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.

We develop an algorithm for the solution of Multiobjective linear plus fractional programming problem (MOL+FPP) when some of the constraints are homogeneous in nature. Using homogeneous constraints, first we construct a transformation matrix T which transforms the given problem into another MOL+FPP with fewer constraints. Then, a relationship between these two problems, ensuring that the solution of the original problem can be recovered from the solution of the transformed problem, is established. We repeat this process of transformation until all the homogeneous constraints are removed. Then, we discuss the multi objective programming part, for which fuzzy programming methodology is proposed which works for the minimization of perpendicular distances between two hyper planes (curves) at the optimal points of the objective functions. A suitable membership function is defined with the help of the supremum perpendicular distance. A compromised optimal solution is obtained as a result of the minimization of the The supremum perpendicular distance. The corresponding optimal solution to the original problem is obtained using the transformation matrix. Finally, an example is given to illustrate the proposed model.