Mobile Robots
How Many Mobile Robots Does a Warehouse Actually Need?
A fleet sizing method that survives contact with reality: round-trip time, congestion loss, charging overhead, peak factor and the buffer that stops the whole thing failing on day one.
Fleet size equals required trips per hour, divided by trips per hour per robot, divided by (1 minus congestion loss), then multiplied by a peak factor. The naive version of that calculation typically undersizes a fleet by 20 % to 35 %, because congestion, charging and peak-hour demand are each left out.
The five-step calculation
- Required trips per hour at peak. Not the daily average divided by hours. Take the busiest hour of the busiest realistic day, because that is when the system either works or visibly fails.
- Round-trip time per robot. Travel out, dock and load, travel back, dwell, unload, plus amortised charging.
- Trips per hour per robot is 3,600 divided by that round trip.
- Congestion loss from robot density: negligible below roughly 0.5 robots per 100 m² of drivable area, 10 % to 15 % near 1.0, and 25 % or more above 1.5.
- Availability for charging beyond the amortised portion, faults, blocked routes and manual intervention. Use 92 % to 95 % for a mature installation and lower for a new one.
A worked example
| Step | Value | Note |
|---|---|---|
| Lines required at peak hour | 1,450 | From order profile analysis |
| Lines per trip | 2.4 | Average picks per shelf presentation |
| Trips required per hour | 604 | 1,450 / 2.4 |
| Round-trip time | 199 s | Measured on the pilot route |
| Trips per hour per robot | 18.1 | 3,600 / 199 |
| Naive fleet size | 33.4 | 604 / 18.1 |
| Drivable area | 6,200 m² | Excludes racking footprint |
| Density at 34 robots | 0.55 / 100 m² | Congestion loss about 6 % |
| After congestion | 35.5 | 33.4 / 0.94 |
| After 93 % availability | 38.2 | 35.5 / 0.93 |
| Fleet, rounded up | 39 | 17 % above the naive figure |
The peak factor argument
Sizing to average demand guarantees failure at peak, and sizing to absolute peak wastes capital that idles most of the year. The workable approach is to size to the 95th percentile hour and design an explicit overflow: a manual picking fallback, a longer shift, or deferred replenishment work that can be pushed out of the peak window.
Peak to average factors of 1.3 to 1.8 are common in distribution. A site running 800 lines per hour on average and 1,450 at peak has a factor of 1.81, and its fleet is genuinely determined by the peak.
Sizing for a site that will change
Fleets are bought once and live for years, while order profiles change every season. Three design decisions determine whether the fleet can grow without a second project.
- Charger headroom. Install charging capacity for the fleet you expect in three years, not the one you buy now. Cabling and floor work during a live operation costs far more than during the original installation.
- Aisle width. An aisle that permits two robots to pass costs shelf positions but removes the deadlock class of failure entirely. Retrofitting width is impossible; retrofitting robots is easy.
- Fleet software licensing. Check how the licence scales. Per-robot licensing that steps at 25 or 50 vehicles can make the 26th robot cost several times the 25th.
A practical convention is to size the physical infrastructure for 150 % of the day-one fleet and buy vehicles to 100 %. Vehicles have lead times measured in weeks; floor work has lead times measured in shutdowns.
Cheaper alternatives to more robots
| Measure | Typical gain | Relative cost |
|---|---|---|
| Slotting fast movers near stations | 10 to 25 % | very low |
| Increasing lines per trip through batching | 15 to 40 % | low |
| Traffic rule and intersection tuning | 5 to 20 % | low |
| Additional pick station | 10 to 30 % | medium |
| Additional chargers at idle points | 4 to 10 % | low |
| Additional robots | linear, then diminishing | high |
Batching is the strongest single lever in most installations, because it attacks the numerator of the whole calculation. Raising lines per trip from 2.4 to 3.1 cuts required trips from 604 to 468 per hour and removes nine robots from the example above.
Frequently asked questions
How do I calculate the number of mobile robots I need?
Divide required trips per hour by trips per hour per robot, then divide by one minus the congestion loss, then divide by expected availability. Trips per hour per robot is 3,600 divided by the measured round-trip time.
Why is the naive calculation always too low?
It omits congestion, charging beyond the amortised portion, faults and peak demand. Together these typically add 20 % to 35 % to the fleet, and each of them is invisible in a small pilot.
Should I size to average or peak demand?
To roughly the 95th percentile hour, with an explicit overflow plan such as manual fallback or deferrable replenishment. Peak to average factors of 1.3 to 1.8 are normal in distribution, so average sizing fails predictably.
What is a safe robot density?
Below about 0.5 robots per 100 m² of drivable area congestion is negligible. Around 1.0 expect 10 % to 15 % loss, and above 1.5 expect 25 % or more, with deadlock risk rising sharply.
What is cheaper than buying more robots?
Batching more picks into each trip, slotting fast-moving items closer to the stations, tuning traffic rules and adding a pick station. Batching in particular reduces the required trips directly and can remove a quarter of the fleet.
Sources
- ISO 3691-4, safety requirements for driverless industrial trucksInternational Organization for Standardization, speed and field requirements limiting effective travel speed
- Robotics at NISTNational Institute of Standards and Technology, robot performance measurement and test methods
- World Robotics, service robots report seriesInternational Federation of Robotics, logistics deployment scale