A Fuzzy Additive DEA Framework for Conditional Short-Run Scale-Direction Assessment with Quasi-Fixed Inputs and Minimum Service-Level Constraints

Hossein Nakhai, Marzieh; Rostamy Malkhalifeh, Mohsen; Hosseinzadeh Lotfi, Farhad

doi:10.30473/coam.2026.79995.1484

Articles in Press

Document Type : Research Article

Authors

Department of Mathematics, SR.C., Islamic Azad University, Tehran, Iran

https://doi.org/10.30473/coam.2026.79995.1484

Abstract

A fuzzy additive data envelopment analysis (DEA) framework is developed to evaluate the scale direction in the short run when part of the capacity is quasi-fixed and a minimum service level is required. A common-realization triangular possibility method is formulated as two sign-dependent linear programs, and the scale parameter is studied over the optimal face to reduce dependence on an arbitrary solver-selected optimal solution. The framework is applied to 2024 National Transit Database (NTD) data for 284 directly operated motor-bus agencies. The additive model, the capacity-restricted model, the deterministic capacity- and service-constrained model, and the baseline fuzzy model identify 8, 16, 34, and 28 agencies on the frontier, respectively. The baseline fuzzy frontier includes 15 agencies with an increasing direction, 11 with no improvement, and 2 with a decreasing direction, according to the specified LP rule. Fleet size and the number of revenue hours are strongly correlated (Pearson r = 0.9909). A 21-point service-floor sensitivity analysis, an independent LP implementation, alternative treatments of uncertainty, and stratified-sample models show that the results depend strongly on the assumed technology and on the uncertainty assumptions. In particular, scaling the service floor with the scale parameter changes the classification of the baseline frontier to 3, 5, and 20 agencies in the increasing, zero-improvement, and decreasing categories, respectively. The mathematical results establish feasibility and boundedness, the exactness of the two-sign-branch decomposition, and the identifiability of the effective fuzzy spread ε_f = δ(1 - η). The scale-direction classifications describe the specified global constrained program and should not be interpreted as estimates of local production elasticity.

Highlights

A conditional fuzzy additive DEA model assesses short-run scale direction with quasi-fixed fleet capacity
A minimum service-level constraint keeps benchmarks from gaining efficiency by cutting service
Two sign-dependent linear programs give an exact formulation of the common-realization fuzzy model
Optimal-face scale intervals make direction labels independent of the solver’s choice of optimum
Applied to 284 U.S. bus agencies, with sensitivity analyses of service floor, fuzzy spread, and thresholds

Keywords

Main Subjects

Optimal Operational Scheduling

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A Fuzzy Additive DEA Framework for Conditional Short-Run Scale-Direction Assessment with Quasi-Fixed Inputs and Minimum Service-Level Constraints

References

References

Articles in Press, Corrected Proof Available Online from 10 November 2026

Articles in Press, Corrected Proof
Available Online from 10 November 2026