Introduction to Management Science 8th Edition by Bernard W. Taylor III Chapter 13 Project Management Chapter 13 - Project Management

Chapter Topics The Elements of Project Management The Project Network Probabilistic Activity Times Activity-on-Node Networks and Microsoft Project Project Crashing and Time-Cost Trade-Off Formulating the CPM/PERT Network as a Linear Programming Model Chapter 13 - Project Management

Overview Uses networks for project analysis. Networks show how projects are organized and are used to determine time duration for completion. Network techniques used are: CPM (Critical Path Method) PERT (Project Evaluation and Review Technique) Developed during late 1950’s. Chapter 13 - Project Management

Elements of Project Management Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity. Project Management is concerned with control of an activity for a relatively short period of time after which management effort ends. Primary elements of Project Management to be discussed: Project Team Project Planning Project Control Chapter 13 - Project Management

The Elements of Project Management The Project Team Project team typically consists of a group of individuals from various areas in an organization and often includes outside consultants. Members of engineering staff often assigned to project work. Most important member of project team is the project manager. Project manager is often under great pressure because of uncertainty inherent in project activities and possibility of failure. Project manager must be able to coordinate various skills of team members into a single focused effort. Chapter 13 - Project Management

Network for Building a House The Elements of Project Management The Project Network A branch reflects an activity of a project. A node represents the beginning and end of activities, referred to as events. Branches in the network indicate precedence relationships. When an activity is completed at a node, it has been realized. Figure 13.2 Network for Building a House Chapter 13 - Project Management

Network for Building a House with Activity Times The Project Network Planning and Scheduling Network aids in planning and scheduling. Time duration of activities shown on branches: Figure 13.3 Network for Building a House with Activity Times Chapter 13 - Project Management

Expanded Network for Building a House Showing Concurrent Activities The Project Network Concurrent Activities Activities can occur at the same time (concurrently). A dummy activity shows a precedence relationship but reflects no passage of time. Two or more activities cannot share the same start and end nodes. Figure 13.4 Expanded Network for Building a House Showing Concurrent Activities Chapter 13 - Project Management

Paths Through the House-Building Network The Project Network Paths Through a Network Table 8.1 Paths Through the House-Building Network Chapter 13 - Project Management

The Project Network The Critical Path (1 of 2) The critical path is the longest path through the network; the minimum time the network can be completed. In Figure 13.5: Path A: 1  2  3  4  6  7, 3 + 2 + 0 + 3 + 1 = 9 months Path B: 1  2  3  4  5  6  7, 3 + 2 + 0 + 1 + 1 + 1 = 8 months Path C: 1  2  4  6  7, 3 + 1 + 3 + 1 = 8 months Path D: 1  2  4  5  6  7, 3 + 1 + 1 + 1 + 1 = 7 months Chapter 13 - Project Management

Alternative Paths in the Network The Project Network The Critical Path (2 of 2) Figure 13.6 Alternative Paths in the Network Chapter 13 - Project Management

Earliest Activity Start and Finish Times The Project Network Activity Scheduling – Earliest Times ES is the earliest time an activity can start. ESij = Maximum (EFi) EF is the earliest start time plus the activity time. EFij = ESij + tij Figure 13.7 Earliest Activity Start and Finish Times Chapter 13 - Project Management

Latest Activity Start and Finish Times The Project Network Activity Scheduling – Earliest Times LS is the latest time an activity can start without delaying critical path time. LSij = LFij - tij LF is the latest finish time. LFij = Minimum (LSj) Figure 13.8 Latest Activity Start and Finish Times Chapter 13 - Project Management

Earliest and Latest Activity Start and Finish Times The Project Network Activity Slack Slack is the amount of time an activity can be delayed without delaying the project. Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal. Shared Slack is slack available for a sequence of activities. Figure 13.9 Earliest and Latest Activity Start and Finish Times Chapter 13 - Project Management

Calculating Activity Slack Time (1 of 2) The Project Network Calculating Activity Slack Time (1 of 2) Slack, Sij, computed as follows: Sij = LSij - ESij or Sij = LFij - EFij Figure 13.10 Activity Slack Chapter 13 - Project Management

Calculating Activity Slack Time (2 of 2) The Project Network Calculating Activity Slack Time (2 of 2) Table 8.2 Activity Slack Chapter 13 - Project Management

Probabilistic Activity Times Activity time estimates usually can not be made with certainty. PERT used for probabilistic activity times. In PERT, three time estimates are used: most likely time (m), the optimistic time (a) , and the pessimistic time (b). These provide an estimate of the mean and variance of a beta distribution: mean (expected time): variance: Chapter 13 - Project Management

Network for Installation Order Processing System Probabilistic Activity Times Example (1 of 3) Figure 13.11 Network for Installation Order Processing System Chapter 13 - Project Management

Activity Time Estimates for Figure 13.11 Probabilistic Activity Times Example (2 of 3) Table 8.3 Activity Time Estimates for Figure 13.11 Chapter 13 - Project Management

Network with Mean Activity Times and Variances Probabilistic Activity Times Example (3 of 3) Figure 13.12 Network with Mean Activity Times and Variances Chapter 13 - Project Management

Earliest and Latest Activity Times Probabilistic Activity Times Earliest and Latest Activity Times and Slack Figure 13.13 Earliest and Latest Activity Times Chapter 13 - Project Management

Activity Earliest and Latest Times and Slack Probabilistic Activity Times Earliest and Latest Activity Times and Slack Table 8.4 Activity Earliest and Latest Times and Slack Chapter 13 - Project Management

Probabilistic Activity Times Expected Project Time and Variance The expected project time is the sum of the expected times of the critical path activities. The project variance is the sum of the variances of the critical path activities. The expected project time is assumed to be normally distributed (based on central limit theorem). In example, expected project time (tp) and variance (vp) interpreted as the mean () and variance (2) of a normal distribution: = 25 weeks 2 = 6.9 weeks Chapter 13 - Project Management

Probability Analysis of a Project Network (1 of 2) Using normal distribution, probabilities are determined by computing number of standard deviations (Z) a value is from the mean. Value is used to find corresponding probability in Table A.1, Appendix A. Chapter 13 - Project Management

Normal Distribution of Network Duration Probability Analysis of a Project Network (2 of 2) Figure 13.14 Normal Distribution of Network Duration Chapter 13 - Project Management

Probability Analysis of a Project Network Example 1 (1 of 2) Z value of 1.90 corresponds to probability of .4713 in Table A.1, Appendix A. Probability of completing project in 30 weeks or less: (.5000 + .4713) = .9713. 2 = 6.9  = 2.63 Z = (x-)/  = (30 -25)/2.63 = 1.90 Chapter 13 - Project Management

Probability the Network Will Be Completed in 30 Weeks or Less Probability Analysis of a Project Network Example 1 (2 of 2) Figure 13.15 Probability the Network Will Be Completed in 30 Weeks or Less Chapter 13 - Project Management

Probability Analysis of a Project Network Example 2 (1 of 2) Z = (22 - 25)/2.63 = -1.14 Z value of 1.14 (ignore negative) corresponds to probability of .3729 in Table A.1, appendix A. Probability that customer will be retained is .1271 Chapter 13 - Project Management

Probability the Network Will Be Completed in 22 Weeks or Less Probability Analysis of a Project Network Example 2 (2 of 2) Figure 13.16 Probability the Network Will Be Completed in 22 Weeks or Less Chapter 13 - Project Management

Probability Analysis of a Project Network CPM/PERT Analysis with QM for Windows Exhibit 13.1 Chapter 13 - Project Management

Activity-on-Node Networks and Microsoft Project The project networks developed so far have used the “activity-on-arrow” (AOA) convention. “Activity-on-node” (AON) is another method of creating a network diagram. The two different conventions accomplish the same thing, but there are a few differences. An AON diagram will often require more nodes than an AOA diagram. An AON diagram does not require dummy activities because two “activities” will never have the same start and end nodes. Microsoft Project handles only AON networks. Chapter 13 - Project Management

Activity-on-Node Configuration Activity-on-Node Networks and Microsoft Project Node Structure This node includes the activity number in the upper left-hand corner, the activity duration in the lower left-hand corner, and the earliest start and finish times, and latest start and finish times in the four boxes on the right side of the node. Figure 13.17 Activity-on-Node Configuration Chapter 13 - Project Management

House-Building Network with AON Activity-on-Node Networks and Microsoft Project AON Network Diagram Figure 13.18 House-Building Network with AON Chapter 13 - Project Management

Activity-on-Node Networks and Microsoft Project Microsoft Project (1 of 4) Exhibit 13.2 Chapter 13 - Project Management

Activity-on-Node Networks and Microsoft Project Microsoft Project (2 of 4) Exhibit 13.3 Chapter 13 - Project Management

Activity-on-Node Networks and Microsoft Project Microsoft Project (3 of 4) Exhibit 13.4 Chapter 13 - Project Management

Activity-on-Node Networks and Microsoft Project Microsoft Project (4 of 4) Exhibit 13.5 Chapter 13 - Project Management

Project Crashing and Time-Cost Trade-Off Definition Project duration can be reduced by assigning more resources to project activities. Doing this however increases project cost. Decision is based on analysis of trade-off between time and cost. Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time. Crashing achieved by devoting more resources to crashed activities. Chapter 13 - Project Management

Network for Constructing a House Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5) Figure 13.19 Network for Constructing a House Chapter 13 - Project Management

Time-Cost Relationship for Crashing Activity 12 Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5) Crash cost and crash time have linear relationship: total crash cost/total crash time = $2000/5 = $400/wk Figure 13.20 Time-Cost Relationship for Crashing Activity 12 Chapter 13 - Project Management

Normal Activity and Crash Data for the Network in Figure 13.19 Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5) Table 8.5 Normal Activity and Crash Data for the Network in Figure 13.19 Chapter 13 - Project Management

Network with Normal Activity Times and Weekly Activity Crashing Costs Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5) Figure 13.21 Network with Normal Activity Times and Weekly Activity Crashing Costs Chapter 13 - Project Management

Revised Network with Activity 12 Crashed Project Crashing and Time-Cost Trade-Off Example Problem (5 of 5) As activities are crashed, the critical path may change and several paths may become critical. Figure 13.22 Revised Network with Activity 12 Crashed Chapter 13 - Project Management

Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows Exhibit 13.6 Chapter 13 - Project Management

Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (1 of 2) Project crashing costs and indirect costs have an inverse relationship. Crashing costs are highest when the project is shortened. Indirect costs increase as the project duration increases. Optimal project time is at minimum point on the total cost curve. Chapter 13 - Project Management

Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (2 of 2) Figure 13.23 A Time-Cost Trade-Off Chapter 13 - Project Management

Formulating as a Linear Programming Model The CPM/PERT Network Formulating as a Linear Programming Model The objective is to determine the earliest time the project can be completed (i.e., the critical path time). General linear programming model: Minimize Z = xi subject to: xj - xi  tij for all activities i  j xi, xj  0 Where: xi = earliest event time of node i xj = earliest event time of node j tij = time of activity i  j Chapter 13 - Project Management

Example Problem Formulation and Data (1 of 2) The CPM/PERT Network Example Problem Formulation and Data (1 of 2) Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7 subject to: x2 - x1  12 x3 - x2  8 x4 - x2  4 x4 - x3  0 x5 - x4  4 x6 - x4  12 x6 - x5  4 x7 - x6  4 xi, xj  0 Chapter 13 - Project Management

Example Problem Formulation and Data (2 of 2) The CPM/PERT Network Example Problem Formulation and Data (2 of 2) Figure 13.24 CPM/PERT Network for the House-Building Project with Earliest Event Times Chapter 13 - Project Management

Example Problem Solution with Excel (1 of 4) The CPM/PERT Network Example Problem Solution with Excel (1 of 4) Exhibit 13.7 Chapter 13 - Project Management

Example Problem Solution with Excel (2 of 4) The CPM/PERT Network Example Problem Solution with Excel (2 of 4) Exhibit 13.8 Chapter 13 - Project Management

Example Problem Solution with Excel (3 of 4) The CPM/PERT Network Example Problem Solution with Excel (3 of 4) Exhibit 13.9 Chapter 13 - Project Management

Example Problem Solution with Excel (4 of 4) The CPM/PERT Network Example Problem Solution with Excel (4 of 4) Exhibit 13.10 Chapter 13 - Project Management

Probability Analysis of a Project Network Example Problem – Model Formulation xi = earliest event time of node I xj = earliest event time of node j yij = amount of time by which activity i  j is crashed Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46 + 200y56 + 7000y67 subject to: y12  5 y12 + x2 - x1  12 x7  30 y23  3 y23 + x3 - x2  8 y67  1 y24  1 y24 + x4 - x2  4 x67 + x7 - x6  4 y34  0 y34 + x4 - x3  0 xj, yij  0 y45  3 y45 + x5 - x4  4 y46  3 y46 + x6 - x4  12 y56  3 y56 + x6 - x5  4 Chapter 13 - Project Management

Probability Analysis of a Project Network Example Problem – Excel Solution (1 of 3) Exhibit 13.11 Chapter 13 - Project Management

Probability Analysis of a Project Network Example Problem – Excel Solution (2 of 3) Exhibit 13.12 Chapter 13 - Project Management

Probability Analysis of a Project Network Example Problem – Excel Solution (3 of 3) Exhibit 13.13 Chapter 13 - Project Management

PERT Project Management Example Problem Problem Statement and Data (1 of 2) Given the following data determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less. Chapter 13 - Project Management

PERT Project Management Example Problem Problem Statement and Data (2 of 2) Chapter 13 - Project Management

PERT Project Management Example Problem Solution (1 of 4) Step 1: Compute the expected activity times and variances. Chapter 13 - Project Management

PERT Project Management Example Problem Solution (2 of 4) Step 2: Determine the earliest and latest times at each node. Chapter 13 - Project Management

PERT Project Management Example Problem Solution (3 of 4) Step 3: Identify the critical path and compute expected completion time and variance. Critical path (activities with no slack): 1  2  3  4  5 Expected project completion time (tp): 24 days Variance: v = 4 + 4/9 + 4/9 + 1/9 = 5 days Chapter 13 - Project Management

PERT Project Management Example Problem Solution (4 of 4) Step 4: Determine the Probability That the Project Will be Completed in 28 days or less. Z = (x - )/ = (28 -24)/5 = 1.79 Corresponding probability from Table A.1, Appendix A, is .4633 and P(x  28) = .9633. Chapter 13 - Project Management

Chapter 13 - Project Management