Research On Critical Path Determination Method Under Uncertain Conditions

The critical path is the path with the longest duration of activity.The activities that make up the critical path are the key activities.The project can only end after all the key activities are completed.The critical path determines the project’s construction period.The determination of the critical path is very important for the scientific management of the project.Therefore,it is of great significance to study the method of determining the critical path.In fact,due to the existence of uncertain factors such as weather,technology,funding,management,etc.,there is a large amount of uncertainty in project management.The most intuitive manifestation is the uncertainty of the project duration,which brings a great challenge to the determination of critical path.At present,scholars only consider the fuzziness or randomness of the construction period in the study of critical path determination method.Although some achievements have been made,there are still many areas worth further discussion.Based on the previous research on this problem,the thesis uses network planning technology to analyze the project network,describes the uncertainty of project duration from the perspective of risk,improves the existing methods,and proposes a robust optimization method to determine the critical path under the condition of mixed uncertainty.The main research work of the thesis includes the following aspects:1.Based on the related theories of project management,use network planning technology to draw a double-coded network diagram to describe the relationship and schedule between the various processes of the project,and further identify and analyze the risks existing in each project activity.The overall risk level of each activity,the time fluctuation range of each activity is determined,and the fuzzy activity time is obtained.2.Under the condition of fuzzy construction period,according to the deterministic linear programming model,the fuzzy linear programming model is constructed for the critical path problem of fuzzy networks.According to the fuzzy set theory,combined with the α-cut method and the two-level mathematical programming method,the critical path of all possible items is found under different α-cut levels,and the key path is determined by combining the Yager ranking index.3.Based on the above research work,a random fuzzy variable is introduced,that is,the duration of the activity obeys a certain probability distribution,the mean value is fuzzy,and the variance is known.Under such mixed uncertain conditions,an uncertain opportunity constrained programming model for solving critical paths is established.The concepts of α-cut and distribution function are used to transform it into a model with interval parameters.Robust optimization and min-max regret The criterion transforms the interval model into a deterministic model and solves it.Aiming at the above critical path determination methods,an iron ore mine treatment project is taken as the research object,and case analysis is carried out to determine the critical path of the project.The results are analyzed and compared to verify the effectiveness of the above model and algorithm.