The Decision-Dependent Dam

Most optimization under uncertainty treats the uncertainty as exogenous — it’s out there, independent of what you decide. The weather doesn’t care about your crop choice. The stock market doesn’t respond to your personal portfolio allocation. You choose; nature reveals; you adapt.

Cascaded hydroelectric systems violate this assumption. A cascade of dams along a river means water released from one dam flows to the next. The decision to release water at the upstream dam creates the inflow uncertainty for the downstream dam. The uncertainty isn’t exogenous — it’s endogenous. Your decisions at one point in the cascade generate the stochastic environment for decisions at the next point.

This is decision-dependent uncertainty: the probability distribution of future states depends on current choices. Standard stochastic programming handles this badly, because it assumes the scenario tree (the possible futures) is fixed before optimization begins. But here, the scenario tree changes as you optimize — the branches shift depending on the release schedule.

Real-time coordination under decision-dependent uncertainty requires simultaneously optimizing across the cascade while updating the uncertainty model to reflect the decisions being made. The upstream dam can’t optimize independently of the downstream dam, and the downstream dam’s uncertainty is literally generated by the upstream dam’s choices. The coupling isn’t just physical (water flows downhill) — it’s informational (one dam’s decision is another dam’s noise).