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Industrial Mathematics Final Year Topic: Returns-to-Scale Assumptions in a Synthetic Data-Envelopment Analysis

This Industrial Mathematics final year project compares two frontier models using a transparent set of fictional input-output units.

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Why choose this project topic?

A focused study of efficiency frontiers gives you a specific question in mathematical efficiency analysis. It compares two frontier models using a transparent set of fictional input-output units. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do constant- and variable-returns assumptions change efficiency scores and reference units in a bounded DEA example?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for efficiency frontiers with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for efficiency frontiers.
  2. 02Define positive synthetic inputs and outputs with consistent orientation.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do constant- and variable-returns assumptions change efficiency scores and reference units in a bounded DEA example?

A suggested research approach

Define positive synthetic inputs and outputs with consistent orientation. Formulate both linear programmes, verify scores and projections and inspect sensitivity to an added extreme unit or rescaled measurement. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A transparent synthetic input-output table
  • Consistent DEA formulations and orientation definitions
  • Linear-programming and projection-verification tools

Keep your project scope clear

A relative frontier score is model and sample dependent and does not establish an organisation's absolute quality or managerial competence.

Industrial Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

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