[MUSIC] This project is about reducing project duration. There can be several reasons why one may complete the project early, by using the duration of one or more activities in the critical part. Early completion of the project will imply early realization of revenues. And a reduction in indirect overhead costs associated with the project. Some other reasons for reducing the duration of a project may include customer requirements, contract commitments, time to market pressures, bonus for early completion, pressure to move resources to other projects, etc. But the reduction in the duration of some of the activities would typically imply more direct cost than the cost for the normal duration of the activity. So one has to balance between the benefits of completing the project early with the increased direct cost of completing the activities. There are several possible alternatives for reducing the completion time of the project. These include adding additional resources for some activities, scheduling overtime, outsourcing some project work, forming a competent, dedicated, and focused core project team, adopting a Critical-Chain approach to project management, etc. Now we'll consider the problem of reducing some of the activity durations, in order to complete the project early. In order to reduce the duration of an activity from its normal time, we have to incur incremental direct cost, consisting of perhaps overtime payment and our cost of additional resources. The relationship between the incremental data cost and the reduction in activity time is assumed to be linear as shown in the diagram. For each activity whose duration can be reduced, we need to estimate the incremental data cost for each unit reduction and duration. For each activity, there would be a minimum required time beyond which the activity time cannot be re-used. The minimum time and the corresponding data cost are often referred to as crash time and crash cost. The scope of the line in the diagram gives the incremental data cost for each unit introduction in the duration of the activity. You can if necessary, consider certain type of non-linear relationships between the reduction in the activity duration and the increase in direct cost but we will not do so in this module. Let's now consider the same software project example that we used for drawing the network and calculated the early start and late start of each activity. The table shows the normal time and the associated normal direct cost, as well as the crash time and the associated crash cost. From this, we can calculate, as shown in the table, for each activity, the maximum possible reduction from the normal duration and the slope of the assumed linear relationship. Recall that with normal duration for each activity, the project completion time is 11 weeks. The critical part is shown in red in the diagram. Now suppose there's a bonus of 14,000 for each duration in project completion time by one week. Hence we wonder least incremental cost for reducing the project completion time by one week. Clearly the project completion time can be reduced only if you reduce the duration of the activity on the critical part, which is activities A, B, E, F, G, H. In this critical part the duration of only activities B and D can be reduced. For activity B, the incremental cost of reducing the duration by one unit is 25 while the incremental cost of reducing the duration of activity E is 30. Hence it is better to reduce the duration of activity B. Since the bonus is 40 for one week, reduction in project completion time, we reduce the duration of the activity by one unit. That is the duration of the activity be reduced from four weeks to three weeks incurring an incremental cost of 25 while getting a bonus of 40. Thereby having an net gain of 40- 25 = 15. Now the project completion time is 10 weeks. We now have two critical paths as shown red in the diagram. In order to reduce a project completion time further we need to reduce the length of each of the paths A, B, E, F, G, H and A, C, E, F, G,H. Now we have to consider two possibilities, one in which the duration of the activity that is common to both of the paths is reduced by one unit, and the other in which we reduce the duration of two distinct activities, one in each path. Where each activity is in one and only one of the two critical parts. In this example, the activities on the critical parts. An incremental cost of reducing this duration by one week is 30. The other possible is reduce the duration of both activities B and C, increment of direct cost, or 25 plus 25, which is 50. Since 30 is less than 50, and 30 is less than the bonus of 40, it reduced the duration of E by one week. That is from two weeks to one week, thereby having a net gain of 40- 30 = 10. Now the project completion time is 9 weeks. We still have the same two critical paths. Now since all activities except B and C are at their minimum crash duration, the only possibility is to reduce the duration of both activities by one week. This, however, implies that the increase in direct cost would be 50. That is the bonus is only 40, hence, we will not reduce the duration of activities B and C. Note that the bonus is 50 per week, it would reduce the duration of activities B and C by 1 unit and the project completion time would be 8 weeks. No further reduction and project completion time is possible since all the activities in the critical path are at a their minimum duration. Know that default activities and any of the critical path are at their minimum duration,the project completion time cannot be decreased any further. It should be noted as you keep reducing the activity durations. More paths become critical, and more activities are on one or more critical paths. The critical activities must be managed well so that none of them take a longer time than the stipulated duration if the project completion time is not to be delayed. So reducing the project completion time typically implies that the flexibility is lost. And project management becomes more difficult. The above approach to reduce the product duration is conceptually sound but for large problems it becomes very cumbersome and difficult to implement. A linear programming approach solving this problem would be most appropriate. This completes this module. [MUSIC]