Studying Project Portfolio Selection Problem Based On Theory Of Parametric Possibility Distributions

In project portfolio selection,decision makers need to assess the feasibility of a set of projects,select a technically feasible,economically reasonable optimal portfolio of projects,and allocate limited resources to carry out the selected projects.In an increasingly competitive economic environment,it is crucial for the success of a firm that how to identify the most promising subset of projects among a large set of project opportunities and how to use the limited human and technical resources in the most effective way,which also imply how to make the most suitable project portfolio strategy.Meanwhile,the uncertainty contained in various factors,such as future profit,man-hour of project,and competence level of work team,further complicates project selection strategy.Therefore,it is necessary to develop a new approach to dealing with uncertainty in the study of the project portfolio selection and staff assignment problem.The thesis proposes a concept of parametric interval-valued fuzzy variable to characterize the uncertain information of project portfolio selection.This concept provides a flexible parameter-based representation for fuzzy information via para-metric possibility distribution.Based on parametric possibility theory,two classes of credibilistic project portfolio models-fuzzy distributionally robust model and credibilistic parametric optimization model are bulit.More specifically,based on different decision criteria and the influence factors of project portfolio selection,four models are constructed,they are the distributionally robust expected value model with outsourcing opportunity,the credibilistic constrained model with interactions among projects,the maximal credibility model with varaible competence value and competence-oriented dynamic robust optimization model.Considering the charac-teristics of these models,the properties of models are analyzed and four models are transformed into their equivalent mixed integer programming forms.Finally,nu-merical examples illustrate the efficiency of the developed credibilictic optimization models and solution method.The main contributions of this thesis include the following aspects:(i)Theconcept of parametric interval-valued fuzzy variable is proposed,and the numerical characteristics of the lambda selections are discussed;(ii)For fuzzy project portfolio selection problem,two classes of distributionally robust models:the distribution-ally robust expected value model and distributionally robust dynamic optimization model,and two classes of fuzzy parametric optimization models:the optimistic value model and the maximal chance model are built;(iii)By analyzing the prop-erties,the crisp equivalent forms are derived under some common distributions.To solve the equivalent mixed integer programmings,a domain-based decomposition algorithm is designed according to the model characteristic;(iv)The effectiveness of modeling idea and method is illustrated,and the sensitivity of important parameter is analyzed.