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**BA 333 Operations Management**

Project Management PERT/CPM Spring, 1998

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**Lecture Outline Project Management Introduction**

Definition & Background Components event activity critical path PERT/CPM

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**Introduction to Project Management**

Definition to plan, implement, and control the management of large, one time projects Used in Construction, Shipbuilding, Weapons Systems Development, etc. Applies to uncertain technology projects Applies to variable cost resource allocation History of PERT/CPM - Navy/Booze Allen Hamilton Consultants

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**Introduction to Project Scheduling**

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**Components of Project Control Systems**

Predecessor was Gantt Charts Horizontal Bar Charts - Time Lines Tasks Milestones Flow Charts - Relationships Among All Tasks Activities (tasks that take time and resources) sequential vs. concurrent Events (an accomplishment occurring at a specific point in time)

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**Project Characteristics**

Single unit Many related activities Difficult production planning & inventory control General purpose equipment High labor skills

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Examples of Projects

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Examples of Projects Building construction © 1995 Corel Corp.

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**Examples of Projects Sheer to waist pantyhose Building construction**

New product introduction New! Improved! 19 · Nude Sandalfoot Medium to Tall (B) No nonsense Sheer to waist pantyhose © 1995 Corel Corp.

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**Examples of Projects Building construction New product introduction**

Training seminar © Corel Corp.

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**Examples of Projects Building construction New product introduction**

Training seminar Research project © Corel Corp.

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**Project Management Activities**

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**Project Management Activities**

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**Project Management Activities**

Planning Objectives Resources Work break-down sched. Organization

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**Project Management Activities**

Planning Objectives Resources Work break-down sched. Organization Scheduling Project activities Start & end times Network

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**Project Management Activities**

Planning Objectives Resources Work break-down sched. Organization Scheduling Project activities Start & end times Network Controlling Monitor, compare, revise, action

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Project Planning

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**Project Planning Establishing objectives Defining project**

Creating work breakdown structure Determining resources Forming organization © 1995 Corel Corp.

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**Project Organization Often temporary structure**

Uses specialists from entire company Headed by project manager Coordinates activities Monitors schedule & costs Permanent structure called ‘matrix organization’ Eng. Eng. Mkt. Acct. Mgr. © 1995 Corel Corp.

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Project Scheduling

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**Project Scheduling Sequencing activities**

Identifying precedence relationships Determining activity times & costs Estimating material & worker requirements Determining critical activities PERT Test J Build M A M J Design J F Month Activity © 1995 Corel Corp.

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**Project Scheduling Techniques**

Gantt chart Critical Path Method (CPM) Program Evaluation & Review Technique (PERT) © T/Maker Co.

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Gantt Chart

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Gantt Chart

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**PERT & CPM Network techniques Developed in 1950’s**

CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships & interdependencies Each uses a different estimate of activity times

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**Questions Answered by PERT & CPM**

Completion date? On schedule? Within budget? Probability of completing by ...? Critical activities? Enough resources available? How can the project be finished early at the least cost?

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**PERT & CPM Steps Identify activities Determine sequence Create network**

Determine activity times Find critical path Earliest & latest start times Earliest & latest finish times Slack

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**Constructing Networks**

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**Graphical Representation of Events and Activities**

Flow Charting - Uses Nodes and Arrows Arrows An arrow leads from tail to head directionally Nodes A node is represented by a circle Node Arrow

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Activity On Node Task is Represented by Node as the Completion of an Activity Arrows Represent the Sequential Linkages Between Activities For Example, Node 1 is Begin, Node 2 is Complete Task 1, Node 3 is Complete Task 2 1 2 3

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Activity On Arrow Task is Represented by an Arrow Bounded on Either End by a Node (Event) Each Event is Identified by a Number The Activity is Designated by the Leading Event Number and the Following Event Number - i.e. Activity 1 - 2 1 2

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**Designating Task Relationships**

Sequential vs. Concurrent Activities 1 2 3 Sequential Task Relationship 1 2 3 4 Concurrent Task Relationships

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**Designating “DUMMY” Activities**

Represented by Dashed Arrows Show Sequential Relationships Among Tasks, but Take No time or Resources 2 1 4 Dummy Activity 2-3 indicates that both Activities 1-2 and 2-3 must be Completed before beginning Activity 3-4 3

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Network Terms

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Network Terms Project: Obtain a college degree (B.S.)

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Network Terms Project: Obtain a college degree (B.S.) Register 1

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**1 Network Terms Project: Obtain a college degree (B.S.) Register**

Event (Node)

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**1 Network Terms Project: Obtain a college degree (B.S.) Register**

Attend class, study etc. 1 4 Years Event (Node)

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**1 Network Terms Project: Obtain a college degree (B.S.) Register**

Attend class, study etc. 1 4 Years Activity (Arrow) Event (Node)

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**1 2 Network Terms Project: Obtain a college degree (B.S.)**

Receive diploma Register Attend class, study etc. 1 2 4 Years Activity (Arrow) Event (Node) Event (Node)

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**Activity Relationships**

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**Activity Relationships**

1

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**Activity Relationships**

2 A 1 B 3 A & B can occur concurrently

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**Activity Relationships**

A must be done before C & D can begin 2 D A C 1 4 B 3

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**Activity Relationships**

2 D A C 1 4 B 3 E B & C must be done before E can begin

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**Activity Relationships**

A must be done before C & D can begin 2 D A C 1 4 B 3 E A & B can occur concurrently B & C must be done before E can begin

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Dummy Activities Activities are defined often by beginning & ending events Example: Activity 2-3 Every activity must have unique pair of beginning & ending events Computer programs get confused Dummy activities maintain precedence Consume no time or resources

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**Dummy Activities Example**

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**Dummy Activities Example**

2-3 Incorrect 1-2 3-4 1 2 3 4 2-3

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**Dummy Activities Example**

2-3 Incorrect 1-2 3-4 1 2 3 4 2-3 Different activities; same designation

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**Dummy Activities Example**

Incorrect 2-3 1-2 3-4 1 2 3 4 2-3 Correct 1-2 2-4 4-5 1 2 4 5 2-3 3 3-4: Dummy activity

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**Network Diagramming First Step in Project Management**

Begins with a Work Breakdown Lists the “WHAT’ of a Project Begins with Finished Project Consists of Tree Chart, with Each Branch Listing the “WHAT’s” at that Level Then List Each Task that Must Be Completed to Accomplish the “WHAT”

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**Example Work Breakdown**

House Site Prep Masonry Carpentry Finishing Exterior Walls Footings Piers Chimney Mixed Concrete Concrete Poured Forms Removed Forms Laid

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**Listing Of Activities Follows the “WHAT” with List of “HOW”**

Each “WHAT” Results in Detailed List of the “Specific” Tasks Necessary to Accomplish the “WHAT” Followed by Specification of Sequential and Concurrent Relationships Among Tasks Results in Network Flow Diagram Representing the Tasks and Their Relationships

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**Activity Time Estimates**

CPM - One Time Estimate per Activity PERT - Three Time Estimates per Activity a = Optimistic Time Estimate m = Most Likely Time Estimate b = Pessimistic Time Estimate Can Calculate Activity Mean Time Estimate and Variance

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**PERT Time Estimates Activity Mean Time Estimate = te**

Activity Variance Estimate = Sigmae te = (a + 4m + b)/6 Sigmae = (b - a)/6 Can Use Central Limit Theorem to Estimate Project Time

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**Example Network Flow Diagram**

7 6 5 4 3 2 1 A G C I H E B J F

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**Example Activity Characteristics**

b te Sigmae A /3 B /3 C /3 D /3 E /3 F /3 G /3 H /3 I /3 J /3

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**Example Network Flow Diagram**

te =7 7 6 5 4 3 2 1 te =12 te =13 te =11 te =4 te =8 te =7 te =10 te =11 te =10

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**Early Start & Early Finish**

The Early Start Time for an Activity Emanating from an Event is the Earliest Point in Time that an Activity can Begin Determined by the Latest Early Finish of All Activities Terminating in an Event The Early Finish for an Activity is the Sum of its Early Start Time and its te

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**Example Network Flow Diagram**

ES=12 ES=31 te =7 7 6 5 4 3 2 1 te =12 ES=18 ES=0 te =4 te =11 ES=52 te =13 te =8 ES=42 ES=11 te =7 te =10 te =11 te =10

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**Late Start & Late Finish**

The Late Finish Time for an Activity Terminating in an Event is the Point in Time that it can be Completed Without Delaying the Completion of the Project Determined by Assigning to the LF the Value of the Earliest LS of all Activities Emanating from the Event The Late Start for an Activity is it Late Finish minus its te

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**Example Activity Characteristics**

b te Sigmae ES LS EF LF / / / / / / / / / /

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**Example Network Flow Diagram With Critical Path**

ES|LS|EF|LF t2-5=7 12|24|19|31 2 5 t1-2=12 0|2|12|14 t5-6=11 31|31|42|42 t4-5=13 18|18|31|31 t2-4=4 12|14|16|18 t4-6=8 18|34 |26|42 4 1 7 t3-4=7 11|11|18|18 t1-3=11 0|0|11|11 t6-7=10 42|42|52|52 6 3 t3-6=10 11|32|21|42

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**SLACK Total Slack Free Slack Critical Path**

The Length of Delay in an Activity that Won’t Delay the Completion of the Project - LF- EF or LS-ES Free Slack The Length of Delay in an Activity that Won’t Delay the Beginning of Another Activity Critical Path Activities with the Minimum Total Slack - Often Total Slack on Critical Path Activities = 0

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**Probabilistic Estimates**

Use of te and Sigmae Allows One to Make Probabilistic Estimates of Completion Dates By Summing the te‘s of the Activities on the Critical Path You Can Estimate the Duration of the Entire Project By Summing the Variance (Sigmae2) of the Activities on the Critical Path, You Can estimate the Total Variance of the Critical Path and Make One-Sided Interval Estimates of Project Completion Times

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**Probabilistic Estimates Example**

Sigmae (Sigmae)2 /3 4/9 /3 36/9 /3 25/9 /3 49/9 /3 16/9 Variance = 130/9 = 14.4 Std Dev = 3.8 Probability that the Project Duration is Less than 60 days = Pr(T<60) Same as the Probability that Z < (60-52)/3.8 = 2.1 Therefore: Pr(T<60) = Pr(Z<2.1) = (see App. A, H&R, p. 842)

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**PERT Probability Example**

You’re a project planner for General Dynamics. A submarine project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the sub in 50 weeks or less? © Corel Corp.

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**Converting to Standardized Variable**

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**Converting to Standardized Variable**

Assume project completion time follows a normal distribution.

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**Converting to Standardized Variable**

Assume project completion time follows a normal distribution. Normal Distribution

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**Converting to Standardized Variable**

Normal Distribution Standardized Normal Distribution

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**Converting to Standardized Variable**

Normal Distribution Standardized Normal Distribution

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**Obtaining the Probability**

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**Obtaining the Probability**

Standardized Normal Probability Table (Portion) Probabilities in body

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**Obtaining the Probability**

Standardized Normal Probability Table (Portion) .97725 Probabilities in body

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**Critical Path Method Uses Deterministic Time Estimates for Activities**

Also Estimates Cost of Resources Levels for Each Activity Generally You Can increase the Resource Commitment and Reduce the Time Estimate for and Activity Use CPM to Analyze How To Reduce the Critical Path Most Efficiently

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**Benefits & Limitations of PERT/CPM**

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**Benefits of PERT/CPM Useful at many stages of project management**

Mathematically simple Use graphical displays Give critical path & slack time Provide project documentation Useful in monitoring costs

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**Limitations of PERT/CPM**

Clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over emphasis on critical path

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**Conclusion Explained what a project is**

Summarized the 3 main project management activities Drew project networks Compared PERT & CPM Determined slack & critical path Computed project probabilities

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**BA 333 Operations Management**

Project Management PERT/CPM Spring, 1998 THE END

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