2 Learning Objectives Describe project management objectives Describe the project life cycleDiagram networks of project activitiesEstimate the completion time of a projectCompute the probability of completing a project by a specific timeDetermine how to reduce the length of a project effectivelyDescribe the critical chain approach to project management
3 Definitions Project (or program): Project management: Milestones: a series of related jobs or tasks directed towards some major output requiring a significant amount of time for completion.Project management:planning, directing, and controlling resources (people, equipment, materials) to meet the technical, cost, and time constraints of a project (or program).Milestones:tasks or events planned to be completed at certain times during the program or project.
4 Definitions Project: Activities: Precedence relationships: An endeavor with specific objectives & multiple activities with defined precedence relationships, to be completed within a limited durationActivities:Specific tasks that must be completed & require resourcesPrecedence relationships:A natural order between activities, where some tasks must be complete before others can begin
5 Five Project Life Cycle Phases Conception: identify the needFeasibility analysis or study: costs benefits, and risksPlanning: who, how long, what to do?Execution: doing the projectTermination: ending the project
7 Network Planning Techniques Program Evaluation & Review Technique (PERT):Developed to manage the Polaris missile projectMany tasks pushed the boundaries of science & engineeringTasks’ duration = probabilistic; method = activity on arrow.Critical Path Method (CPM):Developed to coordinate maintenance projects in the chemical industryA complex undertaking, but individual tasks are routineTasks’ duration = deterministic; method = activity on node.
8 Both PERT and CPMGraphically display the precedence relationships & sequence of activitiesEstimate the project’s durationIdentify critical activities that cannot be delayed without delaying the projectEstimate the amount of slack associated with non-critical activities
9 Notation Activity-on-Arrow (AOA): Activity-on-Node (AON): Each arrow represents an activity & its precedence relationship(s)May require the use of “dummy” arrows if the activity has more than one successor taskNodes used only as end-points for arrowsActivity-on-Node (AON):Uses nodes to represent the activityUses arrows to represent precedence relationships
11 Step 1-Define the Project: Cables By Us is bringing a new product on line to be manufactured in their current facility in some existing space. The owners have identified 11 activities and their precedence relationships. Develop an AON for the project.
13 Step 3 (a)- Add Deterministic Time Estimates and Connected Paths
14 Step 3 (a) (Continued): Calculate the Path Completion Times The longest path (ABDEGIJK) limits the project’s duration (project cannot finish in less time than its longest path)ABDEGIJK is the project’s critical path
15 Some Network Definitions All activities on the critical path have zero slackSlack defines how long non-critical activities can be delayed without delaying the projectSlack = the activity’s late finish minus its early finish (or its late start minus its early start)Earliest Start (ES) = the earliest finish of the immediately preceding activityEarliest Finish (EF) = is the ES plus the activity timeLatest Start (LS) and Latest Finish (LF) depend on whether or not the activity is on the critical path
19 Revisiting Cables By Us Using Probabilistic Time Estimates
20 Using Beta Probability Distribution to Calculate Expected Time Durations A typical beta distribution is shown below, note that it has definite end pointsThe expected time for finishing each activity is a weighted average
27 Gantt Chart Showing the Latest Possible Start Times if the Project Is to Be Completed in 44.83 Weeks
28 Estimating the Probability of Completion Dates Using probabilistic time estimates offers the advantage of predicting the probability of project completion datesWe have already calculated the expected time for each activity by making three time estimatesNow we need to calculate the variance for each activityThe variance of the beta probability distribution is:where p=pessimistic activity time estimateo=optimistic activity time estimate
30 Variances of Each Path through the Network Path NumberActivities on PathPath Variance (weeks)1A,B,D,E,G,H,J,k4.822A,B,D,E,G,I,J,K4.963A,C,F,G,H,J,K2.244A,C,F,G,I,J,K2.38
31 Calculating the Probability of Completing the Project in Less Than a Specified Time When you know:The expected completion timeIts varianceYou can calculate the probability of completing the project in “X” weeks with the following formula:Where DT = the specified project completion timeEFP = the expected completion time of the path
32 Probability of Completion Example: Calculating the probability of finishing the project in 48 weeksUse the z values in Appendix B to determine probabilitiesE.G. for path 1Path NumberActivities on PathPath Variance (weeks)z-valueProbability of Completion1A,B,D,E,G,H,J,k4.821.52160.93572A,B,D,E,G,I,J,K4.961.42150.92223A,C,F,G,H,J,K2.241.0004A,C,F,G,I,J,K2.38
33 Time-Cost Tradeoffs (Crashing the Network) Prepare a CPM-type diagram with activity data: Normal Time (NT), Normal Cost (NC), Crash Time (CT), Crash Cost (CC).Determine the critical path.Determine the cost/unit of time to crash each activity.Shorten the project completion time incrementally at the lowest possible cost.Consider total costs to analyze scheduling options.
34 Reducing the Time of a Project (crashing) ActivityNormal Time (wk)Normal Cost ($)Crash TimeCrash Cost ($)Max. weeks of reductionReduce cost per weekA48,000311,00013,000B630,000535,0005,000C6,000D24,00028,00022,000E1460,0001272,000F6,5001500GH4,000I1,000J6,4001,200K
35 Crashing Costs are considered to be linear Crashing Example: Suppose the Cables By Us project manager wants to reduce the new product project from 41 to 36 weeks.Crashing Costs are considered to be linearLook to crash activities on the critical pathCrash the least expensive activities on the critical path first (based on cost per week)Crash activity I from 3 weeks to 2 weeks $1000Crash activity J from 4 weeks to 2 weeks $2400Crash activity D from 6 weeks to 4 weeks $4000Recommend Crash Cost $7400Will crashing 5 weeks return more than it costs?
37 The Critical Chain Approach The Critical Chain Approach focuses on the project due date rather than on individual activities and the following realities:Project time estimates are uncertain so we add safety timeMulti-levels of organization may add additional time to be “safe”Individual activity buffers may be wasted on lower-priority activitiesA better approach is to place the project safety buffer at the endOriginal critical pathActivity AActivity BActivity CActivity DActivity ECritical path with project bufferProject Buffer
38 Adding Feeder Buffers to Critical Chains The theory of constraints, the basis for critical chains, focuses on keeping bottlenecks busy.Time buffers can be put between bottlenecks in the critical pathThese feeder buffers protect the critical path from delays in non-critical paths
39 Homework HintsProblems : Use CPM deterministic model (A). [10 points]Problems : Use CPM probabilistic model (A). Use the AON diagram for [20 points]Problems : Use CPM deterministic model (A). Crash the project one week at a time—find the lowest cost task to reduce. Watch for the creation of additional critical paths. [10 points]