// case study · distribution center · dock capacity analysis
When the Average Truck Doesn't Exist — Validating a New DC's Dock Door Plan
The Situation
A Montreal-based furniture company was about to break ground on a new distribution center. Their architect had recommended a specific number of dock doors, and the operations team was skeptical. Doors carry permanent capacity implications — once the concrete is poured they are expensive to revisit — and the team wanted a second opinion grounded in the actual behavior of their truck fleet, not rules of thumb.
The ask looked simple on the surface: is this the right door count? Answering it required pulling apart what a “truck” actually is at this facility, and what growth in traffic would look like over the facility's life.
What We Built
Before you can size a dock, you need to understand what comes through it. Averages don't work — a dock serves individual trucks, and those trucks behave very differently depending on what they carry. We built the analysis up from the truck-level distribution.
- ✓Hartigan's Dip Test for bimodality— a formal test of whether the truck-size distribution was a single bell curve or actually two. It flagged the distribution as significantly non-unimodal, giving statistical justification to split the data into modes rather than model it as one population.
- ✓Gaussian Mixture Model (k=2)— fitted two component distributions to the payload data. The result: about 55% of trucks were LTL-class with much smaller typical payloads; about 45%were full truckloads. The blended average sat close to a clean “about 500 units” — except almost no truck in the fleet actually carried anywhere near that number. The average was a fiction.
- ✓Service-time decomposition— every truck consumes a roughly constant fixed component of dock time regardless of payload (yard navigation, check-in, paperwork, dock-out), plus a variable component that scales with units at the company's forklift rate. Applied to each mode, the math was decisive: LTL trucks consume 2.3× more dock time per unit than FTL trucks. Their fixed overhead amortizes over far fewer units, which makes every LTL arrival disproportionately expensive in dock capacity relative to the goods it delivers.
- ✓Growth-adjusted queue model— projected truck arrivals forward using the company's own DC growth curves, and stress-tested a rising LTL share (the historical pattern at their other facilities as volume grew, and the expensive trucks on a per-unit basis).
- ✓Extreme value theory (EVT) on the LTL tail— steady-state utilization wasn't the hardest question; the tail was. EVT applied to the LTL arrival distribution, under projected volume growth, flagged a recurring peak: the long right tail of high-dwell trucks would cluster into a capacity-exceeding event roughly once a month— enough to reliably trigger carrier detention charges or dispatch delays. Not a rare edge case. A recurring monthly cost.
The Result
The architect's door count was right — but for a different reason than the back-of-envelope math would have suggested. Working from the blended average would have pointed to a lower count, because that “average truck” is convenient and completely fictional. The real fleet is a mix of fast-moving FTL and expensive-per-unit LTL, and the capacity margin that fleet requires is larger than the average implies.
More importantly, once we had a real service-time distribution we could compare the cost of adding doors against the cost of congestion. The marginal cost of a door during construction is small. The opportunity cost of trucks waiting in the yard is not — especially once the EVT tail analysis showed that under projected growth, the long LTL tail would cluster into a capacity-exceeding peak roughly once a month, recurring enough to make carrier detention charges and dispatch delays a predictable operating cost. We recommended adding doors beyond the architect's baseline to absorb that growth and that tail.
Satellite imagery of the facility today shows the expansion was the right call. The extra capacity is in use, the facility isn't running congested at peak, and the doors that were “extra” on paper are doing real work.
Knowing the average doesn't matter if the average truck doesn't exist.
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