2. UNCLASSIFIED The Surface-Weighted Options Ranking Technique Peter Williams, Peta Erbacher and Fred DJ Bowden Land Operations Division As presented at the 21 st MCDM Conference, Finland, June 13 – 17, 2011.

3. UNCLASSIFIED The Evolution of SWORT Began with some work on TOPSIS Filar, J.A., Gaertner, P.S. and Lu, W.M, “Aggregation of Tactical Performance Measures: An Operations Research Perspective” TOPSIS is a Data Envelop Technique. Key aspect include:  Defining the frontier solution boundary using LP  Determining each option’s relationship to this boundary  Ranking the options based on this relationship The issues with this were:  Lack of flexibility in how criteria are combined  Amount of processing power required to generate frontier boundary SWORT solves these issues and provides non-linear weightings

4. UNCLASSIFIED SWORT at its Basic Data Envelop Analysis Technique Allows for: 1.Non-linear weights on criteria  Able to weight regions 2.Computationally inexpensive 3.Provides degree of separation between the Options 4.Sensitivity analysis on weightings Can be explained intuitively to decision maker Enables them to describe how weighting regions should look Will use 2 criteria to illustrate the technique

5. UNCLASSIFIED Once the frontier surface, S, has been chosen appropriate for the problem, the SWORT ‘value’ for an option P is calculated as: Distance to P Distance to S through P S P V = SWORT Description

6. UNCLASSIFIED SWORT Description Once the frontier surface, S, has been chosen appropriate for the problem, the SWORT ‘value’ for an option P is calculated as: S P1 P3 P4 P2 OptionSWORT Ranking 12 (0.67) 23 (0.61) 31(0.90) 44 (0.40) Distance to P Distance to S through P V =

7. UNCLASSIFIED SWORT Description It can be shown using a parametric representation that this value V is given by: V = 1/t where, S(Pt) = 0 Hence, the calculations for most surfaces are very simple and can be solved analytically.

8. UNCLASSIFIED Example Surface –Plane Features: Equivalent to the SAW method A constant weight for each attribute A weighted sum is calculated Preferred Options: Score well in most of the criteria 0 1 1 S P

9. UNCLASSIFIED Example Surface –Plane Features: Equivalent to the SAW method A constant weight for each attribute A weighted sum is calculated Preferred Options: Score well in most of the criteria

10. UNCLASSIFIED Example Surface –Plane Features: Equivalent to the SAW method A constant weight for each attribute A weighted sum is calculated Preferred Options: Score well in most of the criteria Example Purchasing a car which needs to have good ratings for fuel efficiency, cost, size, colour, safety, engine capacity and age. 0 1 1 S

11. UNCLASSIFIED Example Surface – Ellipse Features: Non-linear behaviour A greater emphasis placed on "individual" attributes. Preferred Options: Option which ranks very highly in one or more areas. Example Recruiting an athlete for a sports team. They need to have speed, strength, intelligence, skill and height. However, if one person is particularly good in one attribute, they may be perfect for a specific position on the field.

12. UNCLASSIFIED Example Surface – Inverse Function Features: Extreme emphasis on scoring well in all attributes Any poor score will have a large and negative impact Through the application of asymptotes it is possible to enforce minimum 'cut-off' values for attributes Preferred Options: Contributions from all attributes are better than individual brilliance Example Evaluating a military system which must reach minimum levels of armour, firepower, speed and deployability. If it fails in any one category it is not acceptable. Ideally, looking for a system that has it all.

13. UNCLASSIFIED Example Surface - Parabolas Features: Two upper and right parabolas Effectiveness decreases if you have even representation in both attributes Preferred Options: Very good in one Attribute and average in the other. Effectiveness decreases if both Attributes are prominent, or one is absent Example Interior design for a new office building. The Attributes could be the architecture and the design. Highly detailed and intricate construction is good. Lavish and expensive furniture and decorations are good. Having both overwhelms the senses and creates an eyesore.

14. UNCLASSIFIED Extension to n Criteria Most surfaces are readily extensible to a higher number of criteria. E.g. n-Dimensional Ellipsoids:

15. UNCLASSIFIED Working Example: Background Considered the “value” of Seven different Body Armours (C1, C2,…, C7). Problem had 12 Attributes by which to rank the Options. Data was collected from participants for each of the Attributes. The associated weightings for each of the Attributes were established during field experimentation and trials. The central tendency of each of the Attributes, for each Body Armour, were used to get the attribute values. The SWORT value for each Option was then calculated.

16. UNCLASSIFIED Working Example: SWORT Tool - Ellipse C1C2C3C4C5C6C7 Rank 1 (1.00) 5 (0.43) 6 (0.18) 4 (0.87) 2 (0.94) 3 (0.92) 7 (0.00)

17. UNCLASSIFIED Working Example: Results The Body Armours ranked according to the surface used. C1C2C3C4C5C6C7 Plane 1 (1.00) 5 (0.50) 6 (0.26) 4 (0.84) 3 (0.91) 2 (0.93) 7 (0.00) Ellipse 1 (1.00) 5 (0.43) 6 (0.18) 4 (0.87) 2 (0.94) 3 (0.92) 7 (0.00) Inverse 3 (0.93) 7 (0.00) 5 (0.05) 6 (0.40) 2 (0.94) 1 (1.00) 4 (0.70)

18. UNCLASSIFIED Working Example: Results The Body Armours ranked according to the surface used. C1C2C3C4C5C6C7 Plane 1 (1.00) 5 (0.50) 6 (0.26) 4 (0.84) 3 (0.91) 2 (0.93) 7 (0.00) Ellipse 1 (1.00) 5 (0.43) 6 (0.18) 4 (0.87) 2 (0.94) 3 (0.92) 7 (0.00) Inverse 3 (0.93) 7 (0.00) 5 (0.40) 6 (0.05) 2 (0.94) 1 (1.00) 4 (0.70)

19. UNCLASSIFIED Summary Presented a new MCDM method – SWORT. This method: 1.Non-linear weights on Criteria.  Able to weight regions. 2.Computationally inexpensive. 3.Provides degree of separation between the Options. 4.Sensitivity analysis on weightings. Is Easily extendable to n Criteria.

20. UNCLASSIFIED Questions