231 EXTENDING THE PERT MODEL FOR PROBABILISTIC ACTIVITY DIRECT COSTS Mihir Dash, Professor School of Business Alliance University, India Introduction Project management is the process of designing, planning, and implementing a set of activities to accomplish a particular goal or task (Tache et al., 2013). The two critical performance measures which project managers attempt to control are project duration, i.e. the total time taken to perform all of the activities required to achieve the goal, and project cost, i.e. the total cost incurred in implementing the project. The two most common approaches to project management are the Critical Path Method (CPM; Kelley and Walker, 1959) and the Project Evaluation and Review Technique (PERT; Fazar, 1959). CPM starts by analysing the project into all the activities/tasks (categorized within a work breakdown structure) required to achieve the goal, each with a definite and known completion time, along with a structure of dependencies/precedence relationships between the activities, and a set of logical endpoints or milestones delineating different stages of the project. This structure of dependencies is modelled as an activity network, either with “activities on arrows” (AOA), in which nodes represent milestones/events, arrows represent activities, and the dependency structure is expressed through incoming and outgoing arrows at each node; or with “activities on nodes” (AON), in which nodes represent activities, and arrows represent dependencies between activities. CPM first calculates the earliest times at which each activity can start and finish, and the earliest times at which each of the milestones/events would be reached, and identifies the project duration, i.e. the earliest time at which all activities in the project can be completed. CPM also works backwards and calculates the latest times at which each activity should start and finish, and each milestone should be reached, without affecting the project duration. The critical path is identified as the chain of activities joining the starting node of the project with the ending node of the project with longest duration, for which the earliest and latest times coincide. Activities that are on the critical path are critical activities, which must start and finish at their earliest times, failing which the project will get delayed; the same holds true for milestones on the critical path. On the other hand, activities that are not on the critical path are non-critical, so that they can be delayed to some extent without affecting the project duration. The total float of an activity is the maximum time that the activity can be delayed without affecting the project duration; however, this leaves no scope for delay in any other activity. The free float of an activity is the maximum time that the activity can be delayed without affecting the project duration and the total float time of all subsequent activities. The independent float of an activity is the maximum time that the activity can be delayed without affecting the project duration and the total float time of all other activities, precedent and subsequent. The float times of activities play an important role in project scheduling. Critical