Optimization of the product portfolio has been recognized as a critical problem in industry, manage-ment, economy and so on. It aims at the selection of an optimal mix of the products to o er in the target market. As a probability function, reliability is an essential objective of the problem which linear models often fail to evaluate it. Here, we develop a multiobjective integer nonlinear constraint model for the problem. Our model provides opportunities to consider the knowledge transferring cost and the environmental e ects, as nowadays important concerns of the world, in addition to the classical factors operational cost and reliability. Also, the model is designed in a way to simultane-ously optimize the input materials and the products. Although being to some extent complicated, the model can be e ciently solved by the metaheuristic algorithms. Finally, we make some numerical experiments on a simulated test problem.

Generally, an engineering design problem has multiple objective functions. Some of these problems can be formulated as multiobjective geometric programming models. On the other hand, often in the real world, coefficients of the objective functions are not known precisely. Coefficients may be interpreted as fuzzy numbers, which lead to a multiobjective geometric programming with fuzzy parameters. In this paper, we solve the multiobjective geometric programming problem with fuzzy parameters by applying a linear ranking function. The linear ranking function is used to compare fuzzy numbers. Finally, a numerical example is given.

In this paper the problem under consideration is multi objective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multi objective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality conditions are obtained for efficient and properly efficient solutions. Some duality results are established for multi objective Schaible type dual.

In this paper, the concept of ¶*-quasiconvexity is introduced by using convexifactors. Mond-Weir-type and Schaible-type duals are associated with a multiobjective fractional programming problem, and various duality results are established under the assumptions of ¶*-pseudoconvexity and ¶*-quasiconvexity.