2Learning ObjectivesUnderstand how to plan, monitor, and control projects using PERT/CPM.Determine earliest start, earliest finish, latest start, latest finish, and slack times for each activity.Understand the impact of variability in activity times.Understand important role of software such as Microsoft Project in project management.
3Project Planning Specific questions that are considered: What is goal or objective of project?What are various activities (or tasks) that constitute project?How are these activities linked?What are precedence relationships between activities?What is time required for each activity?What other resources (such as labor, raw materials, and machinery) are required for each activity?
4Project Scheduling Questions to be answered: When will project be completed?What is schedule for each activity?What are critical activities in project?What are non-critical activities in project?By how much can a non-critical activity be delayed without affecting completion time of entire project?If variability in activity times is considered, what is probability project will be completed by a specific deadline?
5Project ControllingControl of large projects involves close monitoring of schedules, resources, and budgets.Questions to be answered:At any particular date or time, is project on schedule, behind schedule, or ahead of schedule?At any particular date or time, is money spent on project equal to, less than, or greater than budgeted amount?Are there enough resources available to finish project on time?If project is to be finished in shorter amount of time, what is best way to accomplish this at least cost?
6Gantt Chart for a New Voice Recognition System Project ActivitiesApr.MayJuneJulyAug.a. Design Systemb. Build Prototypec. Test Prototyped. Estimate Material Costse. Estimate Labor Costsf. Refine Designg. Build the final Producth. Demonstrate the producti. Market the Product
7Drawing Project Network There are two major approaches for drawing a project network -- Activity on Node (AON), and Activity on Arc (AOA).Although both approaches are popular in practice, many project management software packages, including Microsoft Project 2000, use AON networks.Focus is on AON networks.
8CPM and PERT Network techniques Developed in 1950’s CPM by DuPont for chemical plants (1957)PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958)Consider precedence relationships and interdependenciesEach uses a different estimate of activity times
9CPM/PERTCPM stands for Critical Path Method. It is Project Scheduling with Known Activity Times (CPM)PERT stands for Program Evaluation Review Technique. It is Project Scheduling with Uncertain Activity Times (PERT)PERT/CPM is used to plan the scheduling of individual activities that make up a project.PERT/CPM can be used to determine the earliest/latest start and finish times for each activity, the entire project completion time and the slack time for each activity.
10Project NetworkA project network can be constructed to model the precedence of the activities.The nodes of the network represent the activities.The arcs of the network reflect the precedence relationships of the activities.A critical path for the network is a path consisting of activities with zero slack.
11Determining the Critical Path Step 1: Make a forward pass through the network as follows: For each activity i beginning at the Start node, compute:Earliest Start Time = the maximum of the earliest finish times of all activities immediately preceding activity i. (This is 0 for an activity with no predecessors.)Earliest Finish Time = (Earliest Start Time) + (Time to complete activity i.The project completion time is the maximum of the Earliest Finish Times at the Finish node.
12Determining the Critical Path Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the Finish node to the Start node. At a given node, j, consider all activities ending at node j. For each of these activities, (i,j), compute:Latest Finish Time = the minimum of the latest start times beginning at node j. (For node N, this is the project completion time.)Latest Start Time = (Latest Finish Time) - (Time to complete activity (i,j)).
13Determining the Critical Path Step 3: Calculate the slack time for each activity by:Slack = (Latest Start) - (Earliest Start), or= (Latest Finish) - (Earliest Finish).A critical path is a path of activities, from the Start node to the Finish node, with 0 slack times.
14Uncertain Activity Times In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution.An activity’s mean completion time is:t = (a + 4m + b)/6Each activity’s completion time variance is:S2 = ((b-a)/6)2a = the optimistic completion time estimateb = the pessimistic completion time estimatem = the most likely completion time estimateThe variance of the critical path is: 2 = S2
15Uncertain Activity Times In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times.The overall project completion time is assumed to have a normal distribution with mean equal to the sum of the means along the critical path and variance equal to the sum of the variances along the critical path.
16Network for construction of a new building Example 1 A project comprises of the following activities and their predecessors.Activity Description PredecessorA Survey site --B Initial design --C Obtain approval A,BD Select architect CE Establish budget CF Finalize design D,EG Obtain financing EH Hire contractor F,GDraw a network for this project.
17Critical Path Method (CPM) Example 2 A project comprises of the following activities and their predecessors.Immediate ExpectedActivity Predecessor time (days)A - 2B - 6C A 4D B 3E C, D 1a. Draw a network and determine the critical path. How long will it take to complete the project? b. Provide a detailed activity schedule for the project.
18Program Evaluation and Review Technique (PERT) Example 3 For the following activities and their predecessors and the three time estimates (days):Activity Predecessor Optimistic (a) Most Probable (m) Pessimistic (b)ABC A 4 5 6D B 7 8 9E C, D a. Compute the expected completion time for each activity. b. Draw a network and determine the critical path based on the expected completion times.c. What is the probability of finishing the project in less than 19 days?d. What is the probability of finishing the project in less than 23 days?
19Network for construction of a new building Refer to Example 1-Your turn A project comprises of the following activities and their predecessors.Activity Description Predecessor Time (Days)A Survey siteB Initial designC Obtain approval A,B 24D Select architect C 8E Establish budget C 12F Finalize design D,E 30G Obtain financing E 24H Hire contractor F,G 16Draw a network for this project and determine the critical path. How long would it take to finish this project?