DEA-NETWORK-SBM - Network Slacks-Based Measure DEA with Window Analysis

Non-parametric network efficiency - Multi-stage slacks-based measure (SBM) with window analysis for longitudinal performance; input and output slacks aggregated across K stages and T-w+1 windows

Tone, K., Tsutsui, M.2009doi:10.1016/j.ejor.2008.05.027 ↗

Overview

DEA-NETWORK-SBM combines Tone & Tsutsui's (2009) Network SBM model with window analysis (Klopp 1985) for longitudinal multi-stage efficiency. The SBM objective directly measures input/output slacks (unlike radial measures), making it unit-invariant and non-radial. Linking constraints (free link activities) allow intermediate products to be endogenously determined. Stage weights ω_k reflect relative importance (best determined via ANP). η^p_o = 1: overall efficient in window p. τ^p_ko = 1: stage-k efficient. Unlike radial DEA, SBM scores are not biased by choosing proportional projections.

Output: Efficiency, higher is better
Data: Crisp
Size: 5+ alternatives, K*(m_k+r_k) ≤ n*w criteria works best
Used for: R&D organizational performance (multi-stage value creation), supply chain multi-stage efficiency, hospital production chains (diagnosis → treatment → discharge), innovation systems (input → knowledge → commercialisation)

Look elsewhere when

•Single period and single stage - use standard SBM-DEA
•No intermediate linking products between stages - use standard DEA
•Carryover assets between periods needed - use Tone & Tsutsui (2014) dynamic network SBM
•Radial efficiency interpretation preferred - use Network DEA (radial, DEA-NETWORK)

Assumptions to verify

K-stage production network is appropriate for the application
Intermediate linking products between stages are measurable
Free link activities assumption is justified (not all intermediate output must equal intermediate input)
VRS is appropriate (Σλ=1 per stage per window)
Stage weights ω_k derived from reliable source (ANP, expert judgment, or justified equal weights)
Window width w appropriate for data availability

Edge cases and pitfalls

Using equal stage weights without considering relative importance - use ANP or expert judgment for ω_k. Equal weights may distort rankings when stages differ in strategic importance.
Solving the fractional program directly - always apply Charnes-Cooper transformation to convert to a linear program (Eq.7.1 is fractional; LP form is required).
Confusing free link activities with fixed intermediate products - in Network SBM the linking constraints equate stage-f output intensities with stage-h input intensities endogenously (not constrained to observed values).

How to cite

Tone, K.; Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2008.05.027

BibTeX RIS APA (.txt)DOI ↗

System ID, as it appears in reports and the API

DEA-NETWORK-SBM

Overview

Output

Efficiency, higher is better

Data

Crisp

Size

5+ alternatives, K*(m_k+r_k) ≤ n*w criteria works best

Used for

R&D organizational performance (multi-stage value creation), supply chain multi-stage efficiency, hospital production chains (diagnosis → treatment → discharge), innovation systems (input → knowledge → commercialisation)

Look elsewhere when

•Single period and single stage - use standard SBM-DEA
•No intermediate linking products between stages - use standard DEA
•Carryover assets between periods needed - use Tone & Tsutsui (2014) dynamic network SBM
•Radial efficiency interpretation preferred - use Network DEA (radial, DEA-NETWORK)

Assumptions to verify

K-stage production network is appropriate for the application

Intermediate linking products between stages are measurable

Free link activities assumption is justified (not all intermediate output must equal intermediate input)

VRS is appropriate (Σλ=1 per stage per window)

Stage weights ω_k derived from reliable source (ANP, expert judgment, or justified equal weights)

Window width w appropriate for data availability

Edge cases and pitfalls

Using equal stage weights without considering relative importance - use ANP or expert judgment for ω_k. Equal weights may distort rankings when stages differ in strategic importance.

Solving the fractional program directly - always apply Charnes-Cooper transformation to convert to a linear program (Eq.7.1 is fractional; LP form is required).

Confusing free link activities with fixed intermediate products - in Network SBM the linking constraints equate stage-f output intensities with stage-h input intensities endogenously (not constrained to observed values).