Why is it important to know the difference between throughput, capacity, and demand in operations?

What Are Throughput, Capacity, and Demand?

These three quantities define how a system behaves:

• Demand = how much work customers want
• Capacity = how much work the system can handle
• Throughput = how much work the system actually completes

Throughput is never higher than capacity, and never higher than demand.

Why Throughput, Capacity, and Demand Are Not the Same

1. Demand is external

Customers choose how much work arrives. The system has no control over demand.

2. Capacity is internal

Capacity depends on staffing, machines, processing times, and scheduling. It is the system’s maximum sustainable output.

3. Throughput depends on both

Throughput is the minimum of demand and capacity:

\[ \text{Throughput} = \min(\text{Demand},\ \text{Capacity}) \]

4. When demand exceeds capacity, queues form

If demand > capacity, the system becomes congested and delays grow.

5. When capacity exceeds demand, the system is underutilized

If demand < capacity, throughput is limited by demand, not by the system.

How Throughput, Capacity, and Demand Interact (Step by Step)

Step 1: Identify the bottleneck

The bottleneck is the resource with the lowest capacity. It determines the maximum throughput of the entire system.

Step 2: Compare demand to bottleneck capacity

• If demand < bottleneck capacity → system is demand‑limited.
• If demand > bottleneck capacity → system is capacity‑limited.

Step 3: Determine actual throughput

Throughput equals whichever is smaller:

\[ \text{Throughput} = \min(\text{Demand},\ \text{Bottleneck Capacity}) \]

Step 4: Analyze utilization

Utilization of the bottleneck is:

\[ \rho = \frac{\text{Throughput}}{\text{Capacity}} \]

High utilization (ρ close to 1) leads to long waiting times.

Step 5: Evaluate system stability

A system is stable only if:

\[ \text{Demand} < \text{Capacity} \]

If demand ≥ capacity, queues grow without bound.

Step 6: Use Little’s Law to understand flow

Little’s Law links throughput, inventory, and flow time:

\[ L = \lambda W \]

Where:

• L = average number of jobs in system
• λ = throughput
• W = average flow time

As throughput approaches capacity, W increases sharply.

Numerical Example

A call center can handle 40 calls per hour (capacity). Customers call at a rate of 55 calls per hour (demand).

Step 1: Throughput

Throughput = min(55, 40) = 40 calls/hour.

Step 2: Utilization

\[ \rho = \frac{40}{40} = 1 \] The system is fully utilized.

Step 3: Congestion

Because demand > capacity, 15 calls/hour accumulate in queue. Waiting times grow rapidly.