Formula
Net capacity per robot = operating minutes × utilization × (1 − downtime) ÷ cycle minutes. Operating robots = ceiling(tasks ÷ net capacity). Purchase fleet = ceiling(operating robots × (1 + spare allowance)).
What the result means
The purchase fleet is a deterministic planning estimate based on average task time. Congestion, queueing, and uneven task geography can increase the actual requirement.
Validate the result with a site simulation before procurement, especially where robots share narrow aisles, elevators, or workstations.