1. A simple set of tasks in “timeline-schedule” form Req. Gathering Req. Analysis High Level Design Detail Design & Code Test Case DevelopmentTest Execution We will put this in a different form - network form- to facilitate “further planning” t1 t3 t2t4

2. Planning with Network, PERT, & CPM 1.We use a Network of tasks to clearly show the “relationship” among tasks 2.A task requires time and resources 3.major use of network is for scheduling Req. analysis Test case development High level design Detail design & code Test execution Req. gathering

3. Relevant Characteristics of Tasks For each Task, T, (or Activity) –its predecessor tasks are: tasks that must be completed before T –its successor tasks are: tasks that can not begin until T is completed –its parallel tasks are: tasks that are independent and may be performed simultaneously with T

4. Tasks and Immediate Predecessors Table Tasks Immediate Predecessors Duration A B C D E F - A C C D, E 25 40 15 10 25 20 time units B

5. Graphical: Activity-on-Arrow Representation Task Z, 25 time units Task and the duration are represented as an arrow between two nodes, which represent the beginning and end of a task

6. We will be using this notation Graphical: Activity-on-Node Representation Task Z 25 time units The task and the duration are both represented in the Node

7. Activity-on-Node Representation of the 6 Tasks from the Previous Table A 20 B 25 D 15 E 40 C 10 F 25

8. Using the Network in Project Planning Major usage is for determining how long the project will take. The “longest” path through the network is the “expected project duration.” –It is also called the “CRITICAL” Path –** Note that if there is a delay in any of the tasks on a critical path, the result would be a delay in the completion of the overall project.

9. Critical Path of the Previous Network A 20 B 25 D 15 E 40 C 10 F 25 Tasks, A,B,C,E, and F are on the CRITICAL Path The “expected project duration” is 20+25+10+40+25 = 120 time units

10. Earliest Start(ES) and Earliest Finish(EF) of Tasks by Taking a “Forward Pass” through the Network, starting at Task A A 20 B 25 D 15 E 40 C 10 F 25 Task ESEF A B C D E F 55 45 20 0 95 20 55 45 70 120 95 ** ** Note that EF (early finish) of task E is 95, which forces ES (early start) of task F to be 95.

11. Late Start(LS) and Late Finish(LF) of Tasks by Taking a “Backward Pass” through the Network, starting at task F A 20 B 25 D 15 E 40 C 10 F 25 TaskLSLF A B C D E F 55 ** 80 45 20 0 95 20 55 45 95 120 95 ** Note that LS of task D is 80 because it needs only 15 time units to complete task D. But you can’t use it as C’s late finish time.

12. Slack Time Note that for Task D in the previous example : –ES is 55 and EF is 70 –LS is 80 and LF is 95 –so, we can actually take the LS (80)as the actual start time and not affect the over-all project schedule ! Slack time of an activity is defined as the difference in start time between when a (non-critical) task must start at the latest and when it can start at the earliest – Slack Time = (LS – ES) or (LF – EF) –in the above case slack time for task D is 80-55 = 25 time units

13. Free Slack We are interested in slack time that allows us to delay the start of an activity without impacting the start time of its successor. Free Slack of Task x = { (ES of the earliest successor of Task x) – (EF of x) } For Task D of the previous example : –Free Slack = 95 - 70 = 25 –In this case, Slack time is the same as Free Slack; so the start of activity D can be delayed by 25 time units and there is no impact.

14. Another Example A 10 C 15 B5B5 E5E5 D3D3 F5F5 -Activities A,C, F are on the Critical Path. -Next longest path is A,B,E,F Act. ESEFLSLF. A B C D E F 0 10 25 30 25 10 0 15 20 18 25 22 20 15 For Activity B (a non-critical activity): -slack time = LS - ES = 15 - 10 = 5 -free slack = earliest ES - EF = 15 -15 = 0 -this says even if there is a 5 unit of slack time, there is no free time For Activity D (a non-critical activity): -slack time = LS -ES = 22 - 15 = 7 -free slack = earliest ES -EF = 25 - 18 = 7 - this says we can delay activity D by 7 units without hurting the successor activity

15. Program Evaluation & Review Technique (PERT) PERT is based on the critical path that was addressed in the Network technique, except the task time is estimated using “expected” time –Expected task time (e-t-t)for each of the tasks on the critical path is computed as follows: e-t-t = (Optimistic-time + 4*Most-likely-time + Pessimistic-time)/6 Expected “Project” time (EP) = sum of all the e-t-t’s on the “critical path.” So, with PERT, we hope to get a more likely “expected project” time

16. Critical Path Method (CPM) CPM is concerned with the relationship of cost to schedule. –Given a time duration, T, and a cost, C, for a task, what would be the shortest time duration, Ts, if the associated cost, Cs, is allowed to increase? (Be very careful with this because thousands of software managers have been “burned” with this temptation!) –The cost slope for each task on the critical path may be defined as follows: cost slope for task i = | (Ci - Csi) / (Ti- Tsi) | COST TIME (Ti, Ci) (Tsi, Csi) We use absolute value to evade negative slopes TiTsi Csi Ci

17. CPM (cont.) Compute the task slope(s) of all the tasks. The lowest or smallest cost slope is the most effective time/cost trade-off task; however, the most effective one for the project would be the lowest cost slope of the task residing on the critical path. –We would apply more resources to that task to shorten the critical path, thus shortening the total project duration; then go on to look at the next lowest cost slope of tasks on the critical path. –One would stop this process when the “desired” schedule and the affordable cost is reached.