Abstract
The Critical Path Method (CPM) is useful for planning and control of complex projects. The CPM identifies the critical activities in the critical path of an activity network. The successful implementation of CPM requires the availability of clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfil since many of activities will be executed for the first time. Hence, there is always uncertainty about the time durations of activities in the network planning. This has led to the development of fuzzy CPM. In this paper, we use a Lexicographic ordering method for ranking fuzzy numbers to a critical path method in a fuzzy project network, where the duration time of each activity is represented by a trapezoidal fuzzy number. The proposed method is compared with fuzzy CPM based on different ranking methods of fuzzy numbers. The comparison reveals that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path. This new method is simple in calculating fuzzy critical path than many methods proposed so far in literature.
Highlights
A project network is defined as a set of activities that must be performed according to precedence constraints stating which activities must start after the completion of specified other activities (Durbois et al, 2003)
The operation time for each activity in the fuzzy project network is characterized as a positive trapezoidal fuzzy number
A new analytical method using lexicographical ordering ranking for finding critical path in a fuzzy project network has been proposed
Summary
A project network is defined as a set of activities that must be performed according to precedence constraints stating which activities must start after the completion of specified other activities (Durbois et al, 2003). Several studies have investigated the case where activity times in a project are approximately known and are more suitably represented by fuzzy sets rather than crisp numbers (Slyeptosov and Tyshchuk, 2003, Zielinski, 2005, Shankar et al, 2010). This paper presents another approach, which has not been proposed in the literature so far, to analyze the critical paths in a general project network with fuzzy activity times. We compare this method with various fuzzy critical path methods based on ranking of fuzzy numbers (Shankar et al, 2010, 2010; Yao and Lin, 2000)
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