Research On The Theory And Application Of Polynomial Discrete Programming In Project Portfolio Selection

With the rapid development of the global market economy,the investment and financing environment faced by enterprises presents a complex and changeable situation.Generally,in order to obtain more profits or achieve the strategic goal of the organization,decision makers usually need to execute several projects at the same time.How to select the most profitable portfolio from many candidate projects has become an urgent problem that many enterprises need to solve.This kind of problem is called project portfolio selection problem(PPSP).To our knowledge,in order to reflect reality,current models in the literature are concerned about some actual and important factors,such as cardinality constraints,scheduling,employee ability and divisibility,etc.,but less attention has been paid to interdependency/interaction.In fact,interdependency exists widely in project portfolio field,such as resource sharing and benefit complementarity,etc.Therefore,it is of great theoretical and practical value to study portfolio selection with consideration of interdependency.Recognizing the shortcomings of PPSP,0-1 variables are introduced into this paper to represent the interdependency relationship among projects.In a set of candidate projects with interdependency,binary variables x;and xj are often introduced to present the relationship between projects i and j.When xixj ?1,the interdependency of projects i and j is active;otherwise,the interdependency is non-active.This representation leads PPSP to be an integer polynomial discrete programming problem.Generally,polynomial discrete programming problem has been proved as NP-Hard,which means that the exact solution of the problem requires exponential complex time.Heuristic algorithm,which is frequently used,cannot guarantee the global optimal solution.Linearization techniques that can obtain the optimal solution require a large number of constraints,which will lead to heavy computational burden.Therefore,in order to get the optimal solution and improve the efficiency,this paper focuses on the theory and method of polynomial discrete programming and introduces a superiority transformation technique to reduce the polynomial complexity of discrete programming model substantially.In this paper,a large number of numerical experiments are conducted by using GAMS/BARON.The results show that the proposed linear technique can greatly reduce the variables and constraints in the model,and greatly improve computation efficiency.Finally,based on the actual data of Huadian Group,this paper establishes a mathematical model considering the interaction among microgrids,and proposes a new linear algorithm to solve the problem.The results show that the interconnection mode considering interaction can guarantee the reliability of whole microgrid system through energy sharing,use less distributed generators to meet load demands and reduce investment cost at the same time.