A two-stage data envelopment analysis model for measuring performance in three-level supply chains

• We present a two-stage DEA method to evaluate the performance of three-level supply chains.
• A comprehensive evaluation of the entire chain and each of its two-stage sub-chains is provided.
• A numerical example shows the applicability and efficiency of the proposed framework.
• A three-level supply chain is shown to be efficient only if both its minor chains are efficient.
• The proposed method can be easily implemented in any multi-level supply chain.

Data Envelopment Analysis (DEA) has been widely used to evaluate supply chain performances. In conventional DEA, supply chains are represented as black boxes where only the initial inputs and final outputs are considered to measure their efficiency. However, an integrated model measuring both the efficiency of the entire supply chain and that of all its components at all levels is essential for a comprehensive evaluation. This study presents a two-stage DEA method to evaluate the performance of a three-level supply chain including suppliers, manufacturers and distributors. The proposed model can be used both under the constant returns to scale and the variable returns to scale assumptions and can be easily implemented for comprehensive analysis of multi-level supply chains. We present a numerical example to demonstrate applicability of the proposed model and exhibit the efficacy and effectiveness of the proposed algorithms and procedures. In particular, the numerical results demonstrate that the entire supply chain is “comprehensively” efficient only if efficient supplier–manufacturer and manufacturer–distributor relationships are established.