OPER 576 Project ManagementProject Life Cycle StagesSlide 3More PERT/CPM EstimatesSlide 5Slide 6Slide 7Slide 8Slide 9Crashing ActivitiesTime-Cost Tradeoffs in CPMProject & Activity CostsTime & Costs: Normal vs. CrashLinear Time-Cost TradeoffSelecting Activities to CrashBalancing Overhead & Direct CostsSoftware Project SchedulesTime/Cost Trade-off AnalysisWhich Activities are the Best Candidates for Crashing?Options for Crashing ActivitiesPotential Problems with CrashingTime-Cost Tradeoff HeuristicNetwork Crashing ExampleSlide 24Slide 25Slide 26Slide 27Slide 28Slide 29Crashing SummaryOPER 576 Project ManagementReducing Project Duration or Project CrashingGreg Magnan, Ph.D.May 20, 2004Project Life Cycle StagesRecall Pert/CPM EstimatesTaskImmediate PredecesorsOptimistic Most Likely PessimisticA None 3 6 15B None 2 4 14C A 6 12 30D A 2 5 8E C 5 11 17F D 3 6 15G B 3 9 27H E,F 1 4 7I G,H 4 19 2864)(cbajET226acjMore PERT/CPM Estimates•Activity Time Estimates for beta distribution–a: optimistic time, usually about 1 percent chance activity can be completed within a–b: most likely time–c: pessimistic time, usually about 1 percent chance that activity will take longer than c.•Activity j’s expected time (b distribution)•Activity j’s variance (b distribution)PERT NotationD -- the desired project durationTe -- expected project duration pathcriticalanyjejETT one )(Critical path variance = pathcriticaloneanyjj 2Z = number of standard normal deviates from mean =VariancePath CriticaleTD Project Completion ProbabilityWhat is the probability of finishing this project in less than 53 days?p(t < D)TE = 54Z = D - TEcp2tD=53PERT NetworkA(7)B(5.333)C(14)D(5)E(11)F(7)H(4)G(11)I(18)Duration = 54 Days2(A) =22=4 2(C) =16 2(E) =4 2(H) =1 2(I) =16226Optim(j) - Pessim(j). = jTask Optimistic Most Likely Pessimistic VarianceA 3 6 15 4B 2 4 14C 6 12 30 16D 2 5 8E 5 11 17 4F 3 6 15G 3 9 27H 1 4 7 1I 4 19 28 16(Sum the variance along the critical path.)2= 41= 41There is a 43.6% probability that this project will be completed in less than 53 weeks.p(Z < -.156) = .5 - .0636 = .436, or 43.6 %Z = D - T=53- 5441= -.156Ecp2TE = 54p(t < D)tD=53Crashing Activities•Activity & project duration may be influenced by resource allocation decisions…more resources—less time needed•Sometimes, we can expedite completion of a task by assigning more people or equipment. Thus, total direct costs tend to vary inversely with project duration. Indirect costs, however, tend to increase with overall project completion time.TotalCostsIndirectCostsDirectCostsProject durationExpenseTime-Cost Tradeoffs in CPM•Basic Assumption: Some activities can be expedited, at a cost•Why accelerate an activity?–Complete the task in a shorter duration, thereby reducing the duration of the critical path, thereby reducing the length of the project•Avoid late penalties•Earn early completion incentive payments•Time Cost Problem: Determine the optimum project duration based on time-cost tradeoffsProject & Activity Costs•PROJECT DIRECT COSTS: Directly assigned to work package or activity–“Normal” costs for “normal” time•Direct labor expenses•Materials•Equipment•Subcontractors•INDIRECT EXPENSES: Cannot be associated with any work package or activity–Overhead expenses•including supervisory expenses•administration•contractual penalties or early completion incentives–ConsultingTime & Costs: Normal vs. Crash•For the time-only CPM project schedule, we typically assume that activity duration is fixed at its NORMAL TIME, or the duration with the lowest direct activity cost (i.e., NORMAL COST). •However, some activities may be expedited if higher resource levels are available. The shortest activity duration is called CRASH TIME. The cost to complete an activity in that amount of time is called CRASH COST.Linear Time-Cost TradeoffIn theory, the normal or expected duration of a task can be reduced by assigning additional resources to the task TimeCostCrash PointNormal PointSlope (bj) = Increase in cost by reducing task by one time unitNormal timeCrash timeNormal cost Crash cost tjNtjcCjcCjNSelecting Activities to Crash•Cost Slope = Rise / Run•Cost Slope = CC – NC / NT – CT•= CC – NC NT – CT•where,–CC = Crash Cost–NC = Normal Cost–NT = Normal Time–CT = Crash Time•Calculate for each activity on Critical Path= CC – NC = $800 - $400 NT – CT 10 – 5= $400/5 = $80 per unit of timeBalancing Overhead & Direct CostsProject DurationCostIndirect (overhead) CostsDirect CostsTotal CostCrash TimeNormal TimeMinimum Cost SolutionSoftware Project Schedules “Observe that for the programmer, as for the chef, the urgency of the patron may govern the scheduled completion of the task, but it cannot govern the actual completion. An omelet, promised in ten minutes, may appear to be progressing nicely. But when it has not set in ten minutes, the customer has two choices--wait or eat it raw. Software customers have the same choices.The cook has another choice; he can turn up the heat. The result is often an omelet nothing can save--burned in one part, raw in another.”F.P. Brooks, “The Mythical Man-Month”, Datamation, Vol. 20, No 12 (Dec, 1974), pp. 44-52.Time/Cost Trade-off Analysis•You might think that total project costs will increase when we begin to crash activities•But, total project costs consist of both indirect (project-based) costs (PBC) and direct (activity-based) costs (ABC)–ABC (direct) go up when we crash activities in an effort to finish the project early–But, PBC (the indirect costs) go down if we finish the project earlyWhich Activities are the Best Candidates for Crashing? •Any activity that is on the critical path•Activities with relatively long durations•Bottleneck activities (that appear on multiple critical paths)•Activities with relatively low costs to crash•Activities that are not likely to cause quality problems if crashed•Activities that occur relatively early in the schedule and are labor intensiveOptions for Crashing Activities•Adding Resources•Outsourcing Project Work•Overtime•Establishing Core Project Team•Temporary Fixes•Fast-Tracking•Critical Chain PM•Brainstorming•Reducing Scope•Phasing Project DeliverablesPotential Problems with Crashing •Reduced flexibility and less