Non-parametric LP-based method that gives a relative efficiency score to similar units (branches, hospitals, schools) operating with multiple inputs and multiple outputs. The foundational efficiency OR problem; Charnes-Cooper-Rhodes (1978) CCR model; Banker-Charnes-Cooper (1984) BCC model.
In plain words
Sound familiar?
- We are a mid-size bank with 100-500 branches; each branch carries different headcount, floor space, computers, revenue, deposit and loan volumes — we answer 'which branches are efficient and which are not' with simple ratios (revenue per employee) and the multi-input multi-output reality is not reflected.
- We are a multi-site hospital chain with 200-1500 beds; each hospital has different doctor and nurse counts, beds, equipment and produces different numbers of patients + treatment-success rates — efficiency comparison is intuitive and there is no scientific benchmarking structure.
- We are an education directorate (provincial MEB or large private education network) with hundreds of schools; each school has different teachers, budget, classrooms and produces different exam scores + graduate + enrolment counts — there is no consistent model for school efficiency comparison.
- We are a public body running province-by-province efficiency comparisons (e.g. Ministry of Health provincial directorate performance, MEB provincial directorates, regional development agencies); each province produces different outputs with different resources, and single-ratio metrics attract criticism.
- We are a retail or service franchise with 50-500 outlets per year; outlet efficiency comparison has multi-dimensional structure (floor area, headcount, location, inventory investment) and outcomes (revenue, customer count, customer loyalty) — simple ratios fall short.
- We are an agricultural cooperative manager (200+ producers); for producer-level efficiency (inputs: seed + fertiliser + labour vs outputs: yield + quality + cost-adjusted revenue) we are looking into a DEA-based method.
- We work at a regulatory body (BDDK, SPK, Ministry of Health, MEB); we publish sector-wide relative-efficiency reports — DEA-based studies are the canonical reference, but for methodology choice (CCR vs BCC, input- vs output-oriented) we need a structured decision process.
Why it matters
How it's solved
Technical depth
How it's solved
Technical depthIn one sentence: Solve one LP per unit (DMU) — each LP answers “is this unit as efficient as the weighted combination of the others”; units scoring 1 are efficient (on the frontier), units scoring under 1 receive concrete peer references (which efficient units they should learn from).
This problem appears in Operations Research (the discipline that uses math and computers to solve business decisions) literature as Data Envelopment Analysis (DEA) — the foundational efficiency-OR problem, a non-parametric (no assumed production function) LP-based method. The foundational work dates to the late 1970s and 1980s: the CCR model (Constant Returns to Scale) formulated as an LP per DMU, and the BCC model (Variable Returns to Scale) which adds a scale-dependent convex frontier. DEA is now a 40+ year academic field with 10,000+ papers. The solution runs in three stages:
1. Modelling. Input data: (a) DMU set (Decision Making Units — homogeneous units) — N units to compare (e.g. 200 bank branches, 80 hospitals, 500 schools, 81 provinces), each DMU of similar structure (same operation type, comparable scale), (b) input vector — for each DMU, m inputs (e.g. for a branch: headcount, floor space, computer count, rent; for a hospital: doctor count, nurses, beds, equipment, budget), inputs are resource consumptions to be reduced, (c) output vector — for each DMU, s outputs (e.g. for a branch: deposit volume, loan count, customer count, revenue; for a hospital: patients, surgeries, treatment success, average length-of-stay inverse), outputs are results to be increased, (d) sample-size check — Cook-Seiford (2009) rule: N ≥ 3 × (m + s); e.g. 5 inputs + 4 outputs requires at least 27 DMUs; otherwise the model is under-determined and almost every DMU comes out efficient, (e) CCR vs BCC choice — CCR (Charnes-Cooper-Rhodes 1978) assumes all DMUs share the same scale efficiency; BCC (Banker-Charnes-Cooper 1984) is a scale-dependent convex frontier (the scale advantage of a large branch is recognised); BCC + scale-efficiency decomposition separates technical from scale inefficiency, (f) input-oriented vs output-oriented — input-oriented: hold outputs fixed and shrink inputs (branch scenario: customer count fixed, reduce headcount + space); output-oriented: hold inputs fixed and grow outputs (hospital scenario: doctors + beds fixed, grow patients + success). Decision variables (CCR LP formulation, after the Charnes-Cooper transformation, a separate LP per DMU ‘o’): u_r (weight for each output r, r=1..s), v_i (weight for each input i, i=1..m); constraints: for each DMU j, sum_r u_r × y_rj - sum_i v_i × x_ij ≤ 0 (no DMU’s virtual ratio exceeds 1), sum_i v_i × x_io = 1 (normalisation); objective: maximise sum_r u_r × y_ro (the virtual ratio of DMU o). The efficiency score is θ*_o = optimal objective value, 0 < θ*_o ≤ 1.
2. Solver-driven decision. N LPs are solved for N DMUs (one LP per DMU); modern open-source LP solvers (built on the same simplex foundation as Charnes-Cooper-Rhodes 1978 — Dantzig 1947) solve 1000+ DMU models with 10-20 inputs + outputs in seconds; commercial or mature open-source LP solvers suffice, no MIP requirement (classical DEA is pure LP). Stage one: for each DMU, the efficiency score θ*_o and the efficient peers λ*_j (which efficient DMUs the inefficient DMU is projected onto, weighted). Stage two — slack-based supplementary measurement: a weakness of radial DEA (CCR/BCC) is that the efficiency score can be 1 yet there can still be slack (unused input or shortfall in output); Tone (2001) SBM (Slack-Based Measure) is the non-radial model; it includes all slacks. Stage three — super-efficiency (Andersen and Petersen 1993): ranking among efficient DMUs (classical DEA gives a score of 1 to every efficient DMU, with no internal ranking); the super-efficiency model excludes the DMU from its own peer set and computes a score > 1 (a ranking among the efficient ones). Stage four — Malmquist productivity index: time-dependent dynamic (DEA is single-period static); Caves-Christensen-Diewert (1982) Malmquist-DEA plus Färe-Grosskopf-Lindgren-Roos (1992); productivity change between two periods is decomposed into technical change + efficiency change. Stage five — Tobit regression: regression analysis of the determinants of DEA scores (0-1 censored) against DMU characteristics (age, location, scale); Simar-Wilson (2007) is the modern bootstrap-based revision. Algorithm choice: core DEA needs CCR + BCC + slack analysis; advanced analysis adds super-efficiency + Malmquist + Tobit.
3. Field integration. Output in four layers: (a) operational — efficiency score table per DMU (θ*, ranking, percentile); a peer-benchmark report per inefficient DMU (“branch X is at 0.74 efficiency, its peers are Y and Z — projected onto 52% of Y + 48% of Z”); a slack report (how many input units to reduce + how many output units to grow for improvement), (b) planning — annual efficiency benchmarking report (DMU comparison, ranking trend across years, Malmquist productivity decomposition of yearly change), (c) strategic / investment — investment-decision support (which DMU to channel resources to, which to consolidate, which peer example to scale), objective evidence for budget allocation, (d) regulatory / publication — sector-wide relative-efficiency reports (for regulators such as BDDK, SPK, Ministry of Health, MEB), objective methodology for performance-based oversight of public bodies. Upstream integration: enterprise systems (DMU records — branch, hospital, school masters), financial reporting (input-output data — revenue, expense, patient counts, exam scores), CRM (customer/patient/student counts), BI / dashboard platform (efficiency-score visualisation). Quarterly efficiency committee: score trend, peer-guided improvement plans for inefficient DMUs, outlier DMU detection, sample-size check (when new DMUs are added, does N ≥ 3(m+s) still hold), Malmquist productivity report.
Alternatives
Manual + single-ratio metrics + spreadsheet
FreeZero licence
Who it fits: Small scale (≤30 DMUs), 1-2 inputs + 1-2 outputs, periodic benchmarking
- + Zero software cost
- + Familiar tool for the operations team
- + Fast computation, easy to understand
- + Marginally useful when DMU count is low
- − Multi-input multi-output reality is ignored
- − Single-ratio metric (revenue / employee) yields misranking
- − No peer benchmark — inefficient units lack concrete improvement guidance
- − No CCR/BCC, scale efficiency, Malmquist
- − 5-20M TRY of operational margin missed per year at 100+ DMU scale
Spreadsheet + LP add-in, hand-coded DEA model
FreeZero to low licence (within an office suite)
Who it fits: Medium scale (30-100 DMUs), first DEA pilot, academic research
- + Low investment, runs with an LP add-in
- + CCR + BCC core model can be built
- + Transparent to set up with academic references
- + Suitable for university collaboration (40+ theses on YÖK as reference implementations)
- − Hand-coding an LP per DMU is tedious at 100+ DMU scale
- − Slack analysis, super-efficiency, Malmquist are awkward by hand
- − Outlier detection is not automatic
- − Sample-size discipline depends on the practitioner
- − Weak version and revision control
Generic DEA software (academic / SMB)
Enterprise200K-1M TRY licence + 60K-300K TRY/year maintenance (regional market observation)
Who it fits: Medium-large scale (100-500 DMUs), annual benchmarking, in-house analytics team
- + CCR + BCC + SBM + super-efficiency + Malmquist modules integrated
- + Automatic outlier detection, sample-size check
- + Automatic peer-benchmark reports
- + Dashboard visualisation
- + Local-language interface and support
- − Mid-range licence cost
- − Dependence on a specific DEA tool
- − Integration of leading-edge models (network DEA, dynamic DEA) may be limited
- − Data-export format control is critical
Open-source solver + academic DEA reference + consulting
Open SourceLicence free; 12-20 weeks internal development + consulting, or 400K-1.2M TRY
Who it fits: Organisation with a tech + OR team, integration with existing BI/analytics, academic partnership
- + No licence cost
- + The core models of the efficiency-analysis method are well-documented in canonical textbooks and can be implemented on open-source solvers
- + CCR + BCC + SBM + super-efficiency + Malmquist + Tobit all have open-source reference implementations
- + 40+ YÖK theses as academic references
- + Full data ownership
- + Transparent methodology for regulatory/academic publication
- − In-house OR + statistics specialist + infrastructure team required
- − 4-9 months from academic prototype to field-ready system
- − Maintenance responsibility on the operator
- − Operations-team interface is a separate build
International BI / performance-management platform + DEA module
Enterprise500K-3M EUR licence + 200K-800K EUR/year maintenance
Who it fits: Large scale (500+ DMUs), multi-site organisation, regulatory publication requirement, banking / insurance / healthcare prime operator
- + Mature DEA module covering all models (CCR, BCC, SBM, super-efficiency, Malmquist, network DEA)
- + BI dashboard + drill-down DMU analysis
- + Integrated Tobit regression + modern bootstrap-based revision
- + Standard regulatory-reporting templates
- + Automatic multi-period comparison
- − High licence + long (12-24 months) rollout
- − Local-regulation customisation adds project length
- − Wide training programme for operations + analytics teams
- − DEA methodology parameter control may be black-box
- − High single-supplier lock-in risk
Recommendation
Ask in the meeting
- Is the choice between CCR and BCC automatic or left to the user? In which conditions is CCR vs BCC recommended — does the system carry a methodology guide?
- How is the input-oriented vs output-oriented selection made? Can both orientations be computed in parallel and a peer-benchmark comparison produced?
- Is the slack-based measure (SBM, a non-radial model) supported? How are non-radial extra slacks reported?
- Is the super-efficiency model supported for ranking among efficient units? Is there an automatic procedure for flagging extreme super-efficiency scores (>2)?
- Is the Malmquist productivity index supported for time-dependent dynamic analysis? Is the decomposition of productivity change into technical change + efficiency change automatic?
- Is outlier DMU detection (DMUs that distort the frontier with extreme low-input or extreme high-output) automatic? Is the sample-size rule (N ≥ 3 × (m + s)) enforced by the system?
- Is a second-stage analysis regressing the scores against determinant factors (Tobit regression or a bootstrap-based modern revision) supported?
- If the contract ends, in which standard format (CSV, JSON, parametric model file) can we export DMU definitions, input-output history, DEA score archive, peer-benchmark reports and Malmquist analysis history?
Technical details
Editor’s note
This is the 100th problem on OptDir — the cornerstone of the efficiency-measurement family. It compares similar units operating with multiple inputs and multiple outputs and gives a comprehensive efficiency score beyond single-ratio metrics (revenue/employee, patients/bed).
In plain language, the problem is called “branch comparison”, “hospital efficiency benchmark” or “school performance ranking”. In the academic literature its canonical name is Data Envelopment Analysis (DEA), the foundational efficiency-OR problem. Charnes, Cooper and Rhodes (1978) introduced the CCR model in the European Journal of Operational Research (the founding text of DEA); Banker, Charnes and Cooper (1984) added the BCC model (variable returns to scale) in Management Science; Cooper, Seiford and Tone (2007) is the canonical textbook; Cook and Seiford (2009) is the 30-year summary; Emrouznejad and Yang (2018) survey 40 years (1978-2016) of DEA literature with 10,000+ academic papers. In modern industry it is the field-standard approach for relative-efficiency benchmarking in banking, insurance, healthcare, education, public services and agriculture; in TR, DEA-based efficiency studies are the canonical reference in regulatory reports by BDDK, SPK, the Ministry of Health and MEB.
The point most often overlooked in this segment: the choice between CCR (constant returns to scale) and BCC (variable returns to scale). CCR (Charnes-Cooper-Rhodes 1978, the original model) assumes all DMUs share the same scale efficiency — large and small branches at the same scale-independence. In practice: a large branch looks automatically efficient under CCR thanks to scale advantages, and small branches are unfairly penalised. BCC (Banker-Charnes-Cooper 1984) is a scale-dependent convex frontier — the scale advantage of a large branch is recognised; it decomposes technical efficiency (utilisation) and scale efficiency (scale). CCR score = technical efficiency × scale efficiency; BCC separates the factor. Practitioners commonly use CCR; BCC is more realistic, and reporting both in parallel is essential for correct decision support.
Second overlooked point: the sample-size adequacy rule. The Cook-Seiford (2009) rule: number of DMUs N ≥ 3 × (number of inputs m + number of outputs s). For example, a 5-input + 4-output model needs at least 27 DMUs; otherwise the model is under-determined and almost every DMU comes out efficient — statistically meaningless. Practitioners feed 30 DMUs into a 10-input + 8-output model and produce an “everyone’s efficient” report; that report is methodologically broken. The rule must be re-checked whenever a DMU is added or the input-output list is expanded.
Third overlooked point: outliers break the frontier. The most critical weakness of DEA: an outlier unit (anomalously high output or anomalously low input — data-entry error, special-status DMU) pushes the frontier outward and the score of every other unit falls incorrectly. Without outlier detection (e.g. flagging units with super-efficiency score > 2, bootstrap-based confidence-interval checks) DEA results can be manipulated or misdirected.
Fourth overlooked point: the subjectivity of input-output selection. The input-output list of a DEA model materially changes the results. On the same 200 branches, an “(headcount + space) input + (revenue) output” model and an “(headcount + space + computers + rent) input + (revenue + customer count + loan count) output” model produce different rankings. Deliberate-manipulation risk (favourable inputs-outputs are added so an inefficient unit looks efficient) is documented in the literature. Input-output selection is a methodological decision — it must be set with stakeholders via a transparent process and not changed afterwards.
Distinction from #018 (Markowitz Portfolio): #018 is financial asset selection / weighting — trade-off between expected return and risk (mean-variance); DEA is relative-efficiency measurement — unit comparison, production function (multi-input multi-output). Different domains — the common thread: both are optimisation-based objective metrics, and both are practically sensitive to subjective input choice (covariance matrix vs input-output list).
A step-by-step path for an SMB
Stage 1 — Measure first, plan later. At least 2-3 years of DMU-level data: DMU list (branches, hospitals, schools, etc. — homogeneous units), per-DMU annual input data (headcount, space, computers, budget), per-DMU annual output data (revenue, customer count, patients, exam score). Data quality: consistent definitions (e.g. is ‘headcount’ FTE or head-count, are contractors included), units (TRY, count, m², metres), time consistency (the same period across DMUs). Sample-size check: is N ≥ 3 × (m + s) — if not, narrow the input-output list or expand the DMU set.
Stage 2 — Build the input-output matrix. Following the academic literature (Cook-Seiford 2009; Cooper-Seiford-Tone 2007) and sector-specific DEA studies, set the input-output list through a transparent methodology. For example, a common input-output set for bank branches in the Turkish DEA literature: inputs (headcount, space, rent, IT equipment), outputs (deposit, loan, customer count, revenue). For hospitals: inputs (doctors, nurses, beds, budget), outputs (patients, surgeries, treatment success). Stakeholder agreement: the input-output list is not to be changed afterwards (manipulation risk).
Stage 3 — Pilot. 8-12 weeks. Run CCR + BCC + slack analysis in parallel on a subset (e.g. the most homogeneous 30-50 branches, or one regional directorate); produce outlier detection, sample-size check and a peer-benchmark report. Decisions stay with the manager; DEA gives suggestions. The success criterion is in writing in advance: acceptance rate of improvement plans for inefficient DMUs +30% minimum (thanks to the concrete peer-guided evidence), CCR vs BCC score gap reported (scale-efficiency analysis), outlier detection applied.
Stage 4 — Rollout. Over 6-12 months, expand to the full DMU catalogue + super-efficiency (ranking among efficient units) + Malmquist productivity index (year-on-year change) + Tobit regression (determinant analysis). Quarterly efficiency committee: score trend, status of peer-guided improvement plans for inefficient DMUs, outlier detection, was a new DMU added (sample-size check), has the input-output list stayed the same (methodology consistency).
Risks — what can go wrong
Subjectivity of input-output selection (deliberate-manipulation risk). The input-output list materially shifts the results. The management of an inefficient branch may push to add a ‘rent cost’ input (the branch is in a high-rent area; once added it starts to look efficient). This is documented manipulation risk. Fix: set the input-output list as a methodological decision with stakeholders via a transparent process; align with sector-standard academic references; do not change it later (consistency is required for annual benchmarking). If a change is required, publish before/after comparison.
Outliers distort the frontier. An outlier unit (data-entry error, special-status DMU, abnormal performance) pushes the frontier outward; every other unit’s score drops incorrectly. Fix: outlier detection (manual review of units with super-efficiency score > 2; bootstrap-based confidence-interval analysis — Simar-Wilson 2007); if the outlier is a data-entry error, fix it; if it is special status, exclude it from the model and report it separately.
Ignoring the sample-size rule (N < 3 × (m + s)). Cook-Seiford (2009) rule: DMU count ≥ 3 × (inputs + outputs). Push 30 DMUs into a 10-input + 8-output model and almost every DMU comes out efficient — statistically meaningless. Fix: narrow the input-output list to fit the DMU count (e.g. 5 inputs + 4 outputs needs at least 27 DMUs); aggregate less-critical inputs into a single variable (e.g. all operating costs as one ’total operating cost’ input). Re-check the rule whenever a new DMU is added or the list is expanded.
Wrong CCR/BCC choice (scale-independence assumption breaks). CCR (constant returns to scale) treats large and small DMUs as scale-equivalent; in practice large branches look automatically efficient under CCR. BCC (variable returns to scale) is scale-dependent; it decomposes technical vs scale efficiency. Fix: always report both CCR and BCC in parallel; compute scale efficiency = CCR score / BCC score; choose the methodology based on sector and the DMU scale range (narrow range — CCR suffices; wide range — BCC is essential).
Single-supplier DEA-software lock-in. Without a contractual clause for ‘annual standard-format export (CSV, JSON) of DMU definitions, input-output history, DEA score archive, peer-benchmark reports and Malmquist analysis history’, years of accumulated efficiency-analysis memory get locked to the vendor. While regulatory/academic publication needs methodological transparency (CCR/BCC selection parameters, outlier-detection thresholds), a black-box DEA tool cannot provide that. The contract must require methodology parameter export and standard-format output.
A technical view of the solution method
| Approach | Typical scale | Solve time | Notes |
|---|---|---|---|
| Single-ratio metrics + spreadsheet | Small, ≤30 DMUs | instant | Multi-input multi-output ignored |
| CCR (Charnes-Cooper-Rhodes 1978) | Medium, 30-300 DMUs | seconds | Foundational; scale-independent assumption |
| BCC (Banker-Charnes-Cooper 1984) | Medium, 30-300 DMUs | seconds | Scale-dependent; technical + scale-efficiency decomposition |
| SBM (Tone 2001 — Slack-Based Measure) | Medium, 30-300 DMUs | seconds | Non-radial, includes slacks |
| Super-efficiency (Andersen-Petersen 1993) | Medium, ranking efficient ones | seconds | Ranking among efficient DMUs; also used for outlier detection |
| Malmquist productivity (Färe et al 1992) | Medium, multi-period | minutes | Time-dependent dynamic; productivity + technical + efficiency change decomposition |
| Tobit regression / Simar-Wilson (2007) bootstrap | Medium, second-stage analysis | minutes | Regression of DEA scores against determinants |
| Network DEA / Dynamic DEA | Complex multi-stage processes | minutes | Modern extensions — Färe-Grosskopf 2000+; limited practical adoption |
| Stochastic / chance-constrained DEA | Under uncertainty | minutes | Modern extension; input-output data uncertainty |
Objective function choice:
- Objective 1 — Input-oriented (reduce inputs): Outputs fixed, minimise inputs; bank-branch scenario (customer count fixed, reduce headcount + space).
- Objective 2 — Output-oriented (grow outputs): Inputs fixed, maximise outputs; hospital scenario (doctors + beds fixed, grow patients + success).
- Objective 3 — Non-oriented (both): SBM Tone (2001) — input reduction + output growth together; preferred in modern practice.
- Objective 4 — Profit-focused: Profit-maximising DEA (Färe et al 1985) — costs as inputs, revenues as outputs, profit-oriented efficiency.
DEA variants — pick by sector:
- CCR (Charnes-Cooper-Rhodes 1978): Foundational, scale-independent, starting model.
- BCC (Banker-Charnes-Cooper 1984): Scale-dependent, technical + scale efficiency decomposition.
- SBM (Tone 2001): Slack-based, non-radial, modern practical standard.
- Super-efficiency (Andersen-Petersen 1993): Ranking among the efficient ones.
- Malmquist-DEA (Färe-Grosskopf-Lindgren-Roos 1992): Multi-period productivity-change decomposition.
- Network DEA (Färe-Grosskopf 2000+): Multi-stage process (e.g. bank: deposit-taking → loan-making → revenue).
- Stochastic DEA: Chance-constrained model under data uncertainty.
- Two-stage DEA + Tobit / Simar-Wilson (2007): Second-stage determinant analysis.
Academic references
Listed in the sources block of this page’s frontmatter. Charnes-Cooper-Rhodes (1978) foundational CCR; Banker-Charnes-Cooper (1984) BCC scale-dependent; Cooper-Seiford-Tone (2007) canonical textbook; Cook-Seiford (2009) 30-year summary and sample-size rule; Emrouznejad-Yang (2018) 40-year literature survey (10,000+ papers); Tone (2001) SBM; Andersen-Petersen (1993) super-efficiency; Simar-Wilson (2007) bootstrap-based second stage; YÖK Theses Centre, 40+ theses from the Turkish academy (among the most-published OR topics in TR).
Sources
- Charnes, A., Cooper, W. W. and Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. Foundational paper for the CCR model; the founding text of DEA.
- Banker, R. D., Charnes, A. and Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092. BCC model — the scale-dependent (variable returns to scale) extension.
- Cooper, W. W., Seiford, L. M. and Tone, K. (2007). Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software (2nd ed.). Springer. The canonical textbook of the field.
- Cook, W. D. and Seiford, L. M. (2009). Data envelopment analysis (DEA) — Thirty years on. European Journal of Operational Research, 192(1), 1-17. Thirty-year summary of DEA, sample-size rule and methodology guide.
- Emrouznejad, A. and Yang, G.-L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978-2016. Socio-Economic Planning Sciences, 61, 4-8. A 40-year survey of DEA literature; 10,000+ academic papers.
- Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130(3), 498-509. SBM (Slack-Based Measure) — the non-radial model.
- Andersen, P. and Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10), 1261-1264. Super-efficiency model, ranking among efficient DMUs.
- Simar, L. and Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric models of production processes. Journal of Econometrics, 136(1), 31-64. Bootstrap-based second-stage DEA + Tobit modern revision.
- YÖK Theses Centre — keyword ‘veri zarflama’ or ‘DEA’ or ‘verimlilik analizi’ — 40+ theses from the Turkish academy (among the most-published OR topics in TR). tez.yok.gov.tr
Glossary
- Data Envelopment Analysis
- Non-parametric LP-based frontier-efficiency method that measures the relative technical efficiency of similar units (DMUs) operating with multiple inputs and multiple outputs.
- Decision Making Unit
- Unit of analysis in DEA — a similar entity (one of N homogeneous organisations) being benchmarked; consumes multiple inputs to produce multiple outputs.
- MIP
- An optimization model where some decision variables are forced to be whole numbers (e.g. number of trucks, number of shifts).
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