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1 Spreadsheet Modeling & Decision Analysis: A Practical Introduction to Management Science, 3e by Cliff Ragsdale

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-2 Project Management Chapter 14

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-3 Introduction to Project Management u Projects can be simple (planning a company picnic) or complex (planning a space shuttle launch). u Successfully completing a project requires: –knowledge of the tasks involved –accurate estimates of time and resources required –knowledge of physical and logical relations between the various tasks u Project management techniques –Critical Path Method (CPM) –Program Evaluation and Review Technique (PERT) u Spreadsheets can be used to manage projects, but dedicated project management software is often more effective.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-4 An Example: Lightner Construction u Tom Lightner is the owner of Lightner Construction, a general contracting company specializing in the construction of single-family residences and small office buildings. u Tom frequently has numerous construction projects going on at the same time and needs a formal procedure for planning, monitoring, and controlling each project. u He is aware of various project scheduling techniques but has never used them. u He wants to see how he might apply such techniques to one of the home-building projects he will be undertaking in the near future. The following slide summarizes each of the major activities required for this project.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-5 Summary of Activities TimeImmediate RequiredPredecessor ActivityDescription (in days)Activity Aexcavate3-- Blay foundation4A Crough plumbing3B Dframe10B Efinish exterior8D Finstall HVAC4D Grough electric6D Hsheet rock8C, E, F, G Iinstall cabinets5H Jpaint5H Kfinal plumbing4I Lfinal electric2J Minstall flooring4K, L

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-6 An Activity-On-Node (AON) Network Install Cabinets A B C D E F G H I J K L M Excavate Lay Foundation Rough Plumbing Frame Finish Exterior HVAC Rough Electric Sheet Rock Paint Final Plumbing Final Electric Install Flooring

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-7 A Comment of Project Networks u Projects can also be depicted using Activity- On-Arc (AOA) networks. u This book uses AON networks (which the author views as superior to AOA). u Some software packages use AOA networks, so you should at least be aware that they exist.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-8 An Activity-on-Arc (AOA) Network 1 2 3 4 5 6 7 8 9 10 11 1213 Excavate Lay Foundation Rough Plumbing Frame Finish Exterior HVAC Rough Electric Sheet Rock Paint Install Cabinets Final Plumbing Final Electric Install Flooring A B C D G F E H I J K L M

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-9 Start and Finish Points u AON networks must have unique start and finish points. A B C D E A B C D E start finish

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-10 CPM: An Overview u A Forward Pass through the network determines the earliest times each activity can start and finish. u A Backward Pass through the network determines the latest times each activity can start and finish without delaying completion of the project. u The longest path through the network is the critical path.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-11 Information Recorded for Each Node i titi EST i EFT i LST i LFT i t i = time required to perform activity i EST i = earliest possible start time for activity i EFT i = earliest possible finish time for activity i LST i = latest possible start time for activity i LFT i = latest possible finish time for activity i

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-12 The Forward Pass u The earliest start time for the initial activity in a project is time zero. u The EST of an activity is equal to the latest (or maximum) early finish time of the activities directly preceding it. u The EFT of an activity is equal to its earliest start time plus the time required to perform the activity.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-13 Results of the Forward Pass H 2533 8 E 1725 8 J 3338 5 I 3338 5 K 42 4 L 3840 2 M 4246 4 A 0 3 3 F 1721 4 G 1723 6 D 717 10 C 7 3 B 3 7 4 Note: EST H =MAX(EFT C,EFT E,EFT F,EFT G )=25

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-14 The Backward Pass u The LFT for the final activity in a project is equal to its EFT as determined by the forward pass. u The LFT for any other activity is equal to the earliest (or minimum) LST of the activities directly following (or succeeding) it. u The LST of an activity is equal to its LFT minus the time required to perform the activity.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-15 Results of the Backward Pass Note: LFT H =MIN(LST I,LST J )=33 LFT D =MIN(LST E,LST F,LST G )=17 LFT B =MIN(LST C,LST D )=7 H 2533 8 E 1725 8 J 3338 5 I 3338 5 K 42 4 L 3840 2 M 4246 4 A 0 3 3 F 1721 4 G 1723 6 D 717 10 C 7 3 B 3 7 4 0 3 37 2225 17 7 25 2125 19 2533 38 3540 42 40 4246 38

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-16 The Critical Path Note: Slack = LST i -EST i or LFT i -EFT i H 2533 8 E 1725 8 J 3338 5 I 3338 5 K 42 4 L 3840 2 M 4246 4 A 0 3 3 F 1721 4 G 1723 6 D 717 10 C 7 3 B 3 7 4 0 3 37 2225 17 7 25 2125 19 2533 38 3540 42 40 4246 38 Slack=0 Slack=15 Slack=0 Slack=4 Slack=2 Slack=0 Slack=2 Slack=0

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-17 Determining The Critical Path u Critical activities have zero slack and cannot be delayed without delaying the completion of the project. u The slack for non-critical activities represents the amount of time by which the start of these activities can be delayed without delaying the completion of the entire project (assuming that all predecessor activities start at their earliest start times).

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-18 Project Management Using Spreadsheets u The early and late start and finish times for project activities can be done in a spreadsheet, but the calculations are tedious. See file Fig14-11.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-19 A Gantt Chart for the Example Problem

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-20 An LP Model for Earliest Start Times MIN:T A + T B +... + T M Subject to:T B T A + t A T C T B + t B T D T B + t B T E T D + t D T F T D + t D T G T D + t D T H T C + t C T H T E + t E T H T F + t F T H T G + t G T I T H + t H T J > T H + t H T K T I + t I T L T J + t J T M T K + t k T M T L + t L T i 0, for all i

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-21 Implementing the Model See file Fig14-14.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-22 An LP Model for Latest Start Times MAX:T A + T B +... + T M Subject to:T B T A + t A T C T B + t B T D T B + t B T E T D + t D T F T D + t D T G T D + t D T H T C + t C T H T E + t E T H T F + t F T H T G + t G T I T H + t H T J > T H + t H T K T I + t I T L T J + t J T M T K + t k T M T L + t L T M T i 0, for all i

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-23 Implementing the Model See file Fig14-14.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-24 Project Crashing u It is often possible to complete activities more quickly than normal by applying more resources (better equipment, over time, etc). u This is referred to as “crashing” the project. u We may want to determine the optimal way of crashing a project to: –complete it more quickly than originally scheduled –keep it on schedule if critical activities were delayed

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-25 Computing Crash Times and Costs See file Fig14-21.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-26 Determining the Earliest Crash Completion Time MIN:T M + t m - C M Subject to:T B - T A >= t A - C A T C - T B >= t B - C B T D - T B >= t B - C B T E - T D >= t D - C D T F - T D >= t D - C D T G - T D >= t D - C D T H - T C >= t C - C C T H - T E >= t E - C E T H - T F >= t F - C F T H - T G >= t G - C G T I - T H >= t H - C H T J - T H >= t H - C H T K - T I >= t I - C I T L - T J >= t J - C J T M - T K >= t K - C K T M - T L >= t K - C L C i <= allowable crash days for activity i T i, C i >= 0, for all i

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-27 Implementing the Model See file Fig14-21.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-28 Cost/Time Trade-Off Curve $0 $2,000 $4,000 $6,000 $8,000 $10,000 $12,000 $14,000 $16,000 $18,000 $20,000 272829303132333435363738394041424344454647 Completion Time (in days) Crash Cost

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-29 PERT: An Overview u CPM assumes all activity times are known with certainty or can be estimated accurately. u PERT accounts for uncertainty in activity times by using three time estimates: a i = duration of activity i assuming the most favorable conditions b i = duration of activity i assuming the least favorable conditions m i = estimate of the most likely duration of activity i PERT then estimates expected duration t i and variance v i of each activity’s duration as:

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-30 PERT Overview Continued The expected (or mean) time required to complete any path in the network is the sum of the expected times (the t i ) of the activities on the path. Assuming the individual activity times in a project are independent of one another, we may also calculate the variance of the completion time for any path as the sum of the variances (the v i ) of the activities on the path. u PERT considers the path with the largest expected completion time to be the critical path. u PERT’s reasoning may be flawed...

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-31 PERT Example C A B D a=2 m=4 b=6 t =4 v=0.444 a=8 m=9 b=10 t =9 v=0.111 a=3 m=5 b=7 t =5 v=0.444 a=2 m=8 b=14 t =8 v=4.0 Path:Expected Time: Variance: A - B - D A - C - D 4 + 9 + 5 =18 4 + 8 + 5 = 17 1.000 4.889

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-32 Distribution of Completion Times 101112131415161718192021222324 Path Completion Time Probability Density "Critical" Path A-B-D "Non-Critical" Path A-C-D u If we want to finish within 21 days, which path is most critical?

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-33 Simulating a Project Network u The solution to the “problem” with PERT is to use simulation. u We can model activity times easily using a triangular distribution... 0 1 2 3 4 5 6 Time Required Probability Density a m b

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-34 Simulating The Project Network See file Fig14-32.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-35 Microsoft Project u Dedicated project management software such as MS Project can greatly simplify the process of organizing, planning, and controlling projects. u A trial version of MS Project is included on the CD-ROM accompanying this book.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 14-36 End of Chapter 14

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