DEA-BCC - Data Envelopment Analysis (BCC / VRS model)

Overview

BCC extends CCR by adding the convexity constraint Σλ_j=1, allowing Variable Returns to Scale (VRS). BCC efficiency ≥ CCR efficiency always. Use BCC when DMUs operate at different scales (e.g., hospitals of varying sizes). Scale efficiency = CCR/BCC reveals whether inefficiency stems from scale vs. pure technical causes.

Output

Efficiency, higher is better

Data

Crisp

Size

6+ alternatives, p+q ≤ m/3 criteria works best

Used for

Healthcare efficiency benchmarking, education sector performance, banking and financial institutions, logistics and supply chain, public sector DMUs with varying scale

Look elsewhere when

Assumptions to verify

• All inputs and outputs strictly positive
• DMUs are homogeneous (same industry/activity type)
• VRS assumption justified (DMUs operate at different scales)
• Sufficient DMUs relative to dimensions: m ≥ 3·(p+q)

Edge cases and pitfalls

• Confusing BCC efficiency (pure technical) with CCR efficiency (overall). BCC=1 does not mean the DMU is at optimal scale.

• Using BCC with too few DMUs: VRS frontier can declare nearly all DMUs efficient (frontier crowding). Rule of thumb: m ≥ 3·(p+q).

• Mixing input/output orientation between CCR and BCC when computing scale efficiency.

Works with

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