| Vose Software

Industry: Construction and Infrastructure
Product: ModelRisk
Application: Managing Material Shortages in Large-Scale Infrastructure Projects


Seven Supply Chains, and the Project Only Needs One to Fail

On a $600M urban-transit project, the procurement schedule shows every critical material — structural steel, precast segments, rebar, bearings, rail, signalling — arriving exactly on its need date. That schedule is built on median lead times. Run the same lead times as distributions, with the supply-disruption probabilities the last few years have taught every contractor to respect, and the picture inverts: there is a 96% probability that at least one critical material slips more than four weeks, and the resulting schedule-delay cost has a mean of $2.7M and a P90 of $5.0M. The deterministic plan shows zero shortage risk because it was built on the one number — the median — that hides it.

Material-shortage risk is not really about any single material. It is about the fact that a 30-month programme touches seven independent supply chains, each with its own lead-time distribution and disruption probability, and the project only needs one of them to fail at the wrong moment.

The shortage risk rolls through the project like a wave

Each material is exposed during the quarter it is needed — and the materials are needed in sequence, so the shortage risk migrates across the programme:

Probability of a >2-week material shortage by class and project quarter

Early quarters are dominated by rebar and cement risk; the structural-steel and precast windows peak around quarters 3–4; bearings and rail in the middle; signalling and E&M — the longest-lead, most disruption-prone class — owns the final quarters with a 56% shortage probability at its need date. No single quarter is quiet. A procurement team watching a deterministic Gantt sees none of this, because every bar lands on its planned date by construction.

What the deterministic schedule cannot price

The deterministic schedule assigns the project a zero-dollar shortage contingency, because at median lead times nothing is late. The simulation prices the real exposure:

Material-shortage delay cost distribution

The mean shortage-delay cost is $2.7M, the P90 is $5.0M, and there is roughly an 8% chance the delay cost exceeds $6M. None of this is in the base budget. The distinction the chart forces is between "the plan shows no late deliveries" and "the plan has a one-in-eleven chance of a $6M shortage bill" — and only the second is a number a project director can reserve against.

Each material is modelled as its own supply chain

Every critical class carries three uncertainties:

  • Lead timeLogNormal around the supplier-quoted median, with class-specific dispersion. Long-lead engineered items (signalling, bearings) have wider lead-time distributions than commodities (cement, rebar).
  • Disruption probability — a Bernoulli event per material (10–25% by class) representing a genuine supply-chain break (mill outage, shipping disruption, tariff action) that adds a heavy Gamma-distributed extra delay on top of the normal lead-time variability. This is the fat tail; a lead-time distribution alone understates it.
  • Critical-path coupling — a concurrency factor captures the float that absorbs some overlapping delays, so project cost is not a naive sum of every material's lateness.

How much resilience spend buys what confidence

Buffer stock, dual sourcing and pre-arranged expediting are a continuous lever. Sweeping the resilience budget and reading off the probability of avoiding any critical shortage turns the procurement question into an investment decision:

P(no critical material shortage) vs supply-resilience spend

At zero resilience spend, the probability that no class slips more than two weeks is low — seven supply chains make a clean run unlikely. The first ~$3M of spend (buffer stock on the long-lead items plus dual sourcing on the two most disruption-prone classes) moves the probability sharply; beyond that the curve flattens, because the residual risk is irreducible lead-time variability that no buffer fully removes. The 90% target is reachable on the "no slip > 2 weeks" criterion but expensive on the stricter "no slip at all" criterion — which is itself the finding: chasing zero shortage is not worth it; capping shortages at two weeks is.

Which supply chains drive the tail

Tornado: drivers of the P90 shortage-delay cost

The P90 cost is dominated by the signalling / E&M lead-time tail and the precast-segment disruption probability — the two longest-lead, highest-consequence classes. Commodity materials (cement, rebar) barely move the answer despite being ordered in the largest quantities. This redirects the procurement team away from the high-volume commodities they instinctively manage and toward the two engineered classes that actually own the tail.

Three sourcing strategies, three cost curves

The decision is which sourcing posture to adopt. Comparing single-source JIT against dual-sourcing and a strategic-buffer-plus-dual approach — each with its own up-front premium — on total cost (premium + shortage delay):

Total shortage cost by sourcing strategy

Single-source JIT carries no premium but the fattest tail. Dual-sourcing the key items costs ~$1.8M up front and pulls the P95 in materially. The strategic-buffer-plus-dual posture costs ~$3.4M but compresses the tail the most. For a project whose contract carries liquidated damages on the opening date, the right posture is the one whose tail — not whose mean — sits inside the owner's risk appetite, and the CDF crossing is exactly where that trade-off becomes visible.

What the model changed

  • A shortage contingency was funded — roughly the P90 ($5M) replaced the deterministic schedule's implicit $0, ending a structural under-reserve.
  • Dual sourcing authorised for signalling/E&M and precast — the two classes the tornado identified as owning the tail — rather than spread thinly across all seven.
  • Order dates pulled forward on the long-lead items by the lead-time P75, not the median, converting hidden lateness into explicit early-order working capital.
  • Liquidated-damages exposure quantified for the project board from the delay-cost distribution rather than a single "we expect to be on time" assertion.

ModelRisk Functionality Used

  • Per-material LogNormal lead-time distributions with class-specific dispersion — making the difference between a commodity and an engineered long-lead item explicit.
  • Bernoulli × Gamma disruption layer on top of each lead time — the supply-break fat tail a lead-time distribution alone misses.
  • Critical-path concurrency factor so overlapping delays are partially absorbed by float rather than naively summed.
  • Resilience-spend threshold sweep turning "how much buffer stock?" into a probability-of-no-shortage curve with a readable diminishing-returns elbow.
  • Sensitivity tornado ranking the seven supply chains by contribution to the P90 cost, redirecting management attention to the two that matter.

A material-shortage plan built on median lead times is a prediction that nothing in seven supply chains will go wrong over thirty months. Monte Carlo simulation in ModelRisk replaces that prediction with a distribution — turning "we have no shortage risk" into "we have a 96% chance of at least one slip and a P90 bill of $5M; here is the $1.8M of dual-sourcing that halves the tail."