What is capacity utilization?

Capacity utilization is the share of a system's maximum possible output that it actually uses. A factory producing 800 units when it could produce 1,000 has a utilization of 80%. It guides decisions about investment, pricing and staffing, since idle capacity costs money but a system with no spare capacity cannot absorb surprises.

How it works

The formula is utilization = actual output / maximum output. Low utilization spreads fixed costs over fewer units, so each unit costs more. High utilization lowers unit cost, but waiting times rise sharply as utilization approaches 100%, because any variation in arrivals or service time forms a queue that has no spare capacity to clear. In a simple single-server queue, the average waiting time grows in proportion to ρ / (1 - ρ), where ρ is utilization.

The trade-off is between efficiency and responsiveness. Many operations aim for 70 to 85% where variation is high, and higher where demand is predictable.

Example

Say a clinic has 10 consultation slots per hour and fills 8. Utilization is 80%, and the factor ρ / (1 - ρ) is 0.8 / 0.2 = 4. At 90%, it is 0.9 / 0.1 = 9, so average queueing time more than doubles for ten more points of utilization. At 95% it is 19, nearly five times the 80% value. A small increase in load near the limit has a large effect on waiting. The numbers are an illustration.

How to model it in Machinations

Model capacity as the maximum rate on a Converter or Drain that serves a Queue, and arrivals with a Source whose rate is a Lever. Add a Register that divides actual output by capacity. Play at several arrival rates and chart the Queue length to see waiting rise steeply as utilization approaches 100%.