Paper 3: DEA Weights (Mar Molinero & Portillo)

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  • PICTURES WORTH ONE THOUSAND EQUATIONS Cecilio Mar Molinero
  • PICTURES WORTH ONE THOUSAND EQUATIONS Cecilio Mar Molinero
  • Paper 3: DEA Weights (Mar Molinero & Portillo)

    1. 1. 3rd International Workshop on Innovation and Performance Management University of Kent, UK 1-4 July 2010 WHY DEA WEIGHTS ARE OFTEN WRONGLY CALCULATED AND WHAT CAN BE DONE ABOUT IT Cecilio Mar Molinero , Kent Business School, UK Fabiola Portillo , University of La Rioja, Spain
    2. 2. Summary <ul><li>Production and frontier functions </li></ul><ul><li>Properties of efficient points </li></ul><ul><li>The Linear Programming formulation </li></ul><ul><li>Degeneracy and its graphical interpretation </li></ul><ul><li>Proposed solution </li></ul><ul><li>An example </li></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    3. 3. Isoquants <ul><li>Production and frontier functions </li></ul>
    4. 4. Budget functions <ul><li>Production and frontier functions </li></ul>
    5. 5. Production possibility frontier <ul><li>Production and frontier functions </li></ul>
    6. 6. Returns line <ul><li>Production and frontier functions </li></ul>
    7. 7. DEA-CCR Model <ul><li>The Linear Programming formulation </li></ul>
    8. 8. Empirical Isoquant <ul><li>Degeneracy and its graphical interpretation </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E
    9. 9. Empirical Isoquant <ul><li>Degeneracy and its graphical interpretation </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E Technically and economically efficient points O x 1 Q’( ) Q’( ) x 2 A B C D E Technically and economically efficient points
    10. 10. Empirical Isoquant <ul><li>Degeneracy and its graphical interpretation </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E Technically and economically efficient points O x 1 Q’( ) Q’( ) x 2 A B C D E Technically and economically efficient points
    11. 11. The geometry of degeneracy <ul><li>Degeneracy and its graphical interpretation </li></ul>
    12. 12. The geometry of degeneracy <ul><li>Degeneracy and its graphical interpretation </li></ul>
    13. 13. The geometry of degeneracy <ul><li>Degeneracy and its graphical interpretation </li></ul>
    14. 14. The geometry of degeneracy <ul><li>Degeneracy and its graphical interpretation </li></ul>
    15. 15. Budget line associated with marginal values <ul><li>Proposed solution </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E
    16. 16. Budget line associated with marginal values <ul><li>Proposed solution </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E
    17. 17. Budget line associated with marginal values <ul><li>Proposed solution </li></ul>O x 1 Q’( ) Q’( ) x 2 A B C D E
    18. 18. Fuente: Beasley(1995) Dual values associated with the university of Essex <ul><li>Example: Chemistry departments in UK Universities </li></ul>University Basic Research Grant income Under- Post- graduate graduate students students Solution 1 Solution 2 Solution 3
    19. 19. The end?
    20. 20. 3rd International Workshop on Innovation and Performance Management University of Kent, UK 1-4 July 2010 NON-HOMOGENEITY IN DATA ENVELOPMENT ANALYSIS Cecilio Mar Molinero , Kent Business School, University of Kent, UK
    21. 21. Summary <ul><li>Production and frontier functions </li></ul><ul><li>Properties of efficient points </li></ul><ul><li>The Linear Programming formulation </li></ul><ul><li>Degeneracy and its graphical interpretation </li></ul><ul><li>Proposed solution </li></ul><ul><li>An example </li></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    22. 22. Teaching and Research <ul><li>Models for non-homogeneous organisations </li></ul>
    23. 23. Cecilio Mar Molinero- UPC <ul><li>Models for non-homogeneous organisations </li></ul><ul><li>An equation for the T function </li></ul><ul><li>An equation for the R function </li></ul><ul><li>An equation for the overall unit to be assessed </li></ul><ul><li>To be efficient you need to be efficient at each activity and efficient overall </li></ul>
    24. 24. <ul><li>This model was used for </li></ul><ul><ul><li>NHS trusts in the UK </li></ul></ul><ul><ul><li>Police forces in Spain </li></ul></ul><ul><ul><li>Railways in the US (not published) and Taiwan </li></ul></ul><ul><ul><li>Information system architecture </li></ul></ul><ul><li>There has been a review paper in 2010 </li></ul><ul><li>It is non-linear in the constraints and “simplifications” have been published. </li></ul><ul><li>Not related to Network DEA (Fare and Grosskopft) as both models are contemporaneous. </li></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    25. 25. <ul><li>The model is homogeneous: all units use the same inputs to produce the same outputs, and have the same internal structure. </li></ul><ul><li>Properties studied by means of Kuhn Tucker theory. </li></ul><ul><li>To progress we need to look at envelopment formulation for DEA </li></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    26. 26. <ul><li>Models for non-homogeneous organisations </li></ul>
    27. 27. Unit of assessment that engages only in one activity <ul><li>Models for non-homogeneous organisations </li></ul>
    28. 28. <ul><li>Models for non-homogeneous organisations </li></ul>
    29. 29. Example: Socially responsible financial institutions in Bolivia <ul><li>Models for non-homogeneous organisations </li></ul>
    30. 30. <ul><li>Example: Socially responsible financial institutions in Bolivia </li></ul><ul><li>In Ross Wyatt’s PhD we looked at efficiency in various types of financial institutions in Bolivia: NGOs, Building Societies, Consumer Cooperatives, Commercial Banks, and so on. </li></ul><ul><li>These make microcredit loans, mortgage loans, commercial loans, and consumer loans. </li></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    31. 31.
    32. 32. <ul><li>The idea can be extended to activities that take place in sequence: supply chains are the obvious example. </li></ul><ul><li>In this case we are not interested in specialisation versus diversification, but in vertical integration. </li></ul><ul><li>The model allows for </li></ul><ul><ul><li>outsourcing </li></ul></ul><ul><ul><li>selling partly manufactured components </li></ul></ul><ul><ul><li>buying intermediate components </li></ul></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    33. 33. <ul><li>Example from Huiling Zhao’s PhD: Primary schools in Kent. </li></ul><ul><ul><li>Children in Kent can attend school from ages four to seven (infant schools) and from the ages of seven to eleven (middle schools). </li></ul></ul><ul><ul><li>They can also attend schools from ages four to eleven (primary schools). </li></ul></ul><ul><ul><li>Taking into account poverty (free meals), special needs incidence, and funding, which system delivers the best test results at 11? </li></ul></ul><ul><li>Models for non-homogeneous organisations </li></ul>
    34. 34. <ul><li>Models for non-homogeneous organisations </li></ul>
    35. 35. <ul><li>Models for non-homogeneous organisations </li></ul>
    36. 36. <ul><li>Models for non-homogeneous organisations </li></ul>
    37. 37.
    38. 38. <ul><li>Models for non-homogeneous organisations </li></ul>
    39. 39. Questions? <ul><li>Models for non-homogeneous organisations </li></ul>

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