How to use it
- 1. Costs are ranges, not numbersEach supplier quotes a nominal price that may drift up by ±d. Nobody knows which ones will.
- 2. Turn the Γ dialΓ = how many suppliers you assume go bad at once. Γ=0 is naive; Γ=n is paranoid.
- 3. Watch the price of robustnessNominal cost rises as Γ grows - that premium is what protection costs.
- 4. Stress-test itRun 2,000 random futures and compare the plans: how often does the naive plan blow its budget?
Allocate 1,000 units across suppliers
Suppliers
| Name | Cost | ±dev | Cap | Share |
Robustness
Stress test
Allocation at this Γ. Bar = share; the pale extension is that supplier’s worst-case cost drift. Robust plans spread the order instead of piling onto the cheapest quote.
The price of robustness. Navy = what the plan costs if every quote holds; red = what that same plan costs if all quotes drift. Raising Γ generally costs a little nominally and buys a lot less exposure. Both lines judge every plan on the same yardstick. Navy can dip slightly - only the protected objective is guaranteed to rise with Γ, not its nominal part.
Try these experiments
- At Γ=0 the plan leans on the cheapest, most volatile supplier. Run the stress test: it wins on average and owns the ugliest tail.
- Go to Γ=1 or 2: nominal cost rises a few percent while the p95 and worst-case fall. Robustness buys a thinner tail, not a cheaper bill - that knee is where real procurement sits.
- Give the cheapest supplier a huge ±dev: even at low Γ, robustness quietly walks away from it. Cheap and volatile loses to slightly-dearer and steady.
About this tool
The concept
Robust optimisation plans against an uncertainty set, not a distribution. You need no probabilities - only honest ranges, which procurement teams actually have.
How it works
Bertsimas & Sim: protect against any Γ coefficients hitting their worst value at once. Cost = Σc·x + max|S|≤ΓΣSd·x. Γ tunes conservatism continuously from nominal to full worst-case.
Winning strategy
Γ is a dial, not a dogma. Small Γ buys most of the protection for a small premium - the curve is steep at first and flat later.