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A method for estimating the returns to scale of two-stage supply chains using intermediate data
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S. Ghanaati   , M. Rostamy malkhalifeh , J. Esmaily , M. Momeni |
| Department of Mathematics, SR. C., Islamic Azad University, Tehran, Iran |
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Abstract: (4 Views) |
Estimating the returns to scale (RTS) of two-stage supply chains is a critical topic in Data Envelopment Analysis (DEA). Traditional black-box DEA models calculate RTS by ignoring intermediate data—the essential connecting factors between production stages—which can lead to biased and unreliable evaluations. To address this limitation, this paper proposes a novel method for estimating the overall system’s RTS in a dependent state. By building upon the CCR coverage form model introduced by Banker et al., the proposed approach strictly maintains the internal structural relationship between the first and second stages. Specifically, the RTS of the first stage is estimated initially, and these output changes are then incorporated as input constraints for the second stage to determine the overall system’s RTS. The practical applicability of this proposed method is demonstrated using an empirical dataset of 24 non-life insurance companies in Taiwan. The findings reveal that the dependent model is more restrictive and logically consistent than the independent approach; whenever the overall RTS in the dependent state is constant, at least one of the individual stages also exhibits constant RTS. Ultimately, incorporating intermediate data provides managers and policymakers with a more robust, realistic evaluation tool for capacity planning and resource allocation in complex, multi-stage production environments.
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| Keywords: Data envelopment analysis, returns to scale, supply chain, efficiency. |
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Full-Text [PDF 444 kb]
(4 Downloads)
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Type of Study: Research |
Subject:
General
Received: 2025/11/2 | Accepted: 2025/12/20 | Published: 2026/01/11
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