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Project Management Chapter 3 © 2007 Pearson Education Projects A project is an interrelated set of activities with a definite starting and ending point, which results in a unique outcome for a specific allocation of resources. The three main goals of project management are… 1. Complete the project on time or earlier. 2. Do not exceed the budget. 3. Meet the specifications to the satisfaction of the customer. © 2007 Pearson Education Project Management Project management is a systemized, phased approach to defining, organizing, planning, monitoring, and controlling projects. A collection of projects is called a program, which is an interdependent set of projects with a common strategic purpose. A cross-functional effort: Even though a project may be under the overall purview of a single department, other departments likely should be involved. © 2007 Pearson Education Project Scope and Objectives Defining a project’s scope, time frame, allocated resources and objective, is essential. A Project Objective Statement provides the objectives and essence of the project. Time frame should be specific for start and ending of the project. Necessary resources are also defined, either in dollar terms or in personnel allocation. © 2007 Pearson Education Planning Projects Planning projects involves five steps: 1. Defining the work breakdown structure -a statement of all work that has to be completed. 2. Diagramming the network -- a graphical network 3. Developing the schedule -- specifying start times for each activity 4. Analyzing cost-time trade-offs 5. Assessing risks © 2007 Pearson Education Defining the Work Breakdown Structure A Work Breakdown Structure is simply a statement of all work that has to be completed. Major work components are identified and then broken down into smaller tasks by the project team. This process may involve a hierarchy of work levels. An Activity is the smallest unit of work effort consuming both the time and resources that the project manager can schedule and control. Task Ownership: Each activity must have an owner who is responsible for doing the work. © 2007 Pearson Education Diagramming the Network A Network Diagram visually displays the interrelated activities using nodes (circles) and arcs (arrows) that depict the relationships between activities. Two network planning methods (PERT & CPM) were originally distinctive, but today the differences are minor and will be jointly referred to as PERT/CPM. PERT (Program Evaluation and Review Technique) was utilized when activity times involved risk. CPM (Critical Path Method) was used when activity times were certain. © 2007 Pearson Education Precedence Relationships Precedence relationships determine a sequence for undertaking activities, and specify that any given activity cannot start until a preceding activity has been completed. Activity On Node approach In the AON approach, the nodes (circles) represent activities, and the arcs represent the precedence relationships between them. © 2007 Pearson Education AON S T “S” precedes “T” which precedes “U” U Activity Relationships S & T must be completed before U can be started. T & U cannot begin until S has been completed. T S U T © 2007 Pearson Education S U Activity Relationships U & V can’t begin until S & T have been completed. U cannot begin until S & T have been completed. V cannot begin until T has been completed. S U S U T V T V © 2007 Pearson Education Activity Relationships T & U cannot begin until S has been completed; V cannot begin until both T & U have been completed. S T U © 2007 Pearson Education V St. Adolf’s Hospital Example 3.1 (Modified) Activity A B C D E F G H I J K Description Immediate Predecessor(s) Select administrative and medical staff. — Select site and do site survey. — Select equipment. A Prepare final construction plans and layout. B Bring utilities to the site. B Interview applicants and fill positions in A nursing, support staff, maintenance, and security. Purchase and take delivery of equipment. C Construct the hospital. D Develop an information system. A Install the equipment. E,G,H Train nurses and support staff. F,I © 2007 Pearson Education F,I,J in the text Responsibility Johnson Taylor Adams Taylor Burton Johnson Adams Taylor Simmons Adams Johnson St. Adolf’s Hospital Activity AON Network A B C D E F G H I J K Description I Immediate Predecessor(s) Select administrative and medical staff. — Select site and do site survey. — Select equipment. A F K A Prepare final construction plans and layout. B Bring utilities to the site. B Interview applicants and fill positions in A nursing, maintenance, Startsupport staff, C Finish G and security. Purchase and take delivery of equipment. C Construct the hospital. D D B H J A Develop an information system. Install the equipment. E,G,H Train nurses and support staff. F,I,J E Figure 8.4 © 2007 Pearson Education Responsibility Johnson Taylor Adams Taylor Burton Johnson Adams Taylor Simmons Adams Johnson St. Adolf’s Hospital Activity Description Completion Time A B C D E F G H I J K I 15 Immediate Predecessor(s) Select administrative and medical staff. — Select site and do site survey. — A F KA Select equipment. 12 10 Prepare final construction plans and layout. 6B Bring utilities to the site. B Interview applicants and fill positions in A C G nursing, Startsupport staff, maintenance, Finish 10 35 and security. Purchase and take delivery of equipment. C Construct the hospital. B D H JD Develop an information system. 9 10 40 4A Install the equipment. E,G,H Train nurses and support staff. F,I,J E 24 © 2007 Pearson Education Responsibility Johnson Taylor Adams Taylor Burton Johnson Adams Taylor Simmons Adams Johnson St. Adolf’s Hospital Path Expected Time (wks) Activity Immediate Predecessor(s) Description I Completion Time A-F-K 28 15 A Select administrative and medical staff. A-I-K 33 B Select site and A-C-G-J 61Ado site survey. F C Select equipment. 12 10 B-D-H-J D Prepare final63 construction plans and layout. B-E-J E Bring utilities37 to the site. F G H I J K Interview applicants and fill positions in C G nursing, Startsupport staff, maintenance, 10 35 and security. Purchase and take delivery of equipment. Construct the hospital. B D H Develop an information system. 9 10 40 Install the equipment. Train nurses and support staff. E 24 © 2007 Pearson Education — — KA 6 B B A Responsibility Johnson Taylor Adams Taylor Burton Johnson Finish C JD 4A E,G,H F,I,J Adams Taylor Simmons Adams Johnson St. Adolf’s Hospital The critical path is the longest path! Path Time (wks) A-F-K A-I-K A-C-G-J B-D-H-J B-E-J 28 33 61 63 37 Project Expected Time is 63 wks. © 2007 Pearson Education I A Start B F K C G D H E Finish J St. Adolf’s Hospital Developing the Schedule Earliest Start Time (ES) is the latest earliest finish time of the immediately preceding activities. Earliest Finish Time (EF) is an activity’s earliest start time plus its estimated duration. Latest Start Time (LS) is the latest finish time minus the activity’s estimated duration. Latest Finish Time (LF) is the earliest latest start time of the activities that immediately follow. For simplicity, all projects start at time zero. © 2007 Pearson Education What AON Nodes look like Determined by the earliest finish time of the precedent activity. If there are two or more precedent activities, this time is the same as precedent activity with the latest “Earliest Finish” time. Slack is the difference, if any, between the earliest start and latest start times (or the earliest finish and latest finish times). S = LS – ES or S = LF– EF Slack Activity Earliest Finish Earliest Start This is the Latest Finish time minus the activity time. © 2007 Pearson Education Latest Start Activity Duration Latest Finish The earliest you can complete an activity -- determined by adding the activity time to the earliest start time. The latest you can finish an activity without delaying the project completion date. It is the same as the Latest Start time of the next activity. If there are two or more subsequent activities, this time is the same as the earliest of those “Latest Start” times. St. Adolf’s Hospital I 15 Earliest start time 0 Earliest finish time A 12 F K 12 10 6 C G Start B 9 Earliest Start and Earliest Finish Times © 2007 Pearson Education Finish 10 35 D H J 10 40 4 E 24 St. Adolf’s Hospital 12 I 27 15 0 A 12 12 27 K 33 10 12 12 Start F 22 C 22 6 22 10 0 B 9 9 Latest Start and Latest Finish Times © 2007 Pearson Education 9 D 19 10 9 E 33 24 G 57 Finish 35 19 H 59 40 59 J 63 4 Project finish Time = 63 St. Adolf’s Hospital 12 I 27 15 0 A 12 12 10 12 12 Start F 22 C 22 Latest start time 22 10 0 B 9 9 Latest Start and Latest Finish Times © 2007 Pearson Education 9 D 19 10 9 E 33 24 27 K 33 57 63 6 G 57 Finish 35 19 H 59 40 Latest finish time J 59 63 59 4 63 Latest start time St. Adolf’s Hospital Earliest start time Latest start time A 0 12 2 12 14 I 12 27 42 15 57 Critical path 0 0 B 9 9 9 Latest Start and Latest Finish Times © 2007 Pearson Education Latest finish time F 27 K 33 57 63 12 22 47 10 57 C Start Earliest finish time 12 22 14 10 24 D 9 19 9 10 19 9 E 33 35 24 59 6 G 22 57 24 35 59 H 19 59 19 40 59 Finish J 59 63 59 4 63 Project Schedule A Gantt Chart is a project schedule, usually created by the project manager using computer software, that superimposes project activities, with their precedence relationships and estimated duration times, on a time line. Activity slack is useful because it highlights activities that need close attention. Free slack is the amount of time an activity’s earliest finish time can be delayed without delaying the earliest start time of any activity that immediately follows. Activities on the critical path have zero slack and cannot be delayed without delaying the project completion. © 2007 Pearson Education © 2007 Pearson Education St. Adolf’s Hospital Developing the Schedule The project team must make time estimates for each activity. Activity times may be risky, in which case a probability distribution can be used. For this project the times will be certain. Activity slack is the maximum length of time that an activity can be delayed without delaying the entire project. For St. Adolf’s we can’t go beyond 63 weeks. © 2007 Pearson Education Activity Slack Hospital St. Adolf’s I 12 27 42 15 57 Slack = LS – ES or A 0 12 2 12 14 Slack = LF – EF F C 12 22 14 10 24 Start 0 0 Activity Slack Analysis © 2007 Pearson Education B 9 9 9 27 K 33 57 63 12 22 47 10 57 D 9 19 9 10 19 9 E 33 35 24 59 6 G 22 57 24 35 59 H 19 59 19 40 59 Finish J 59 63 59 4 63 Activity Slack Hospital St. Adolf’s I SlackK = 57 – 27 = 30 or A 0 12 2 12 14 SlackK = 63 – 33 = 30 12 27 42 15 57 F C 12 22 14 10 24 Start 0 0 Activity Slack Analysis © 2007 Pearson Education B 9 9 9 27 K 33 57 63 12 22 47 10 57 D 9 19 9 10 19 9 E 33 35 24 59 6 G 22 57 24 35 59 H 19 59 19 40 59 Finish J 59 63 59 4 63 Node Duration ES A B C D E F G H I J K LS Slack St.12Adolf’s 0 2 Hospital 2 I 9 10 10 24 10 35 40 15 4 6 0 12 9 9 12 22 19 12 59 27 0 14 9 35 47 24 19 42 59 57 0 2 0 26 35 2 0 30 0 30 0 0 Critical Path © 2007 Pearson Education B 9 9 9 12 27 42 15 57 F 27 K 33 57 63 12 22 47 10 57 C 12 22 14 10 24 D 9 19 9 10 19 9 E 33 35 24 59 6 G 22 57 24 35 59 H 19 59 19 40 59 Finish J 59 63 59 4 63 Analyzing Cost-Time Trade-Offs There are always cost-time trade-offs in project management. You can completing a project early by hiring more workers or running extra shifts. There are often penalties if projects extend beyond some specific date, and a bonus may be provided for early completion. Crashing a project means expediting some activities to reduce overall project completion time and total project costs. © 2007 Pearson Education Project Costs The total project costs are the sum of direct costs, indirect costs, and penalty costs. Direct costs include labor, materials, and any other costs directly related to project activities. Indirect costs include administration, depreciation, financial, and other variable overhead costs that can be avoided by reducing total project time. The shorter the duration of the project, the lower the indirect costs will be. © 2007 Pearson Education Cost to Crash To assess the benefit of crashing certain activities, either from a cost or a schedule perspective, the project manager needs to know the following times and costs. Normal time (NT) is the time necessary to complete and activity under normal conditions. Normal cost (NC) is the activity cost associated with the normal time. Crash time (CT) is the shortest possible time to complete an activity. Crash cost (CC) is the activity cost associated with the crash time. © 2007 Pearson Education Cost to Crash per Period CC − NC NT − CT The Cost to Crash per Period = © 2007 Pearson Education Crash Cost − Normal Cost Normal Time − Crash Time St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis Direct cost (dollars) 8000 — Crash cost (CC) 7000 — Linear cost assumption 6000 — 5200 5000 — Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks 4000 — 3000 — 0— Normal cost (NC) | 5 | 6 (Crash time) © 2007 Pearson Education | 7 8 | 9 | 10 | 11 (Normal time) Time (weeks) Direct Cost and Time Data for the St. Adolf’s Hospital Project Activity Normal Time (NT) Normal Cost (NC) Crash Time (CT) Crash Cost (CC) Maximum Time Reduction (wk) A B C D E F G H I J K 12 9 10 10 24 10 35 40 15 4 6 $ 12,000 50,000 4,000 16,000 120,000 10,000 500,000 1,200,000 40,000 10,000 30,000 11 7 5 8 14 6 25 35 10 1 5 $ 13,000 64,000 7,000 20,000 200,000 16,000 530,000 1,260,000 52,500 13,000 34,000 1 2 5 2 10 4 10 5 5 3 1 Totals $1,992,000 © 2007 Pearson Education $2,209,500 Cost of Crashing per Week (CC-NC)/MTR $ 1,000 7,000 600 2,000 8,000 1,500 3,000 12,000 2,500 1,000 4,000 St. Adolf’s Hospital Modeling project schedule in Excel Forward schedule (Earliest time) ES = EF of predecessor, if only one predecessor ES = Max(EF of predecessors), if more than one EF = ES + Activity duration Backward schedule (Latest time) LF = LS of successor, if only one successor ES = Min(LS of successors), if more than one LS = LF - Activity duration © 2007 Pearson Education St. Adolf’s Hospital Optimal crashing using Excel Solver Target cell = Cost or project completion time Changing cells = Crashing time Constraints = Crashing time <= MTR Options: • Non-negative • Tolerance • Estimates, derivative, search © 2007 Pearson Education St. Adolf’s Hospital Pert = Project Evaluation Review Technique Finding probability for project completion time © 2007 Pearson Education Assessing Risks Risk is a measure of the probability and consequence of not reaching a defined project goal. A major responsibility of the project manager at the start of a project is to develop a riskmanagement plan. A Risk-Management Plan identifies the key risks to a project’s success and prescribes ways to circumvent them. © 2007 Pearson Education Statistical Analysis The Statistical Analysis approach requires that activity times be stated in terms of three reasonable time estimates for each activity. 1. Optimistic Time (a) is the shortest time in which a activity can be completed if all goes exceptionally well. 2. Most Likely Time (m) is the probable time for an activity. 3. Pessimistic Time (b) is the longest time required. The expected time for an activity thus becomes… a + 4m + b te = 6 © 2007 Pearson Education Probabilistic Time Estimates Probability Beta Distribution a Optimistic © 2007 Pearson Education m b Mean Pessimistic Time St. Adolf’s Hospital Probabilistic Time Estimates Example 3.5 Calculating Means and Variances I Mean a + 4m + b te = 6 Variance 2 = ( © 2007 Pearson Education A Start B b–a 6 F C G D H 2 ) K E Finish J St. Adolf’s Hospital Probabilistic Time Estimates Example 3.5 Calculating Means and Variances I Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 7 + 4(8) + 15 te = = 9 weeks 6 2 = ( 15 - 7 6 © 2007 Pearson Education 2 ) = 1.78 A Start B F K C G D H E Finish J St. Adolf’s Hospital Probabilistic Time Estimates Example 3.5 Time Estimates (wk) Optimistic Activity (a) A B C D E F G H I J K © 2007 Pearson Education 11 7 5 8 14 6 25 35 10 1 5 Likely (m) Pessimistic (b) 12 8 10 9 25 9 36 40 13 2 6 13 15 15 16 30 18 41 45 28 15 7 Activity Statistics Expected Variance Time (te ) ( 2 ) 12 9 10 10 24 10 35 40 15 4 6 0.11 1.78 2.78 1.78 7.11 4.00 7.11 2.78 9.00 5.44 0.11 St. Adolf’s Hospital I 15 A F K 12 10 6 C G Start 10 35 B D H J 9 10 40 4 E 24 © 2007 Pearson Education Finish St. Adolf’s Hospital I 12 27 42 15 57 A 0 12 2 12 14 F C Start Critical path 0 0 B 9 9 9 12 22 14 10 24 D 9 19 9 10 19 9 E 33 35 24 59 © 2007 Pearson Education 27 K 33 57 63 12 22 47 10 57 6 G 22 57 24 35 59 H 19 59 19 40 59 Finish J 59 63 59 4 63 TE = 63 weeks St. Adolf’s Hospital What is the probability the project will be completed in 65 weeks? Critical Path = B - D - H - J TE = 9 + 10 + 40 + 4 = 63 weeks 2 = (variances of critical path activities) 2 = 1.78 + 1.78 + 2.78 + 5.44 = 11.78 = 11.78 = 3.432 © 2007 Pearson Education St. Adolf’s Hospital Probabilities Critical Path = B - D - H - J T = 65 weeks TE = 63 weeks = 3.432 z= T – TE = 65 – 63 3.432 = 0.58 From Normal table in page 807, for z = 0.58, the table area = 0.7190 The probability that the project will be Completed within 65 days is 71.9% © 2007 Pearson Education St. Adolf’s Hospital Normal distribution: Mean = 63 weeks; = 3.432 weeks Length of critical path Probability of meeting the schedule is 0.7190 Probability of exceeding 65 weeks is 0.2810 63 65 Project duration (weeks) © 2007 Pearson Education St. Adolf’s Hospital Expected project completion time with 98% probability Critical Path = B - D - H - J T = TE + z Normal table for 98%, z = 2.055 T = 63 + 2.055 (3.432) = 70.05 weeks © 2007 Pearson Education St. Adolf’s Hospital Probabilities Path = A - C - G – J Find probability for T = 65 weeks TE = 12 + 10 + 35 + 4 = 61 weeks 2 = (variances of activities) 2 = 0.11 + 2.78 + 7.11 + 5.44 = 15.44 z= T – TE 2 © 2007 Pearson Education From Appendix 2 65 – 61 z= = 1.02 Pz = .8461 15.44 Application 3.1 © 2007 Pearson Education Application 3.1 Solution © 2007 Pearson Education Application 3.2 © 2007 Pearson Education Application 3.2 Critical Path and Project Duration © 2007 Pearson Education Application 3.4 © 2007 Pearson Education Application 3.5 © 2007 Pearson Education Application 3.5 © 2007 Pearson Education Solved Problem 1 © 2007 Pearson Education Solved Problem 1 © 2007 Pearson Education Solved Problem 2 What is the probability of completing the project in 23 weeks? © 2007 Pearson Education Solved Problem 2 © 2007 Pearson Education Solved Problem 2 4.0 8.0 0.0 4.0 A 4.0 Start B 5.5 Finish 9.0 9.0 C 3.5 15.5 15.5 F 9.0 E 6.5 15.5 15.5 9.0 9.0 5.5 5.5 5.5 6.5 © 2007 Pearson Education 12.0 16.0 20.0 4.0 8.0 5.5 5.5 0.0 0.0 D 14.5 15.5 G 4.5 20.0 20.0 Solved Problem 2 © 2007 Pearson Education Using the Normal Distribution appendix, we find that the probability of completing the project in 23 weeks or less is 0.9357.