Project Management Chapter Topics The Elements of Project Management The Project Network Probabilistic Activity Times Project Crashing and Time-Cost Trade-Off QP5013 - PROJECT MANAGEMENT

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 1950s. QP5013 - PROJECT MANAGEMENT

The 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. QP5013 - 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. QP5013 - PROJECT MANAGEMENT

QP5013 - 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. QP5013 - PROJECT MANAGEMENT

The Project Network Planning and Scheduling - Network aids in planning and scheduling. - Time duration of activities shown on branches: Network for building a house with activity times QP5013 - PROJECT MANAGEMENT

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. Expanded network for building a house showing concurrent activities. QP5013 - PROJECT MANAGEMENT

The Project Network Paths Through the Network Expanded network for building a house showing concurrent activities. Paths Through the House-Building Network QP5013 - PROJECT MANAGEMENT

The Project Network The Critical Path The critical path is the longest path through the network; the minimum time the network can be completed. 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 Alternative paths in the network QP5013 - PROJECT MANAGEMENT

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 Earliest activity start and finish times QP5013 - PROJECT MANAGEMENT

The Project Network Activity Scheduling - Latest 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) Latest activity start and finish times QP5013 - PROJECT MANAGEMENT

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. Earliest activity start and finish times QP5013 - PROJECT MANAGEMENT

The Project Network Calculating Activity Slack Time - Slack, Sij, computed as follows: Sij = LSij - ESij or Sij = LFij - EFij Activity Slack   QP5013 - 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: QP5013 - PROJECT MANAGEMENT

Probabilistic Activity Times Example Network with mean activity times and variances QP5013 - PROJECT MANAGEMENT

Earliest and latest activity times QP5013 - PROJECT MANAGEMENT Probabilistic Activity Times Earliest and Latest Activity Times and Slack Earliest and latest activity times Activity Earliest and Latest Times and Slack QP5013 - 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 QP5013 - PROJECT MANAGEMENT

Probability Analysis of the Project Network - 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, App. A. Normal distribution of network duration QP5013 - PROJECT MANAGEMENT

Probability Analysis of the Project Network Example 1 2 = 6.9  = 2.63 Z = (x-)/  = (30 -25)/2.63 = 1.90 - 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. Probability the network will be completed in 30 weeks or less QP5013 - PROJECT MANAGEMENT

Probability Analysis of the Project Network Example 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 Probability the network will be completed in 22 weeks or less QP5013 - PROJECT MANAGEMENT

QP5013 - PROJECT MANAGEMENT Probability Analysis of the Project Network CPM/PERT Analysis with QM for Windows QP5013 - 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. QP5013 - PROJECT MANAGEMENT

Project Crashing and Time-Cost Trade-Off Example Problem (1 of 3) Network for constructing a house Time–cost relationship for crashing activity 1 : 2 Crash cost and crash time have linear relationship: total crash cost/total crash time = $2000/5 = $400/wk QP5013 - PROJECT MANAGEMENT

Project Crashing and Time-Cost Trade-Off Example Problem (2 of 3) QP5013 - PROJECT MANAGEMENT

Project Crashing and Time-Cost Trade-Off Example Problem (3 of 3) Network with normal activity times and weekly activity crashing costs - As activities are crashed, the critical path may change and several paths may become critical. The revised network with activity 1 : 2 crashed QP5013 - PROJECT MANAGEMENT

QP5013 - PROJECT MANAGEMENT Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows QP5013 - PROJECT MANAGEMENT

QP5013 - PROJECT MANAGEMENT Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost 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. The time–cost trade-off QP5013 - PROJECT MANAGEMENT

PERT Project Management Example Problem Problem Statement and Data - 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. QP5013 - PROJECT MANAGEMENT

PERT Project Management Example Problem Solution (1 of 3) Step 1 : Compute the Expected Activity Times and Variances QP5013 - PROJECT MANAGEMENT

PERT Project Management Example Problem Solution (2 of 3) Step 2: Determine the Earliest and Latest Times at each Node 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 QP5013 - PROJECT MANAGEMENT

PERT Project Management Example Problem Solution (3 of 3) 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. QP5013 - PROJECT MANAGEMENT

QP5013 - PROJECT MANAGEMENT Additional Exercises No 10, 12, 16, 18, 24, 25 & 26; page 342 – 351, Chapter 8, Taylor. Please try these questions & we will discuss it during our class. QP5013 - PROJECT MANAGEMENT