real Dutch dike-ring data showed that treating non-uniform rings as if they were uniform produced worse investment decisions than planning segment by segment.

The research was translated into software used by Deltares and the Dutch government in work that informed updated national safety standards under the Dutch Water Act. Those standards shape where and how billions of euros in flood-protection investment are allocated.

For communities living behind these dikes, the practical value is more targeted protection: public investment can be directed to the sections that most affect safety instead of being spread evenly across a ring.

What can the findings mean for other applications?

The same decision structure appears in flood-protection systems far beyond the Netherlands. Levees, seawalls and river defences are also built from segments with different ages, materials and exposure to risk.

As climate conditions change, future work can extend these methods to larger networks and wider ranges of uncertainty, linking segment-level investment decisions with evolving climate information and other forms of protective infrastructure.