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Working example 04 Monte Carlo and value of information

Decisions with incomplete evidence

“We must make a major decision before we have all the information.”

A logistics business must decide whether to build a £12m distribution centre. Demand is uncertain, construction costs can overrun and the ramp-up could take one to three years. A market study is on offer.

How it works

The method in three steps

  1. Describe uncertaintyDemand is normally distributed around the estimate, margin is triangular (£18–£28 per pallet), build cost is log-normal and ramp-up is one, two or three years.D ~ N(μ, σ), m ~ Tri(18, 24, 28), C ~ 12·LogN(0, s)
  2. Simulate valueEach draw produces a 10-year net present value at 8%, with capacity capped at 160,000 pallets a year.NPV = −C + Σ (min(D_t, cap)·m − opex) / 1.08ᵗ
  3. Price the informationExpected value of perfect information (EVPI) bounds what any research is worth; partial EVPI isolates each uncertainty.EVPI = E[max(NPV, 0)] − max(E[NPV], 0)

Try it

The working example

Assumptions

Change what you believe and see whether the decision changes.

Thousand pallets a year at full ramp-up
One standard deviation
Log-normal spread of capital cost
Would resolve demand uncertainty
Expected NPV–
Chance of losing money–Share of simulations with NPV below zero
Value of perfect information–The most any research could be worth
Recommendation–

Range of outcomes

20,000 simulated 10-year NPVs. Orange outcomes lose money.

Which uncertainty is worth resolving?

Expected value of perfect information for each uncertainty, against the cost of a demand study.

Interpretation

From example to engagement

What the example shows

A single-point business case hides the chance of loss and the shape of the downside. Value-of-information analysis turns “we need more data” into a priced question: some uncertainties matter to the decision and are worth paying to reduce, and others are not, however large they look.

With real data

  • Distributions elicited from experts and calibrated against history.
  • Correlations between inputs, such as demand and price.
  • Expected value of sample information (EVSI) for studies that reduce rather than remove uncertainty, and real options for staged investment.