Research On Project Selection And Scheduling Problem Under Uncertain Environment

Project selection problem is concerned with selecting appropriate projects from candidates to optimize allocation of resources and maximize returns under capital and resource limitations. Most studies are based on exact values or random values. However, exact values cannot describe the change of the environment and historical data may be scarce or lose efficacy because of the complexity of reality. This paper discusses the project selection problem in this kind of environment. The project parameters are treated as uncertain variables which are obtained by experts' estimations according to their judgements. The project selection and scheduling problem under an uncertain environment is investigated considering the flexibility of investment start time, which can offer the scientific and reasonable investment bases for investors. Below are the main content and innovation points:(1) A mean-variance and a mean-semi variance model based on uncertainty theory are built to deal with project selection and scheduling problem where historical data of project parameters are insufficient. The initial outlays and net incomes are treated as uncertain variables. Investors can select appropriate projects and schedule them by considering the flexibility of start time to save costs and increase profits. When the distributions of initial outlays and net incomes are symmetrical, variance is employed to measure the return and cost overrun risk. When the distributions are asymmetrical, higher partial semivariance is proposed to measure cost overrun risk and the lower partial semivariance to measure return risk. Deterministic forms of mean-variance model are given in general cases and normal distribution cases. The method to calculate semivariances in general cases is proposed. Since the models are mixed integer programming, a genetic algorithm is designed by executing crossover and mutation processes in two parts of the chromosomes. The numerical examples verify the significance of considering project scheduling and prove the robustness and effectiveness of the algorithm.(2) Since it is difficult to tell the tolerable level towards variance or semivariance, a cost overrun risk index is proposed and a mean-risk index model is established. The initial outlays and net incomes are treated as uncertain variables. Although variance and semivariance can measure return or cost overrun risk, the tolerable levels are different facing different mean values. When mean value is unknown, it is difficult to tell whether the variance or semivariance is within the acceptable limit. The available capital is known before making an investment decision. The idea of risk index is introduced to design a cost overrun risk index. The part higher than available capital can be treated as a loss, and investors can easily tell the tolerable level towards the loss. A mean-risk index model is proposed and deterministic forms in general and uncertain normal distribution cases are given. A hybrid intelligent algorithm integrated genetic algorithm and cellular automation is proposed aimed at searching neighbors of the current optimal chromosome for each generation, which will avoid falling into local optimal solution. The numerical examples verify the importance of considering project scheduling. The optimal solution stays unchanged when changing algorithm parameters, which proves the robustness of the algorithm. The comparison with enumeration method and genetic algorithm proves the effectiveness of the algorithm.(3) Resource limitations are studied as well as capital limitations, and a project selection model and a project selection and scheduling model based on uncertainty theory are proposed considering resource classification and resource sharing constraints. Resources are divided into non-renewable and renewable. There is renewable-resource sharing among projects. The initial outlays, net incomes, the needed amount of resources are treated as uncertain variables. In the project selection model, the selected projects are all assumed to start at zero time and the investment durations are the same. In the project selection and scheduling model, the flexibility of start time is considered and the investment durations are different. When setting up resource sharing constraints, it should be checked whether the projects are selected simultaneously, and further judged whether the projects are being executed simultaneously because the projects cannot share renewable resources if not being executed simultaneously. When solving the project selection model problem, genetic algorithm is proposed since the decision variables only contain 0-1 variables. For the project selection and scheduling model, the decision variables include 0-1 and nonnegative integer variables, a hybrid intelligent algorithm integrated genetic algorithm and cellular automation is designed. The numerical examples prove that considering resource classification and resource sharing constraints can help save resources, optimize allocation of resources and obtain optimal returns. The examples also verify the importance of project scheduling and the robustness of the algorithm. The comparison with enumeration method and genetic algorithm proves the effectiveness of the algorithm.