UBC Theses and Dissertations
Multicriteria linear fractional programming Choo, Eng-Ung
The object of this thesis is to study the multi-criteria linear fractional programming problems (MLFP). The characterizations of efficiency, weak efficiency and proper efficiency are derived. In the bicriteria case, the set E of all efficient solutions of (MLFP) is path-connected by a finite number of line segments and the efficient frontier F(E) can be evaluated by using the row parametric technique in linear programming. The weakly efficient (respectively, properly efficient) solutions can be generated by solving the generalized Tchebycheff norm problems (Tβ) (respectively, (βα)) with different parameters β and α. The set E[sup=W] of all weakly efficient solutions of (MLFP) is compact and path-connected by finitely many line segments. A dual problem is formulated which is a natural extension of the usual dual in linear programming, the Wolfe dual in nonlinear programming and the Isermann dual in multiple objective linear programming. Duality results are established under the assumption that the criteria are concave functions. The matrix of the dual variables of (MLFP) can be evaluated by solving L linear programs. A heuristic arrow search algorithm is developed for solving general multicriteria programming problems interactively. The decision maker merely selects his most preferred one amongst-the presented alternatives. Solutions generated are evenly distributed over the desired neighbourhood of the weakly efficient frontier. The algorithm is convergent in the bicriteria case, with appropriate convexity conditions. When applied to solve (MLFP), the arrow search algorithm uses only the linear programming techniques.
Item Citations and Data