// case study · distribution center · dock capacity analysis
Why a New DC's Door Count Needed to Go Up, Not Down
The Situation
A Montreal-based furniture company was about to break ground on a new central distribution center — a single facility that would consolidate volume from six existing sites (four full DCs and two satellites). 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, understanding what happens when six independent truck-arrival distributions get superimposed into one dock, and how that combined demand would scale as the consolidated business grew.
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 2.1× 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 consolidated tail— steady-state utilization wasn't the hardest question; the combined tail was. Each of the six existing facilities had its own long right tail of high-dwell LTL arrivals. Superimposing those distributions into one dock doesn't average the tails — it stacks them into shared peak hours. Within the LTL modality, EVT showed door demand scaling roughly 2.6× faster than volume in those peaks: a +10% increase in LTL traffic required about +26%more doors to clear the peak without spillover. Applied to the company's projected growth curve, that non-linearity flagged 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. Once you account for the bimodal LTL/FTL fleet — and for the fact that consolidating six facilities into one stacks their long tails rather than averaging them — the capacity margin the new DC requires is meaningfully 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 when door demand scales roughly 2.6×faster than volume in peak hours, and the company's growth curve was pointing up. We recommended adding doors beyond the architect's baseline to absorb both the consolidation tail and the projected growth.
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.
Tails from six DCs don't average out. They stack.
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