Measuring efficiency in DEA in the presence of common inputs
Bibliographic record
Abstract
Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of a set of decision-making units (DMUs). It is commonly assumed that the DMUs are independent of one another, in that each has its own quantities of a set of inputs and outputs. In case this assumption of independence of DMUs holds, decreasing the inputs of one DMU will not affect the inputs of others. The current paper moves beyond the conventional framework and examines a problem setting where there is an interdependence among the DMUs. Consider the case where the members of a given subgroup of DMUs have an input in common, such as would be the case if a set of highway maintenance crews in a district are under the jurisdiction of a district supervisor and district-level resources. The efficiency measurement difficulty created by this “shared’ resource phenomenon is that in attempting to move an inefficient crew towards the frontier by reducing that shared resource (hence penalising that crew), the other crews in that same district will be equally penalised. Specifically, decreasing district resources in relation to their impact on a maintenance crew will cause that resource to decrease as well for other members of the same group. The conventional (input-oriented) DEA model that does not cater for such interdependence situations will fail to address this important issue. To capture this interdependence, we develop a new DEA-like methodology. One of the properties of this new methodology is that its production possibility set cannot be defined in the same manner as in the conventional DEA setting. This is due to the fact that when the DMU under evaluation is projected towards the frontier, the input/output structures of the other units in the same group are altered, unlike the conventional situation where the structures of the other DMUs remain fixed. We apply this new methodology to the problem of evaluating a set of departments in a university setting, where the departments are grouped under various faculties.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.017 | 0.037 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".