Some Methods for Analyzing the Fuzzy Critical Path for a Project Network

Abstract

In today's highly competitive business environment, project management's ability to schedule activities and monitor progress within strict cost, time and performance guidelines is becoming increasingly important to obtain competitive priorities such as on-time delivery and customization. When the activity times in the project are deterministic and known, critical path method (CPM) has been demonstrated to be a useful tool in managing projects in an efficient manner to meet this challenge. However, in practical situations this requirement is usually hard to fulfill, since many of the activities will be executed for the first time. So when project activity times cannot be specified with certainty due to the lack of duration information or poor definitions of the activity, then to deal with such real life situations, Zadeh (1965) introduced the concept of fuzzy set. Since there is always uncertainty about the time duration of activities in the network planning, so fuzzy critical path method (FCPM) was proposed since the late 1970s. This thesis is devoted to critical path analysis under fuzzy environment. The chapter-wise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes basic concepts used throughout the work. Chapter 2 presents brief review of the work done in the area of finding the critical path under fuzzy environment. In Chapter 3, a method based on the ranking value of a fuzzy number is presented to perform critical path analysis in a fuzzy environment. The trapezoidal fuzzy numbers, given by decision makers or characterized by historical data, are utilized to assess the activity times in a project network. To illustrate the presented method a numerical example is solved. Presented method is applied to find fuzzy critical path of an airport’s cargo ground operation system. Chapter 4, In the previous chapter, a method is presented to find fuzzy critical path using ranking function. Although results obtained are mathematically correct, but the obtained results have no physical meaning, since there exists a negative part in calculated values of the latest fuzzy time and total slack fuzzy time, which represents that time may be negative. To overcome this shortcoming a new method is presented in this chapter. Chapter 5, In the previous chapter, all the parameters are represented by trapezoidal fuzzy numbers, but in real life situations it is not always possible to represent all the parameters by same type of fuzzy numbers. In this chapter, a method is presented to find the fuzzy critical path of a given project network by representing the parameters by different types of fuzzy numbers. Chapter6, In the previous chapter, a method is presented to find fuzzy critical path of a given network by representing the parameters by different types of fuzzy numbers. In this chapter, an alternative method is represented to solve same type of problem. It is shown that the results of the presented method and the results obtained by using method in the previous chapter are identical while the method presented in this chapter is easy as compared to the method presented in previous chapter.