Here is a small planning parable. A lane has two regimes. Four weeks out of five, transit takes 3 days. One week in five, congestion pushes it to 8. The average is 4 days. A plan built on 4 days is wrong in every single week: too slow in the normal regime, catastrophically optimistic in the congested one. The average describes a world that never occurs.
Averaging destroys exactly the structure a decision needs. It erases bimodality, correlation, and sequence. Two lanes that both average 4 days can be completely different commercial propositions if one is tight around 4 and the other swings between 2 and 9. A customer promise, a pricing decision, and a capacity commitment all care about the swing, not the center.
Scenario trees restore structure
The corrective is to plan over scenarios: a structured sample of the futures the network could face, each with a probability, each internally consistent. Congestion at the port correlates with congestion at the rail head. A demand surge in one corridor draws down capacity in another. Scenarios carry these dependencies; averages cannot.
Against a scenario tree, the optimizer can do what a good operator does instinctively: make the decisions that must be made now, keep options open where the future will reveal itself, and pre-position recourse where the tree shows real downside. The output is not one schedule but a policy: do this now, and if the world moves that way, do that.
Three futures with the same average.
Switch distributions, then move the commitment you have to hit.
The mean is identical in all three. Your exposure is not.
Where it bites commercially
The commercial edge shows up at the quote. A network that understands its own distributions can price a tight service promise on the stable lane and decline or premium-price the volatile one. A network planning on averages prices both the same, wins the wrong business, and discovers the difference in its margin 6 months later. Expected value is a fine way to summarize the past. It is a poor way to commit the future.