Throughput Analysis

Getting throughput requirements wrong is one of the most expensive mistakes in logistics consulting. Sizing to average volume produces a facility that runs fine in February and collapses in November.

The Three Volume Definitions

Average Day: Annual volume / operating days. Useful for year-average staffing benchmarks. Not useful for sizing infrastructure.

Peak Day: Single highest-volume day in the planning period (e.g., Cyber Monday). Designing to this creates 20-40% idle capacity for most of the year. Not the answer.

Design Day (the one you use): The 95th percentile day during the peak planning period.

How to Calculate Design Day

1. Pull 24 months of daily shipped units (or orders, cases - whatever drives capacity)
2. Sort all observations from lowest to highest
3. Find the 95th percentile value

With 500 operating days of data: the 475th value when sorted ascending = design day.

Why 95th and not 99th? The last 1-2% of peak days are frequently one-time events. Designing fixed infrastructure (dock doors, conveyor capacity) for a 1-in-500-day event means designing for conditions that never repeat in exactly that form.

[!key-insight] Design Day Rule Design Day = 95th percentile of daily volume during peak season. Facility runs without constraint on ~95% of all operating days. The remaining 5% is a flex problem (temp labor, overtime, 3PL overflow) - not an infrastructure problem.

Seasonal Curves: How to Build One

Step 1: Pull 24 months of daily shipped units by process area (not weekly - day-of-week patterns matter).

Step 2: Index each day to the annual daily average. Average day = 1.00.

Step 3: Plot the indexed distribution. Look for:

• Seasonal peak months and their shape (sharp spike vs. gradual ramp)
• Day-of-week patterns within any week
• Holiday-specific spikes (one-time vs. repeating)

Step 4: Calculate the 95th percentile index. This is your design day multiplier.

Step 5: Apply separately by function. Receiving peaks lead shipping peaks by 1-3 days. Don’t size the inbound dock to the same peak as the outbound dock.

Within-Week Patterns (Universal)

• Monday/Tuesday: 115-130% of daily average (burning weekend backlog)
• Wednesday/Thursday: 95-105% (steady state)
• Friday: 85-95%
• Saturday (if operating): 60-80% with reduced crew

[!practitioner-note] Within-week percentage patterns are directional estimates from DC operations experience. The specific bands (115-130%, etc.) are not derived from a published study - exact patterns vary by business type, carrier cut times, and order release policies. Validate against your own order history before using in capacity models.

These compound with seasonal multipliers: a Monday in peak season at an e-commerce operation can run at 400-500% of the annual daily average. That’s the number that breaks docks.

Peak:Average Ratios by Industry Vertical

Order Profile Decomposition

Volume tells you how much. Order profile tells you what kind. The work is in the kind.

The decomposition hierarchy:

Orders → Lines per Order → Units per Line → Cases per SKU → Pallets

Volume Formulas by Process Area

Inbound (Receiving):

Pallets/day = (Annual cases received) / (Cases/pallet) / (Operating days)
Peak pallets/day = Average pallets/day × seasonal multiplier

Picking (Outbound):

Picks/day = Orders/day × Avg lines/order
Units/day = Picks/day × Avg units/pick

Pack/Ship:

Cartons/day = (Each orders × cartonization factor) + (Case orders × pass-through factor)

Growth Factor Planning

Physical infrastructure (building, docks, utilities, rack columns) → size to Year 5 peak Automation/mechanized systems → size to Year 3 Labor standards and process design → size to Year 3 peak

Compound growth formula:

Year N Volume = Current Volume × (1 + Growth Rate)^N

Storage note: Inventory growth typically outpaces order volume growth due to SKU proliferation. An operation growing orders at 15%/yr may grow active SKUs at 25-30%/yr. Size storage to 1.7-2.2× current inventory at Year 5 for most growing operations.

The Sweet Spot for Fixed Automation

Peak-to-average ratio under 3:1 is ideal for fixed automation (conveyors, AS/RS, sortation). Above 3:1, flexible automation (AMRs) often performs better economically - the fleet can be scaled seasonally.

High-ratio example: holiday e-commerce at 60,000 units in December, 10,000 average = 6:1 ratio. Fixed infrastructure at that scale is an expensive anchor for 46 weeks.

Productivity Rate Formulas

Productivity Rate (Rp): Average rate at which a task is completed, expressed in units per hour. Accounts for PF&D allowance. Standard input for labor models and equipment sizing.

Blended Productivity Rate (Rb): Average productivity rate of a process composed of multiple tasks in serial progression. Derived from individual task rates in sequence - equivalent to a weighted harmonic mean when tasks are chained.

Warehouse Travel Formulas

Average Aisles Entered (a): Expected number of aisles a picker enters per trip. Assumes: aisles are equal length, slots evenly distributed across all aisles, pick locations randomly distributed across slots.

Travel Distance (D): Expected travel distance per trip. Assumes: aisles evenly distributed across the facility, stops occur in order (no back-tracking between aisles).

Pair with Design Rate (r_D) and PF&D allowances from Labor Modeling.

Academic grounding

The peak-design, order-profile, and travel-distance methods here are grounded in the canonical warehousing literature in warehouse-or-literature-canonical: de Koster, Le-Duc & Roodbergen (2007) for order-picker travel, Gu, Goetschalckx & McGinnis (2010) for warehouse performance evaluation, and Boysen, de Koster & Weidinger (2019) for e-commerce peak demand.