This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncert...This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.展开更多
A decision support model with the stochastic objective function measuring the benefit contributions of projects and stochastic resource constraint and its decision making analysis procedure with the case study are pre...A decision support model with the stochastic objective function measuring the benefit contributions of projects and stochastic resource constraint and its decision making analysis procedure with the case study are presented for selecting R&D projects, in which the uncertainty in project evaluation and selection, the technical or outcome, cost or resource and benefit or payoff interrelationships among projects, and the experience and knowledge of the R&D manager can be considered.展开更多
文摘This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.
文摘A decision support model with the stochastic objective function measuring the benefit contributions of projects and stochastic resource constraint and its decision making analysis procedure with the case study are presented for selecting R&D projects, in which the uncertainty in project evaluation and selection, the technical or outcome, cost or resource and benefit or payoff interrelationships among projects, and the experience and knowledge of the R&D manager can be considered.
