Industry: Transportation Product: ModelRisk Application: Logistics Planning
A national retailer with a four-distribution-center network across the U.S. needed a fifth DC. The deterministic site-selection model ranked the three finalists — Memphis, Dallas, Salt Lake City — by computing each candidate's expected 5-year cost reduction against the current 4-DC baseline (mean baseline cost: $188 million a year). The deterministic ranking said Memphis wins. The Monte Carlo rebuild in ModelRisk said something more useful: Memphis and Salt Lake City are statistically tied on expected NPV savings (about $21M and $20M respectively), each is the best of the three on roughly half the scenarios (Memphis 51%, Salt Lake City 47%), and Dallas is almost never best (2%) despite reading as a respectable middle option deterministically. The real choice is between two near-identical NPVs at very different capex — exactly the trade a single point estimate hides.
A network-design study rebuilt the candidate-comparison in ModelRisk with coupled demand and LTL-rate uncertainty. The savings-distribution view is what reframed the decision.
Each curve is the distribution of (baseline NPV − candidate NPV) — money saved on the right, value destroyed on the left. Memphis and Salt Lake City sit almost on top of each other near a $20-21M mean saving, both with a tiny probability of destroying value (Memphis ~3%, Salt Lake City ~1%). Dallas trails badly: a $6M mean saving and a 23% chance of destroying value outright, dragged down by its $92M capex. The deterministic ranking's "Memphis wins" is true only at the decimal point — the distribution shows the genuine contest is Memphis vs Salt Lake City, and it is a coin-flip on cost.
The 5-year network cost is dominated by two stochastic inputs:
Annual demand growth was fitted as AR(1) around a 3.4% long-run rate, with annual innovation standard deviation 2.8% — the residual from the company's historical demand series after removing trend and seasonality. Over 5 years this produces a Year-5 demand multiplier with mean 1.13, P10 0.97, P90 1.30. The deterministic plan uses the central 1.13 flat; the stochastic plan sees the spread — including the real chance (P10 below 1.0) that demand actually contracts.
LTL freight rate index was fitted as AR(1) with annual vol 12% around the long-run base — capturing the cyclical cap-tightening of the U.S. LTL market, with a Year-5 index spanning P10 0.82 to P90 1.19. Critically, demand and LTL rate are coupled via a Gaussian copula on the underlying shocks (shock correlation 0.45): high-demand years tend to be high-LTL-rate years, because tight national capacity drives both. The AR(1) smoothing dilutes that to a realized Year-5 demand/rate correlation of about 0.27. Modeling the two inputs as independent — the previous deterministic-style site model — undercounts the right tail of the cost distribution.
The candidate-specific savings are what differentiate the three sites:
The CDFs of total 5-year NPV cost tell the same story as the savings view. The 4-DC baseline (mean $766M, P90 $846M) is the most expensive everywhere. Memphis (mean $744M, P90 $817M) and Salt Lake City (mean $745M, P90 $823M) are nearly coincident across the whole range — Memphis holds a hair-thin lead at the central case and at the right tail, where its larger transport savings outweigh Salt Lake City's lower LTL-rate sensitivity. Dallas (mean $759M, P90 $835M) sits clearly worse than both.
For a retailer whose creditor covenants weight tail cost heavily, the useful finding is not a clean tail-winner — it is that Memphis and Salt Lake City deliver indistinguishable cost distributions, so the decision must be made on the dimensions the cost NPV cannot separate: capex outlay, build risk, and network resilience. That reframing cannot come from a deterministic ranking that simply reports "Memphis wins."
This is the "Why Monte Carlo" beat in network design. The savings distribution at the top of this article shows Memphis and Salt Lake City as near-twins on cost — mean savings $21M and $20M, value-destruction probabilities 3% and 1%. Memphis carries the marginally higher mean and the marginally fatter left tail; Salt Lake City is fractionally more reliable but saves a touch less. Dallas is the clear laggard: a $6M mean saving and a 23% chance of destroying value, the penalty for its $92M capex.
Because the two front-runners are statistically tied on cost, the differentiators are the inputs that don't show up in the NPV mean: Salt Lake City's $65M capex is $13M lighter than Memphis's $78M, and its east-/west-of-Rockies decoupling adds west-coast port-flow resilience that the cost model does not price. Memphis's higher LTL-rate sensitivity (β = 1.20 vs 0.55) means its slim cost lead is also the first to erode if national freight markets tighten harder than the copula assumes.
The baseline the tornado decomposes is Memphis's $21M mean NPV saving. Demand growth rate is the biggest mover, followed by Memphis's own transport-savings calibration uncertainty, then LTL-rate-index volatility. Critically, the demand-LTL correlation is a meaningful mover in its own right, and it is exactly the parameter the previous deterministic model implicitly set to zero. The Memphis-vs-Dallas mean-NPV gap is only about $15M — small enough that a parameter the deterministic model ignored entirely can reorder the ranking.
A distribution-center decision is a multi-year bet on a joint distribution of demand growth and freight-market cycles. Monte Carlo simulation in ModelRisk gives the network-design team the joint distribution and the per-candidate savings shape — and shows that the two front-runners are tied on cost, letting the CFO defend the choice on capex, reliability, and resilience rather than a spurious mean-NPV gap, which is exactly the language the lenders speak.