6533b7defe1ef96bd12768d0
RESEARCH PRODUCT
Solving the Discrete Multiple Criteria Problem using Convex Cones
Jyrki WalleniusStanley ZiontsPekka Korhonensubject
Mathematical optimizationStrategy and ManagementRegular polygonMultiple criteriaPairwise comparisonManagement Science and Operations ResearchDecision makerProxy (statistics)Mathematical proofMathematicsDecision analysismultiattribute programming: multiple criteria convex cones [decision analysis utility/preference]description
An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1984-11-01 | Management Science |