# Project Development Scheduling and Probability of Completion.

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Project Development Scheduling and Probability of Completion

Learning Objectives  To define project Terminology  To illustrate AOA and AON diagrams  To calculate Project Duration, Critical Path, and slack  To compute and interpret probability of completing a project for a specific time

Project Networks  A flow chart that graphically depicts the sequence, interdependencies, and start and finish times of the project job plan of activities that is the critical path through the network.  Provides the basis for scheduling labor and equipment.  Enhances communication among project participants.  Provides an estimate of the project’s duration.  Provides a basis for budgeting cash flow.  Identifies activities that are critical.  Highlights activities that are “critical” and can not be delayed.  Help managers get and stay on plan.

Terminology  Activity (task): an element of the project that requires time.  Merge Activity: an activity that has two or more preceding activities on which it depends.  Parallel (Concurrent) Activities: Activities that can occur independently and, if desired, not at the same time. A C DB

Terminology continued  Path: a sequence of connected, dependent activities.  Critical path: the longest path through the activity network that allows for the completion of all project- related activities; C ABD

Terminology continued  Slack (or Float)  The amount of time an activity can be delayed after the start of a longer parallel activity or activities.  Total slack  The amount of time an activity can be delayed without delaying the entire project.

Terminology continued  Event: a point in time when an activity is started or completed. It does not consume time.  Burst Activity: an activity that has more than one activity immediately following it (more than one dependency arrow flowing from it).  Two Approaches  Activity-on-Node (AON)  Uses a node to depict an activity.  Activity-on-Arrow (AOA)  Uses an arrow to depict an activity. B D A C

CPM  Critical Path Method was developed by Dupont. It is a deterministic model where time estimates are accurate and do not vary. A project is made up of a sequence of activities or tasks that form a network representing a project  The path taking the longest time through this network of activities is called the "critical path". The critical path provides a wide range of scheduling information useful in managing a project. Critical Path Method (CPM) helps to identify the critical path(s) in the project networks. A network diagram is a graphic representation of the project and consists of directed arrows and nodes. To create a workable network diagram a project must have:  well-defined jobs or tasks whose completion marks the end of the project;  independent jobs or tasks;  and tasks that follow a given sequence.

Basic Rules to Follow in Developing Project Networks 1.Networks typically flow from left to right. 2.An activity cannot begin until all preceding connected activities are complete. 3.Arrows indicate precedence and flow and can cross over each other. 4.Each activity must have a unique identify number that is greater than any of its predecessor activities. (AOA) 5.Looping is not allowed. 6.Conditional statements are not allowed.

Illogical Loop 6–10 FIGURE 6.10

Activity Relationships Activity Relationship AOAAON

Activity Relationships S precedes T, which precedes U. AOAAON 12 S 3 T 4 U STU

Activity Relationships S and T must be completed before U can be started. AOAAON S T U 1 2 3 T S 4 U

Activity Relationships T and U cannot begin until S has been completed. AOAAON T U S 3 4 1 T U 2 S

Activity Relationships U and V cannot begin until both S and T have been completed. AOAAON 1 2 4 5 U V S T 3 S T U V

Activity Relationships U cannot begin until both S and T have been completed; V cannot begin until T has been completed. AOAAON S T U V 13 Dummy 5 246 SU TV

Activity Relationships T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed. AOAAON 124 3 ST 5 V U Dummy STV U

St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff. BSelect site and do site survey. CSelect equipment. DPrepare final construction plans and layout. EBring utilities to the site. FInterview applicants and fill positions in nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment. HConstruct the hospital. IDevelop an information system. JInstall the equipment. KTrain nurses and support staff.

St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F G Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F G H Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F G H I Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F G H I J Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network Start A B C D E F G H I J K Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network FinishStart A B C D E F G H I J K Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network A Start 1 2 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network A B Start 1 2 4 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network A B C D Start 1 2 3 5 4 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network F A B C D H E G I Start 1 8 2 3 7 65 4 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network F A B C D H E G J I Start 1 8 2 3 7 65 4 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network F A B C D H E G J I Dummy Start 1 8 2 3 7 65 4 Example 8.1

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AOA Network F A B C D H E G K J I Finish 9 Dummy Start 1 8 2 3 7 65 4 Figure 8.5 Example 8.1

Network Computation Process  Forward Pass—Earliest Times  How soon can the activity start? (early start—ES)  How soon can the activity finish? (early finish—EF)  How soon can the project finish? (expected time—ET)  Backward Pass—Latest Times  How late can the activity start? (late start—LS)  How late can the activity finish? (late finish—LF)  Which activities represent the critical path?  How long can activity be delayed? (slack or float— SL) 6–41

Forward Pass Computation  Add activity times along each path in the network (ES + Duration = EF).  Carry the early finish (EF) to the next activity where it becomes its early start (ES) unless…  The next succeeding activity is a merge activity, in which case the largest EF of all preceding activities is selected. 6–42

St. Adolf’s Hospital Forward Pass: Earliest Start & Earliest Finish

Backward Pass Computation  Subtract activity times along each path in the network (LF - Duration = LS).  Carry the late start (LS) to the next activity where it becomes its late finish (LF) unless  The next succeeding activity is a burst activity, in which case the smallest LF of all preceding activities is selected. 6–44

St. Adolf’s Hospital A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 Backwar d Pass: Latest Start and Latest Finish Times Finish Start

Determining Free Slack (or Float)  Free Slack (or Float)  Is the amount of time an activity can be delayed after the start of a longer parallel activity or activities.  Is how long an activity can exceed its early finish date without affecting early start dates of any successor(s).  Allows flexibility in scheduling scarce resources.  Sensitivity  The likelihood the original critical path(s) will change once the project is initiated.  The critical path is the network path(s) that has (have) the least slack in common. 6–46

Special  Laddering  Activities are broken into segments so the following activity can begin sooner and not delay the work.  Lags  The minimum amount of time a dependent activity must be delayed to begin or end.  Hammock

Probability of completion

Probability of Completing the Project The equation below is used to compute the “Z” value found in statistical tables (Z = number of standard deviations from the mean), which, in turn, tells the probability of completing the project in the time specified.

Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network FinishStart A B C D E F G H I J K Example 8.1

Example 8.6 St. Adolf’s Hospital OptimisticLikelyPessimisticExpectedVariance Activity(a)(m)(b)Time (t e )(  2 ) Time Estimates (wk)Activity Statistics A111213 B7815 C51015 D8916 E142530 F6918 G253641 H354045 I101328 J1215 K567

St. Adolf’s Hospital  2 =  (variances of activities) z = Ts – T E  2  2 = z = Probabilities Critical Path = T = T E =

Z Values and Probabilities 7–53

Z Table

St. Adolf’s Hospital Project duration (weeks) Probability of meeting the schedule is: Length of critical path Normal distribution: Mean = weeks; Probability of exceeding 72 weeks is:

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