BA341 21st Edition Lecture 21 Outline of Last LectureI. Precedence TableII. Gantt ChartIII. Project Network DiagramIV. Sensitivity AnalysisV. PERT Outline of Current LectureVI. Continuing the problem using PERT VII. Cost-Time Trade-offs and Project CrashingVIII. Time-Cost Trade-offsIX. Reducing Project DurationX. Some Time-Cost ModelsXI. Critical Path ModelsXII. CrashingCurrent LectureUsing the Last Lecture, we are now able to answer additional questions:- The probability of finishing the project in 26 days?o First, compute , where o D = the desired project completion timeo TE = expected completion time, i.e., the length of the critical path (sum of ETs for critical activities) o σCP2 = variance of the critical path (sum of variances of critical activities) D= 26, These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. TE = 24 and  σCP2 = 0+ 2.78 +1 = 3.78. Then,  Z= (26-24)/sqrt(3.78)=1.0287≈ 1.03- Now look at the Standard Normal Cumulative Probability Table-o Z=1.03 corresponds to 84.9% (using a normal distribution table)- Now Find the project duration corresponding to 95% confidence o Start from same equation but now solve for D o According to a normal distribution table, a Z of 1.65 corresponds to 95% probabilityo Thus, D= 24 + 1.65*sqrt(3.78)= 27.21 daysoCost-Time Trade-offs and Project CrashingIntroduction- Recall the project objectiveso Performance (scope)o Costo Time- Project manager often forced to make trade-offs between project objectives, e.g., o A delayed project must be expedited in order to be completed by deadlineo Resource constraints lead to changes in project scope and total duration Time-Cost Trade-offs- We will focus next on time-cost models, where the goal is to find either o the most cost-effective approach to reducing the duration of a project, oro the project duration corresponding to minimum cost- Is there a link between activity duration and activity cost?o Direct costs, e.g., overtime costs, hiring costs, leasing/buying resource costs, etc.o Indirect costs, e.g., overhead, various fixed costs Reducing Project Duration- Usually done by adding manpower and/or resources to the project or working overtimeo Note that doubling manpower does not reduce activity durations in half,  e.g., Brook’s Law (IBM): Adding manpower to a late software project makes it even later!- Fast-trackingo Rearrange the logic of project activities, such that (some) critical ones can be done in parallel, rather than sequentially Some Time-Cost Models- Goal: reduce project duration by x days- Constraint: find the most cost-effective approach- Stepso 1) Determine the project inputs: List of project activities and activity sequence Activity durations and costs- Normal Cost (NC) – the lowest expected activity cost- Normal Time (NT) – duration associated with NC- Crash Time (CT) – the shortest possible activity time- Crash Cost (CC) – the cost associated with CTo 2) Find the cost per period (slope), to expedite each activity o 3) Identify the critical path, using normal activity timeso 4) Start crashing (reducing) the activities on the critical path, one activity at a time, one period (e.g., day) at a time, in increasing order of their slopes (the lower the slope, the cheaper the crashing)o 5) Reevaluate the critical path after each one-period crash; if new duration is satisfactory stop, otherwise, go back to step 4 Consider the following example- Project precedence table and crashing info- Want to shorten project by 2 days-- Finding the Critical Path (using normal times)--- Find the critical path (ABE)- Shortening the Project day 1o Identify the critical activity that is cheapest to crash A: slope = $40/day B: slope = $60/day E: slope = $35/day- Activity E has the lowest slope let’s crash E 1 day @a cost of $35- Reevaluate the critical path-- Shortening the project by an additional dayo Identify the critical activities that are cheapest to crash A: slope = $40/day B: slope = $60/day E: cannot be crashed further D: slope = $30/dayo The cheapest alternative to further reduce project duration by 1 day is to crash A 1 day @ a cost of $40- In summaryo The most cost-effective alternative to reducing project duration by 2 days is: Crash E 1 day @ $35 Crash A 1 day @ $40 Final Cost: $75o Can the project duration be further reduced? Yes, minimum project duration is 5 days- Crash B & D 1 day each, at a cost of $60 + $30 = $90o See solved problems in the text for additional