1 Textbook: pp. 405-444 Chapter 11: Project Management
2 Learning Objectives After completing this chapter, students will be able to: Understand how to plan, monitor, and control projects with the use of PERT and CPM. Determine earliest start, earliest finish, latest start, latest finish, and slack times for each activity, along with the total project completion time and total project cost. Reduce total project time at the least total cost by crashing the network using manual or linear programming techniques. Understand the important role of software in project management.
3 Introduction (1 of 2) Managing large-scale, complicated projects effectively is a difficult problem and the stakes are high o The first step in planning and scheduling a project is to develop the work breakdown structure (WBS) o Identify activities that must be performed and their beginning and ending events o Identify time, cost, resource requirements, predecessors, and people responsible for each activity o A schedule for the project then can be developed
4 Introduction (2 of 2) The programme evaluation and review technique (PERT) and the critical path method (CPM) are two popular quantitative analysis techniques for complex projects o PERT uses three time estimates to develop a probabilistic estimate of completion time o CPM is a more deterministic technique o They are so similar they are commonly considered as one technique, PERT/CPM
5 Six Steps of PERT/CPM 1. Define the project and all of its significant activities or tasks. 2. Develop the relationships among the activities. Decide which activities must precede others. 3. Draw the network connecting all of the activities. 4. Assign time and/or cost estimates to each activity. 5. Compute the longest time path through the network; this is called the critical path. 6. Use the network to help plan, schedule, monitor, and control the project. The critical path is important since any delay in these activities can delay the completion of the project!
6 Programme evaluation and review technique (PERT) PERT/CPM (1 of 2) Questions answered by PERT: 1. When will the entire project be completed? 2. What are the critical activities or tasks in the project that is, the ones that will delay the entire project if they are late? 3. Which are the noncritical activities that is, the ones that can run late without delaying the entire project s completion? 4. If there are three time estimates, what is the probability that the project will be completed by a specific date?
7 PERT/CPM (2 of 2) Questions answered by PERT: 5. At any particular date, is the project on schedule, behind schedule, or ahead of schedule? 6. On any given date, is the money spent equal to, less than, or greater than the budgeted amount? 7. Are there enough resources available to finish the project on time?
8 General Foundry Example (1 of 2) General Foundry, Inc. has long been trying to avoid the expense of installing air pollution control equipment The local environmental protection group has recently given the foundry 16 weeks to install a complex air filter system on its main smokestack General Foundry was warned that it will be forced to close unless the device is installed in the allotted period They want to make sure that installation of the filtering system progresses smoothly and on time
9 General Foundry Example (2 of 2) Activities and Immediate Predecessors for General Foundry, Inc.:
10 Drawing the PERT/CPM Network (1 of 2) Two common techniques for drawing PERT networks: o Activity-on-node (AON) nodes represent activities o Activity-on-arc (AOA) arcs represent the activities o The AON approach is easier and more commonly found in software packages o One node represents the start of the project, one node for the end of the project, and nodes for each of the activities o The arcs are used to show the predecessors for each activity
11 Drawing the PERT/CPM Network (2 of 2) Network for General Foundry, Inc.:
12 Activity Times (1 of 6) In some situations, activity times are known with certainty o CPM assigns just one time estimate to each activity and this is used to find the critical path In many projects there is uncertainty about activity times o PERT employs a probability distribution based on three time estimates for each activity, and a weighted average of these estimates is used for the time estimate and this is used to determine the critical path
13 Activity Times (2 of 6) The time estimates in PERT are: Optimistic time (a) = time an activity will take if everything goes as well as possible. There should be only a small probability (say, 1/100) of this occurring. Pessimistic time (b) = Most likely time (m) = time an activity would take assuming very unfavourable conditions. There should also be only a small probability that the activity will really take this long. most realistic time estimate to complete the activity.
14 Activity Times (3 of 6) PERT often assumes time estimates follow a beta probability distribution! Beta Probability Distribution with Three Time Estimates:
15 Activity Times (4 of 6) To find the expected activity time (t), the beta distribution weights the estimates as follows t = a + 4 m + b 6 To compute the dispersion or variance of activity completion time Variance = b 6 a 2
16 Activity Times (5 of 6) Time Estimates (Weeks) for General Foundry, Inc.:
17 Activity Times (6 of 6) General Foundry s Network with Expected Activity Times:
18 How to Find the Critical Path (1 of 11) We accept the expected completion time for each task as the actual time The total of 25 weeks does not take into account that some of the tasks could be taking place at the same time To find out how long the project will take we perform the critical path analysis for the network The critical path is the longest path through the network
19 How to Find the Critical Path (2 of 11) To find the critical path, determine the following quantities for each activity: 1. Earliest start (ES) time: the earliest time an activity can begin without violation of immediate predecessor requirements 2. Earliest finish (EF) time: the earliest time at which an activity can end 3. Latest start (LS) time: the latest time an activity can begin without delaying the entire project 4. Latest finish (LF) time: the latest time an activity can end without delaying the entire project
20 How to Find the Critical Path (3 of 11) Activity times are represented in the nodes Earliest times are computed as Earliest finish time = Earliest start time + Expected activity time EF = ES + t Earliest start = Largest of the earliest finish times of immediate predecessors ES = Largest EF of immediate predecessors
21 How to Find the Critical Path (4 of 11) At the start of the project we set the time to zero Thus ES = 0 for both A and B
22 How to Find the Critical Path (5 of 11) General Foundry s Earliest Start (ES) and Earliest Finish (EF) Times:
23 How to Find the Critical Path (6 of 11) General Foundry s Earliest Start (ES) and Earliest Finish (EF) Times: Use a forward pass through the network!
24 How to Find the Critical Path (7 of 11) Compute latest start (LS) and latest finish (LF) times for each activity by making a backward pass through the network. Latest start time = Latest finish time Expected activity time LS = LF t Latest finish time = Smallest of latest start times for following activities LF = Smallest LS of following activities For activity H LS = LF t = 15 2 = 13 weeks
25 How to Find the Critical Path (8 of 11) General Foundry s Latest Start (LS) and Latest Finish (LF) Times:
26 How to Find the Critical Path (9 of 11) Once ES, LS, EF, and LF have been determined, find the amount of slack time for each activity Slack = LS ES, or Slack = LF EF Activities A, C, E, G, and H have no slack time These are called critical activities and they are said to be on the critical path The total project completion time is 15 weeks Industrial managers call this a boundary timetable
27 How to Find the Critical Path (10 of 11) General Foundry s Schedule and Slack Times:
28 How to Find the Critical Path (11 of 11) General Foundry s Critical Path (A C E G H):
29 Probability of Project Completion (1 of 6) The critical path analysis helped determine the expected project completion time of 15 weeks o Variation in activities on the critical path can affect overall project completion o If the project is not complete in 16 weeks, the foundry will have to close PERT uses the variance of critical path activities to help determine the variance of the overall project Project variance = variances of activities on the critical path
30 Probability of Project Completion (2 of 6) From Table 11.2 we know Hence, the project variance is Project variance 4 4 36 64 4 112 3.111 36 36 36 36 36 36
31 Probability of Project Completion (3 of 6) We know the standard deviation is the square root of the variance, so Project standard deviation T Project variance 3.111 1.76 weeks We assume activity times are independent and that total project completion time is normally distributed A bell-shaped curve can be used to represent project completion dates
32 Probability of Project Completion (4 of 6) Probability Distribution for Project Completion Times:
33 Table --- Appendix A (pp. 568-569) Probability of Project Completion (5 of 6) The standard normal equation can be applied as follows Z Due date Expected date of completion 16 weeks 15 weeks 0.57 1.76 weeks T From Appendix A we find the probability of 0.71566 associated with this Z value That means the probability this project can be completed in 16 weeks or less is 0.716
34 Probability of Project Completion (6 of 6) Probability of General Foundry s Meeting the 16-Week Deadline:
35 What PERT Was Able to Provide 1. The project s expected completion date is 15 weeks 2. There is a 71.6% chance that the equipment will be in place within the 16-week deadline 3. Five activities (A, C, E, G, H) are on the critical path 4. Three activities (B, D, F) are not critical but have some slack time built in 5. A detailed schedule of activity starting and ending dates has been made available
38 Sensitivity Analysis and Project Management (1 of 3) The time required to complete an activity can vary from the projected or expected time: o If the activity is on the critical path, the completion time of the project will change o This will also have an impact on ES, EF, LS, and LF times for other activities o Exact impact depends on the relationship between the various activities
39 Sensitivity Analysis and Project Management (2 of 3) A predecessor activity is one that must be accomplished before the given activity can be started A successor activity is one that can be started only after the given activity is finished A parallel activity is one that does not directly depend on the given activity o Once these have been defined, we can explore the impact that an increase (decrease) in an activity time for a critical path activity would have on other activities in the network
40 Sensitivity Analysis and Project Management (3 of 3) Impact of an Increase (Decrease) in an Activity Time for a Critical Path Activity:
41 PERT/COST PERT is an excellent method of monitoring and controlling project length but it does not consider the very important factor of project cost PERT/Cost is a modification of PERT that allows a manager to plan, schedule, monitor, and control cost as well as time
42 Four Steps of the Budgeting Process (1 of 2) Step 1: Identify all costs associated with each of the activities. Then add these costs together to get one estimated cost or budget for each activity. Step 2: If you are dealing with a large project, several activities can be combined into larger work packages. A work package is simply a logical collection of activities. Since the General Foundry project we have been discussing is small, each activity will be a work package.
43 Four Steps of the Budgeting Process (2 of 2) Step 3: Convert the budgeted cost per activity into a cost per time period. To do this, we assume that the cost of completing any activity is spent at a uniform rate over time. Thus, if the budgeted cost for a given activity is $48,000 and the activity s expected time is 4 weeks, the budgeted cost per week is $12,000 ($48,000/4 weeks). Step 4: Using the earliest and latest start times, find out how much money should be spent during each week or month to finish the project by the date desired.
44 Budgeting for General Foundry (1 of 6) The Gantt chart below illustrates this process Determine how much will be spent on each activity during each week and fill these amounts into a chart in place of the bars Gantt Chart for General Foundry Example:
45 Budgeting for General Foundry (2 of 6) Activity Cost for General Foundry, Inc.:
46 Budgeting for General Foundry (3 of 6) Budgeted Cost ($1,000s) for General Foundry, Inc., Using Earliest Start Times:
47 Budgeting for General Foundry (4 of 6) Budgeting using the earliest start time gives a result that resembles the Gantt chart shown previously If latest start times and used expenditures are delayed until the latest possible time Any budget between these two ranges may be chosen
48 Budgeting for General Foundry (5 of 6) Budgeted Cost ($1,000s) for General Foundry, Inc., Using Latest Start Times:
49 Budgeting for General Foundry (6 of 6) Budget Ranges for General Foundry:
50 Monitoring and Controlling Project Costs (1 of 3) Ensure the project is progressing on schedule Cost overruns are kept to a minimum Status of the entire project should be checked periodically o Is the project on schedule? o What is the value of work completed? o Are there any overruns?
51 Monitoring and Controlling Project Costs (2 of 3) The value of work completed, or the cost to date for any activity Value of work completed = (Percentage of work complete) (Total activity budget) The activity difference Activity difference = Actual cost Value of work completed
52 Monitoring and Controlling Project Costs (3 of 3) Monitoring and Controlling Budgeted Cost:
53 Project Crashing (1 of 2) Projects will sometimes have deadlines that are impossible to meet using normal procedures By using exceptional methods, it may be possible to finish the project in less time Costs usually increase Reducing a project s completion time is called crashing
54 Project Crashing (2 of 2) Start by using the normal time to create the critical path The normal cost is the cost for completing the activity using normal procedures If the project will not meet the required deadline, extraordinary measures must be taken o The crash time is the shortest possible activity time and will require additional resources o The crash cost is the price of completing the activity in the earlier-than-normal time
55 Four Steps to Project Crashing (1 of 2) Step 1: Find the normal critical path and identify the critical activities. Step 2: Compute the crash cost per week (or other time period) for all activities in the network using the formula. Crash cost /Time period = Crash cost Normal cost Normal time Crash time
56 Four Steps to Project Crashing (2 of 2) Step 3: Select the activity on the critical path with the smallest crash cost per week. Crash this activity to the maximum extent possible or to the point at which your desired deadline has been reached. Step 4: Check to be sure that the critical path you were crashing is still critical. Often, a reduction in activity time along the critical path causes a noncritical path or paths to become critical. If the critical path is still the longest path through the network, return to step 3. If not, find the new critical path and return to step 3.
57 General Foundry (1 of 3) Suppose: o General Foundry has been given 14 weeks instead of 16 weeks to install the new equipment o A bonus was on the line if equipment is installed in 12 weeks or less The critical path for the project is 15 weeks What options does the firm have?
58 General Foundry (2 of 3) Normal and Crash Data for General Foundry, Inc.:
59 General Foundry (3 of 3) Crash and Normal Times and Costs for Activity B:
60 Project Crashing with Linear Programming (1 of 5) Linear programming can be used to find the best project crashing schedule Decision variables for General Foundry: X A = EF for activity A X B = EF for activity B X C = EF for activity C X D = EF for activity D X E = EF for activity E X F = EF for activity F X G = EF for activity G X H = EF for activity H X start = start time for project (usually 0) X finish = earliest finish time for the project Y = the number of weeks that each activity is crashed Y A = the number of weeks activity A is crashed and so forth up to Y H
61 Project Crashing with Linear Programming (2 of 5) General Foundry s Network with Activity Times:
62 Project Crashing with Linear Programming (3 of 5) Objective function: Minimise crash cost = 1,000Y A + 2,000Y B + 1,000Y C + 1,000Y D + 1,000Y E + 500Y F + 2,000Y G + 3,000Y H Crash Time Constraints: Project Completion Constraint: Y A 1 Y E 2 X finish 12 Y B 2 Y F 1 Y C 1 Y G 3 Y D 1 Y H 1
63 Project Crashing with Linear Programming (4 of 5) Constraints Describing the Network: EF time EF time for predecessor + Activity time EF EF predecessor + (t Y), or X X predecessor + (t Y) For activity A, X A X start + (2 Y A ) or X A X start + Y A 2 For activity B, X B X start + (3 Y B ) or X B X start + Y B 3 For activity C, X C X A + (2 Y C ) or X C X A + Y C 2 For activity D, X D X B + (4 Y D ) or X D X B + Y D 4 For activity E, X E X C + (4 Y E ) or X E X C + Y E 4 For activity F, X F X C + (3 Y F ) or X F X C + Y F 3 For activity G, X G X D + (5 Y G ) or X G X D + Y G 5 For activity G, X G X E + (5 Y G ) or X G X E + Y G 5 For activity H, X H X F + (2 Y H ) or X H X F + Y H 2 For activity H, X H X G + (2 Y H ) or X H X G + Y H 2 H finished X finish X H
65 Other Topics in Project Management Subprojects o For extremely large projects, an activity may be made of several smaller sub-activities Milestones o Major events in a project are often referred to as milestones Resource Levelling o Software o o Adjusts the activity start away from the early start so that resource utilisation is more evenly distributed over time Numerous project management software packages They can be used to develop budget schedules, adjust future start times, and level resource utilisation
66 Homework --- Chapter 11 End of chapter self-test 1-18 (pp. 432) Compile all answers into one document and submit at the beginning of the next lecture! On the top of the document, write your Pinyin-Name and Student ID. Please read Chapter 12!