Lecture 9: Project Planning - engr.uvic.camech350/Lectures/MECH350-Lecture-9.pdf · 5 Elements of...

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MECH 350Engineering Design I

University of VictoriaDept. of Mechanical Engineering

Lecture 9: Project Planning

© N. Dechev, University of Victoria

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CRITICAL PATH METHODDETERMINING THE CRITICAL PATHPROGRAM EVALUATION AND REVIEW TECHNIQUE: PERT

Outline:


Detailed Design-Detailed Analysis-Simulate & Optimize-Detail Specifications-Drawings, GD&T

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Project Planning within the “General” Design Process


Identify Need-Talk with Client-Project Goals-Information Gathering

Conceptualization-Brainstorming-Drawing/Visualization-Functional Decomp.-Morphologic Chart

Preliminary Design & Planning-Prelim. Specifications-Prelim. Analysis-Decision Making-Gantt Charts & CPM

Report/Deliver-Oral Presentation-Client Feedback-Formal Design Report

Prototyping-Prototype Fabrication-Concept Verification

Testing/Evaluation-Evaluate Performance-Are Objectives Met?-Iterate Process Steps 2 - 7 as needed

Problem Definition-Problem Statement-Information Gathering-Design Objectives(quantifiable/measurable)

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CRITICAL PATH METHODIs a graphical network diagram approach to project planningShows logical precedence relationshipsAttempts to identify major bottlenecks in a project schedule

Project Planning Tools: CPMCritical Path Method


[ Hyman, Fundamentals of Engineering Design]

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Elements of the CPM Diagram:

Activity: Ongoing effort on a project activity for a specific duration. Activities are labelled with name/letter and duration.Event: Represents a discrete state (event), or decision point, etc... and it is assumed the event consumes ‘no time’. Events are usually not labelled.



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Table of Activities, Duration and Precedence Relations:




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GENERAL RULES for CPM diagram construction:(1) The network diagram must start at a single “Start” event and end at a single “Finish/End” event.(2) Consecutive activities must be separated by events.(3) Any pair of events cannot be connected by more than one activity, without an intervening event.(4) If a single activity (R) must precede several unrelated activities (S, T, etc...), the relation is depicted as Fig. A:(5) If several unrelated activities (S, T, etc...) must precede an activity (R), the relation is depicted as Fig. B:



RS

T

RS

TFig. A Fig. B

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Dummy Activities (if necessary):




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Approach to using the CPM method:(1) Generate the table of “Activities, Duration and Precedence Relations”. This can be done as a team, especially for establishing/estimating Duration and Precedence of activities.(2) Find all activities that have no ‘precedence requirement’, and draw them using arrows emanating from “start” event. Terminate these arrows with an “event” circle. Scratch these activities from your table.(3) Find all activities preceded by the activities drawn in the previous step. Place them as appropriate on the network diagram. Terminate them with an “event” circle, and scratch them from the table list.(4) Repeat step (3) and ‘iterate and backtrack’ if necessary.(5) All activities must eventually terminate at single “End” event.



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Constructing CPM Diagrams:




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Constructing CPM Diagrams:




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Example 7.4.1 from Textbook (done in class)

Project Planning Tools: CPMExample:


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The critical path is defined as: “The sequence of activities from project start to project end, such that a delay in any one of those activities, will delay the completion of the entire project”

We need to identify the ‘critical path’ for a given CPM network diagram, and hence identify all the critical activities.

Project Planning Tools: CPMDetermining the Critical Path


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Determining the ‘critical path’ can be done ‘ad-hoc’ by tracing the various paths from start to finish.

Hence, the critical path here is: A-B-F-G-H-K, which is 19 units in duration.




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For more ‘complex CPM diagrams’, there is a systematic approach to determining the critical path.

This is done by first determining (for each activity):Earliest Start (ES): The earliest possible time the activity can begin.

Next, we determine the:Project Duration: Least possible time to complete the project.

Finally, we determine (for each activity):Latest Start (LS): The latest possible time activity can begin without delaying the project. Defined as: Proj.Dur. - (longest possible reverse path to activity)Total Float (TF): Defined as (LS - ES)



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For the previous example, we have:




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The project duration is equal to the sum of the duration of all activities along the critical path.

The TF for each activity in the Table, is the amount of time by which that activity can be delayed, without causing a delay in the project duration.

The critical path is defined as the sequence of activities in the Table, for which TF = 0.

Any delay in an activity that is on the critical path, will cause a delay in the project duration.



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The CPM has application to very practical problems, likely to occur during your professional careers.

Consider the results of Table 7.4. Immediately, you can see: The project has a duration of 19 time-units.The critical path is: A-B-F-G-H-K, therefore, you must “pay special attention to these activities” as a project manager. If any of these is delayed, the whole project is delayed!Float Analysis and Re-allocation. Assume you have limited staff (20 people) and limited money. Using Table 7.1 alone, perhaps someone assigned 10 people to handle activities I & J. However, after CPM, you can see I & J have lots of “margin” due to float, and perhaps it is better to re-assign/adjust people to activities on “the critical path”.

Project Planning Tools: CPMSummary


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This method is similar to the CPM. However, PERT is more advanced, since each activity can incorporate a ‘duration uncertainty’.

Advanced Project Planning Tools: PERTProgram Evaluation and Review Technique


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Using PERT, each activity is assigned ‘three time estimates’ as attributes, which are:

to (optimistic estimate)_______________________________________

tm (mode (most likely) estimate)_______________________________________

tp (pessimistic estimate)_______________________________________

Note: The values to and tp represent the left and right terminus respectively, of a Beta probability density function.

Project Planning Tools: PERTProgram Evaluation and Review Technique


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As an example, the previous network diagram can be modified to include estimation uncertainty, as follows:




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The method to determine the critical path with PERT is similar to CPM, however, the activity duration is known as “expected time, te”.The first step is to calculate te for each activity, based on the weighted average of tm, and the midpoint of (to + tp)/2. This is done with the formula:



Activity Expected Time, te

A 3.00B 3.00C 4.83D 1.67E 3.33F 2.67G 2.17H 4.17I 1.17J 3.17K 5.83

Given the times from Fig. 7.15, the te values are:

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Next, we compute the Earliest Start, Latest Start, and Total Float for each activity as:

Based upon the evaluation of the ‘Total Float = 0’ for certain activities, we find that the critical path is: C-D-F-G-H-K, and the project duration, Te is 21.34



Activity Expected Time, te Earliest Start Latest Start Total FloatA 3.00 0.00 0.50 0.50B 3.00 3.00 3.50 0.50C 4.83 0.00 0.00 0.00D 1.67 4.83 4.83 0.00E 3.33 6.50 14.85 8.34F 2.67 6.50 6.50 0.00G 2.17 9.17 9.17 0.00H 4.17 11.34 11.34 0.00I 1.17 4.83 14.34 9.51J 3.17 11.34 18.17 6.83K 5.83 15.51 15.51 0.00

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Hence, the critical path for PERT is drawn as:




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One of the main advantages of the PERT technique, is the ability to determine the ‘probability’ that a project will be completed within a specified time, Ts.In order to achieve this, the “Variance” for each activity must be calculated assuming a Beta-distribution, using the equation:

σ2=((tp - to)/6))2

Hence:



Activity Expected Time, te Variance, σ2

A 3.00 0.44B 3.00 0.11C 4.83 1.36D 1.67 0.44E 3.33 0.44F 2.67 1.00G 2.17 0.25H 4.17 0.25I 1.17 0.25J 3.17 0.69K 5.83 2.25

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In order to determine the “probability” that the project will be completed by a “specified time, Ts,” we can state the problem as: Find Pr(T < Ts).

First, the random variable T in the equation above, must be converted to the standard variable z, using the equation:

zs = (Ts - Te)/σT

Where: σT is defined as the standard deviation of the time to project completion, which is based upon the critical path and is found by:

σT = (σ2C + σ2D + σ2F + ...)1/2



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Once the standard variable zs is obtained, the probability for various values of zs can be found using Table 5.1 in the text (duplicated below for convenience):



z* -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00

Pr(z < z*) 0.001 0.003 0.006 0.012 0.023 0.040 0.067 0.106 0.159 0.227 0.308 0.401 0.500

Table 5.1. Abbreviated Table of Cumulative Distribution Function for the Standard Normal Distribution.[ Hyman, Fundamentals of Engineering Design]

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For example, for the network diagram of Page 9, determine the probability that the project completion time will be less than 20 units. Hence this can be written as: Find Pr(T < Ts), were Ts=20.

Project Planning Tools: PERTExample #1:


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For the same network diagram of Page 9, determine the probability that the project completion time will take longer than 24 units. Hence this can be written as: Find Pr(T > Ts), were Ts=24.

Project Planning Tools: PERTExample #2:


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Like CPM, the PERT has application to very practical and realistic problems, likely to occur during your professional careers.

PERT has all the benefits of CPM, plus, you can make realistic estimations of activity durations that account for uncertainty in the estimates.

PERT also allows for the computation of “probability” of going over-time on the “expected project duration”. Such information is highly important in project management.

Project Planning Tools: PERTSummary


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Lecture 9: Project Planning - engr.uvic.camech350/Lectures/MECH350-Lecture-9.pdf · 5 Elements of...

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