How to use it
- 1. Commit before you knowStage 1: book capacity now, at a cheap rate. Stage 2: demand lands, and you fix the gap expensively.
- 2. Meet the three answersRP solves all scenarios at once. EEV plans on the average. WS is the impossible clairvoyant.
- 3. Read VSSThe Value of the Stochastic Solution is what planning on the average costs you. It is almost never zero.
- 4. Read EVPIWhat a perfect forecast would be worth - the gap between RP and clairvoyance.
Book capacity now, demand lands later
Scenarios (demand, probability)
Mean demand = . EEV plans for exactly this number - and that is the trap.
Economics
Book too little → pay spot. Book too much → eat the waste. Classic newsvendor, but now with a real recourse decision.
Expected total cost against the stage-1 booking. Red dot = RP optimum; grey dot = what EEV books (the mean); the dashed floor is wait-and-see.
The scenario tree: one decision now, then nature moves, then recourse. Bar width = probability; the number is that scenario’s recourse action at x*.
Try these experiments
- Push spot to $60: RP books far above the mean - buying insurance against the expensive tail. EEV can’t see the tail at all, so VSS explodes.
- Set salvage = booked cost: waste becomes free, so book for the worst case. VSS shrinks toward zero.
- Note VSS ≥ 0 and EVPI ≥ 0 always - a theorem, not a coincidence. Try to break it; you can’t.
About this tool
The concept
Two-stage stochastic programming: decide here and now under uncertainty, then take a recourse action once the world reveals itself. Real plans live in stage 1.
How it works
minx cx + Eξ[Q(x,ξ)], where Q is the cheapest fix-up in that scenario. WS = E[min per scenario]; EEV = the mean-demand plan evaluated on reality; VSS = EEV − RP; EVPI = RP − WS.
Winning strategy
Never plan on the average. The mean scenario often has zero probability, and optimising for it silently ignores exactly the tail that hurts you.