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In today’s highly competitive and fluctuating environment, project management is a very important field employed for scheduling activities and monitoring the progress. To gain competitive priorities such as on-time delivery and customization we need an accomplished project management (Chen and Tsai, 2011). Since the late 1950s, critical path method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of projects. In CPM method, the feasible duration time required to perform a specific project is determined. However, there are many situations that the project manager must reduce the scheduled completion time of a project to meet a deadline requested (Lin, 2008). In this situation, we come up against project crashing problem. Project crashing analysis or project time-cost trade off problem is concerned with shortening the project duration time by accelerating some of its activities at an additional cost. The objective of project crashing is to reduce project duration while minimizing the cost of crashing (Lin, 2008). The project duration time can be shortened by the acceleration of the critical activity times. And, the acceleration of the activity times can be achieved using more resources (using more productive equipment, material or hiring more workers) which means higher costs. Project crashing problems analyze how to modify project activities so as to achieve the trade-off between the project cost and the completion time (Ma and Ke, 2009).
Project crashing and time-cost trade off problems have been extensively investigated. Based upon whether the parameters, activity duration, cost etc., are certain or not, project crashing problems can be categorized into two types: deterministic scheduling and non-deterministic scheduling (Leu et al. 2001, Chen and Tsai 2011). In general, the cost and duration of an activity are accepted as certain and the project crashing problems are solved using deterministic solution techniques. In reality, due to uncertain environment conditions, such as inflation, climate changes, space congestion, productivity level, lack of accurate data etc., there can be uncertainty in the parameters. This leads to non-deterministic project crashing problems. In the solution of these problems, generally, PERT and simulation techniques have been used. However, in PERT the use of probabilistic distributions assumes that the past performance of the activity has been observed and the distribution has been modeled from these observations (McCahon, 1993). But, it is possible that an activity which has never performed before can take place in the project (McCahon 1993, Liu 2003). In recent years, fuzzy set theory has been used to model the uncertainty that is associated with activity duration and cost in project crashing problems. The main advantages of methodologies based on fuzzy set theory are that they do not require prior predictable regularities or posterior frequency distributions, and they can deal with imprecise information based on human experts’ subjective judgment (Chen and Tsai 2011).