An Alternative Solution to Multi Objective Linear Fractional Programming Problem by Using Geometric Programming Technique

In this study, we have proposed an alternative solution to the multi objective linear fractional programming problems. This method deals with every objective of multi objective linear fractional programming problems gradually by using geometric programming technique to find the pareto optimal solution. The proposed solution procedure has been used in numeric examples and results have been compared with the real solution values. Keywords: multi objective, fractional programming, geometric programmin

Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming

We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. By using suitable G-invex functions, we establish G-Karush-Kuhn-Tucker necessary and sufficient optimality conditions, and G-Fritz John necessary and sufficient optimality conditions of our nondifferentiable multiobjective programs. Our optimality conditions generalize and improve the results in Antczak (2009) to the nondifferentiable case

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

On resource complementarity in activity networks: preliminary results

The methodology of project management has been widespread in organizations of different functions and sizes. In this context, we address the issue of optimal resource allocation, and more specifically, the analysis of complementarity of resources (primary resource and supportive resource) in a project. We develop a conceptual system capable of determining the ideal mixture of resources allocated to the activities of a project, such that the project is completed on time with minimal cost. In this paper, we present the mathematical model, development details and the preliminary results obtained.Fundação para a Ciência e a Tecnologia (FCT