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A Case Study: The Reliable Construction Co. Project (Section 16.1) Using a Network to Visually Display a Project (Section 16.2) Scheduling a Project with PERT/CPM (Section 16.3) Dealing with Uncertain Activity Durations (Section 16.4) Considering Time-Cost Tradeoffs (Section 16.5) Scheduling and Controlling Project Costs (Section 16.6) Project Management With PERT/CPM Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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Reliable Construction Company Project The Reliable Construction Company has just made the winning bid of $5.4 million to construct a new plant for a major manufacturer. The contract includes the following provisions: A penalty of $300,000 if Reliable has not completed construction within 47 weeks. A bonus of $150,000 if Reliable has completed the plant within 40 weeks. Questions: 1. How can the project be displayed graphically to better visualize the activities? 2. What is the total time required to complete the project if no delays occur? 3. When do the individual activities need to start and finish? 4. What are the critical bottleneck activities? 5. For other activities, how much delay can be tolerated? 6. What is the probability the project can be completed in 47 weeks? 7. What is the least expensive way to complete the project within 40 weeks? 8. How should ongoing costs be monitored to try to keep the project within budget? 16-2

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Activity List for Reliable Construction ActivityActivity Description Immediate Predecessors Estimated Duration (Weeks) AExcavate—2 BLay the foundationA4 CPut up the rough wallB10 DPut up the roofC6 EInstall the exterior plumbingC4 FInstall the interior plumbingE5 GPut up the exterior sidingD7 HDo the exterior paintingE, G9 IDo the electrical workC7 JPut up the wallboardF, I8 KInstall the flooringJ4 LDo the interior paintingJ5 MInstall the exterior fixturesH2 NInstall the interior fixturesK, L6 16-3

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Project Networks A network used to represent a project is called a project network. A project network consists of a number of nodes and a number of arcs. Two types of project networks: Activity-on-arc (AOA): each activity is represented by an arc. A node is used to separate an activity from its predecessors. The sequencing of the arcs shows the precedence relationships. Activity-on-node (AON): each activity is represented by a node. The arcs are used to show the precedence relationships. Advantages of AON (used in this textbook): considerably easier to construct easier to understand easier to revise when there are changes 16-4

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Reliable Construction Project Network 16-5

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The Critical Path A path through a network is one of the routes following the arrows (arcs) from the start node to the finish node. The length of a path is the sum of the (estimated) durations of the activities on the path. The (estimated) project duration equals the length of the longest path through the project network. This longest path is called the critical path. (If more than one path tie for the longest, they all are critical paths.) 16-6

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The Paths for Reliable’s Project Network PathLength (Weeks) Start A B C D G H M Finish = 40 Start A B C E H M Finish = 31 Start A B C E F J K N Finish = 43 Start A B C E F J L N Finish = 44 Start A B C I J K N Finish = 41 Start A B C I J L N Finish =

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Earliest Start and Earliest Finish Times The starting and finishing times of each activity if no delays occur anywhere in the project are called the earliest start time and the earliest finish time. ES = Earliest start time for a particular activity EF = Earliest finish time for a particular activity Earliest Start Time Rule: ES = Largest EF of the immediate predecessors. Procedure for obtaining earliest times for all activities: 1. For each activity that starts the project (including the start node), set its ES = For each activity whose ES has just been obtained, calculate EF = ES + duration. 3. For each new activity whose immediate predecessors now have EF values, obtain its ES by applying the earliest start time rule. Apply step 2 to calculate EF. 4. Repeat step 3 until ES and EF have been obtained for all activities. 16-8

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ES and EF Values for Reliable Construction for Activities that have only a Single Predecessor 16-9

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ES and EF Times for Reliable Construction 16-10

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Latest Start and Latest Finish Times The latest start time for an activity is the latest possible time that it can start without delaying the completion of the project (so the finish node still is reached at its earliest finish time). The latest finish time has the corresponding definition with respect to finishing the activity. LS = Latest start time for a particular activity LF = Latest finish time for a particular activity Latest Finish Time Rule: LF = Smallest LS of the immediate successors. Procedure for obtaining latest times for all activities: 1. For each of the activities that together complete the project (including the finish node), set LF equal to EF of the finish node. 2. For each activity whose LF value has just been obtained, calculate LS = LF – duration. 3. For each new activity whose immediate successors now have LS values, obtain its LF by applying the latest finish time rule. Apply step 2 to calculate its LS. 4. Repeat step 3 until LF and LS have been obtained for all activities

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LS and LF Times for Reliable’s Project 16-12

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The Complete Project Network 16-13

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Slack for Reliable’s Activities ActivitySlack (LF–EF)On Critical Path? A0Yes B0 C0 D4No E0Yes F0 G4No H4 I2 J0Yes K1No L0Yes M4No N0Yes 16-14

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Spreadsheet to Calculate ES, EF, LS, LF, Slack 16-15

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The PERT Three Estimate Approach Most likely estimate (m) = Estimate of most likely value of the duration Optimistic estimate (o) = Estimate of duration under most favorable conditions. Pessimistic estimate (p) = Estimate of duration under most unfavorable conditions

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Mean and Standard Deviation An approximate formula for the variance ( 2 ) of an activity is An approximate formula for the mean ( ) of an activity is 16-17

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Time Estimates for Reliable’s Project ActivityompMeanVariance A1232 1/91/9 B C D E /94/9 F G H I J39981 K44440 L M1232 1/91/9 N5 96 4/94/

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Pessimistic Path Lengths for Reliable’s Project PathPessimistic Length (Weeks) Start A B C D G H M Finish = 70 Start A B C E H M Finish = 54 Start A B C E F J K N Finish = 66 Start A B C E F J L N Finish = 69 Start A B C I J K N Finish = 60 Start A B C I J L N Finish =

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Three Simplifying Approximations of PERT/CPM 1. The mean critical path will turn out to be the longest path through the project network. 2. The durations of the activities on the mean critical path are statistically independent. Thus, the three estimates of the duration of an activity would never change after learning the durations of some of the other activities. 3. The form of the probability distribution of project duration is the normal distribution. By using simplifying approximations 1 and 2, there is some statistical theory (one version of the central limit theorem) that justifies this as being a reasonable approximation if the number of activities on the mean critical path is not too small

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Calculation of Project Mean and Variance Activities on Mean Critical PathMeanVariance A2 1/91/9 B41 C104 E4 4/94/9 F51 J81 L51 N6 4/94/9 Project duration p = 44 2 p =

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Probability of Meeting Deadline 16-22

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Probability of Meeting a Deadline P(T ≤ d) – – – – – – – – – –

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Spreadsheet for PERT Three-Estimate Approach 16-24

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Considering Time-Cost Trade-Offs Question: If extra money is spent to expedite the project, what is the least expensive way of attempting to meet the target completion time (40 weeks)? CPM Method of Time-Cost Trade-Offs: Crashing an activity refers to taking special costly measures to reduce the duration of an activity below its normal value. Special measures might include overtime, hiring additional temporary help, using special time-saving materials, obtaining special equipment, etc. Crashing the project refers to crashing a number of activities to reduce the duration of the project below its normal value

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Time-Cost Graph for an Activity 16-26

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Time-Cost Trade-Off Data for Reliable’s Project Time (weeks) Cost Maximum Reduction in Time (weeks) Crash Cost per Week Saved ActivityNormalCrashNormalCrash A21$180,000$280,0001$100,000 B42320,000420,000250,000 C107620,000860,000380,000 D64260,000340,000240,000 E43410,000570, ,000 F53180,000260,000240,000 G74900,0001,020,000340,000 H96200,000380,000360,000 I75210,000270,000230,000 J86430,000490,000230,000 K43160,000200,000140,000 L53250,000350,000250,000 M21100,000200, ,000 N63330,000510,000360,

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Marginal Cost Analysis for Reliable’s Project Initial Table Length of Path Activity to Crash Crash Cost ABCDGHM ABCEHM ABCEFJKN ABCEFJLN ABCIJKN ABCIJLN

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Marginal Cost Analysis for Reliable’s Project Table After Crashing One Week Length of Path Activity to Crash Crash Cost ABCDGHM ABCEHM ABCEFJKN ABCEFJLN ABCIJKN ABCIJLN J$30,

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Marginal Cost Analysis for Reliable’s Project Table After Crashing Two Weeks Length of Path Activity to Crash Crash Cost ABCDGHM ABCEHM ABCEFJKN ABCEFJLN ABCIJKN ABCIJLN J$30, J$30,

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Marginal Cost Analysis for Reliable’s Project Table After Crashing Three Weeks Length of Path Activity to Crash Crash Cost ABCDGHM ABCEHM ABCEFJKN ABCEFJLN ABCIJKN ABCIJLN J$30, J$30, F$40,

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Marginal Cost Analysis for Reliable’s Project Final Table After Crashing Four Weeks Length of Path Activity to Crash Crash Cost ABCDGHM ABCEHM ABCEFJKN ABCEFJLN ABCIJKN ABCIJLN J$30, J$30, F$40, F$40,

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Project Network After Crashing 16-33

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Using LP to Make Crashing Decisions Restatment of the problem: Consider the total cost of the project, including the extra cost of crashing activities. The problem then is to minimize this total cost, subject to the constraint that project duration must be less than or equal to the time desired by the project manager. The decisions to be made are the following: 1. The start time of each activity. 2. The reduction in the duration of each activity due to crashing. 3. The finish time of the project (must not exceed 40 weeks). The constraints are: 1. Time Reduction ≤ Max Reduction (for each activity). 2. Project Finish Time ≤ Desired Finish Time. 3. Activity Start Time ≥ Activity Finish Time of all predecessors (for each activity). 4. Project Finish Time ≥ Finish Time of all immediate predecessors of finish node

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Spreadsheet Model 16-35

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Mr. Perty’s Conclusions The plan for crashing the project only provides a 50 percent chance of actually finishing the project within 40 weeks, so the extra cost of the plan ($140,000) is not justified. Therefore, Mr. Perty rejects any crashing at this stage. The extra cost of the crashing plan can be justified if it almost certainly would earn the bonus of $150,000 for finishing the project within 40 weeks. Therefore, Mr. Perty will hold the plan in reserve to be implemented if the project is running well ahead of schedule before reaching activity F. The extra cost of part or all of the crashing plan can be easily justified if it likely would make the difference in avoiding the penalty of $300,000 for not finishing the project within 47 weeks. Therefore, Mr. Perty will hold the crashing plan in reserve to be partially or wholly implemented if the project is running far behind schedule before reaching activity F or activity J

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Scheduling and Controlling Project Costs PERT/Cost is a systematic procedure (normally computerized) to help the project manager plan, schedule, and control costs. Assumption: A common assumption when using PERT/Cost is that the costs of performing an activity are incurred at a constant rate throughout its duration

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Budget for Reliable’s Project Activity Estimated Duration (weeks) Estimated Cost Cost per Week of Its Duration A2$180,000$90,000 B4320,00080,000 C10620,00062,000 D6260,00043,333 E4410,000102,500 F5180,00036,000 G7900,000128,571 H9200,00022,222 I7210,00030,000 J8430,00053,750 K4160,00040,000 L5250,00050,000 M2100,00050,000 N6330,00055,

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PERT/Cost Spreadsheet (Earliest Start Times) 16-39

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PERT/Cost Spreadsheet (Earliest Start Times) 16-40

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PERT/Cost Spreadsheet (Latest Start Times) 16-41

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PERT/Cost Spreadsheet (Latest Start Times) 16-42

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Cumulative Project Costs 16-43

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PERT/Cost Report after Week 22 Activity Budgeted Cost Percent Completed Value Completed Actual Cost to Date Cost Overrun to Date A$180,000100%$180,000$200,000$20,000 B320, ,000330,00010,000 C620, ,000600,000–20,000 D260, ,000200,0005,000 E410, ,000400,000–10,000 F180, ,00060,00015,000 I210, ,000130,00025,000 Total$2,180,000$1,875,000$1,920,000$45,

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