基于模糊网络的项目工期计算及优化

Project Duration Calculation and Optimization Based on Fuzzy Network

提出了基于不确定的活动持续时间和上下游活动间的不确定信息传递关系的模糊网络的项目进度计划问题。把不确定的活动持续时间看作模糊数,用模糊时间因子表示上下游活动间的不确定信息传递关系。通过模糊设计结构矩阵表达了模糊网络,设计了模糊网络的项目工期计算模型,引入项目按要求工期完工概率和活动边际工期贡献率来解决模糊网络的关键路线和项目的工期优化,并通过示例验证了方法的有效性。

In the past years, CPM and PERT have been demonstrated to be important tools for project planning and have been widely used in project management. In CPM, the activity duration is determined and the information transfer relationship between the upstream and downstream activities can＇t be represented. The PERT network describes the activity duration through three time parameters which obey the beta distribution, but can＇t express the information transfer between activities. In fact, projects are always in complex and changing environment, the upstream and downstream activities is overlap, the activity duration and the information transfer relationship are uncertain. Therefore, research on project schedule plan based on fuzzy network in which the activity duration is uncertain and the information transfer relationship between the upstream and downstream activities is also uncertain has practical significance. Project schedule plan based on fuzzy network can achieve project duration reasonable optimization and improve the utilization of resources. This paper describes the project schedule plan problem with the fuzzy design structure matrix, taking into account not only the uncertain activity duration but also the uncertain information transfer relationship between the upstream and downstream activities. Compared with the traditional CPM / PERT network, project schedule plan based on fuzzy design structure matrix has more expansion form of expression and larger information of project plan. It is more in line with project reality comparing with the research considering single random factor only, and it can also combine project duration calculation and resource-duration optimization effectively in the design of algorithm. Fuzzy design structure matrix is used to describe fuzzy project network. The paper develops the model of calculating project duration through fuzzy operation in fuzzy network environment. The probability of project completion as required duration（MCR） and the marginal duration contribution rate （MCR）are introduced to solve critical path in fuzzy network and project resource-duration optimization. The first part of this paper describes fuzzy project network with fuzzy design structure matrix. In fuzzy design structure matrix, the diagonal triangle fuzzy number represents the uncertain activity duration, the area under diagonal is fuzzy information output time factor and the area above diagonal is fuzzy information input time factor. The fuzzy information output and input time factor matrix are established to develop uncertain information transfer relationship between the upstream and downstream activities. The second part proposes the model of calculating project duration in fuzzy network. Firstly this part establishes the rules of fuzzy number operation, and then calculates the fuzzy earliest start time and fuzzy earliest finish time, finally calculates the fuzzy project duration. The third part researches the optimization of project duration in fuzzy network. This paper establishes the formula of the probability of project completion as required duration （PCR） through comparing the fuzzy project duration calculated in the second part with the project required duration. The marginal duration contribution rate （MCR） is the change value of PCR after the activity duration reducing one unit. The path criticality is the sum of activity＇s MCR in the path. Project critical path is the path which has the highest path criticality. The project resource-duration optimization can be solved by the MCR and PCR. The last part is an example to verify the effectiveness of the proposed method and summary. Project duration can be calculated by the fuzzy operation. The PCR is calculated through comparing the fuzzy project duration with the project required duration. The MCR is the change value of PCR after the activity duration reducing one unit. The introduction of PCR and MCR can come to the project critical path. The MCR can illustrate if the reduce of activity duration can decrease project duration or not, the PCR and MCR can achieve resources-duration optimization and improve the utilization of resources.