1.040/1.401 Project Management Spring 2007 Deterministic Planning Part I Dr. SangHyun Lee Department of Civil and Environmental Engineering Massachusetts Institute of Technology

Project Management Phase FEASIBILITY CLOSEOUT DEVELOPMENT OPERATIONS Fin.&Eval. Risk Estimating Planning&Scheduling DESIGNPLANNING Organization

Outline  Objective  Bar Chart  Network Techniques  CPM

Objective What are some of the Different Representations for Deterministic Schedules ? What are some of the Different Representations for Deterministic Schedules ? What are some Issues to Watch for? What are some Issues to Watch for?

Outline Objective Objective  Bar Chart  Network Techniques  CPM

Gantt Chart Characteristics n Bar Chart n Henry L. Gantt n World War I n Ammunition Ordering and Delivery n Activities Enumerated in the Vertical Axis n Activity Duration Presented on the Horizontal Axis n Easy to Read

Simple Gantt Chart

Gantt (Bar) Charts Very effective communication tool Very popular for representation of simpler schedules Can be cumbersome when have >100 activities Key shortcoming: No dependencies captured Most effective as reporting format rather than representation

Hierarchy of Gantt Charts

Activity Aggregation Source: Shtub et al., 1994 Hammock Activities Hammock Activities A graphical arrangement which includes a summary of a group of activities in the project. A graphical arrangement which includes a summary of a group of activities in the project. Duration equal to longest sequence of activities Duration equal to longest sequence of activities

Activity Aggregation Source: Shtub et al., 1994 Milestones Milestones A task with a zero duration that acts as a reference point marking a major project event. Generally used to mark: beginning & end of project, completion of a major phase, or a task for which the duration is unknown or out of control. A task with a zero duration that acts as a reference point marking a major project event. Generally used to mark: beginning & end of project, completion of a major phase, or a task for which the duration is unknown or out of control. Flag the start or the successful completion of a set of activities Flag the start or the successful completion of a set of activities

Outline Objective Objective Bar Chart Bar Chart  Network Techniques  CPM

Network Scheduling A network is a graphical representation of a project plan, showing the inter-relationships of the various activities. A network is a graphical representation of a project plan, showing the inter-relationships of the various activities. When results of time estimates & computations are added to a network, it may be used as a project schedule. When results of time estimates & computations are added to a network, it may be used as a project schedule. Source: Badiru & Pulat, 1995 Activity A Event i Event j Activity on Arrow AOA Activity on Node AON Activity A Activity B

Advantages Communications Communications Interdependency Interdependency Expected Project Completion Date Expected Project Completion Date Task Starting Dates Task Starting Dates Critical Activities Critical Activities Activities with Slack Activities with Slack Concurrency Concurrency Probability of Project Completion Probability of Project Completion Source: Badiru & Pulat, 1995

Network - Definitions Source: Badiru & Pulat, 1995 Finish I H G D E F Start A B C Arc Node (Activity) Milestone Dummy Merge Point Burst Point

Network - Definitions Source: Badiru & Pulat, 1995 Predecessor Activity of D Successor Activity of F Finish I H G D E F Start A B C

Definitions (Cont’d) Source: Badiru & Pulat, 1995 Activity Time and resource consuming effort with a specific time required to perform the task or a set of tasks required by the project Dummy Zero time duration event used to represent logical relationships between activities Milestone Important event in the project life cycle Node A circular representation of an activity and/or event

Definitions (Cont’d) Arc Arc A line that connects two nodes and can be a representation of an event or an activity A line that connects two nodes and can be a representation of an event or an activity Restriction / Precedence Restriction / Precedence A relationship which establishes a sequence of activities or the start or end of an activity A relationship which establishes a sequence of activities or the start or end of an activity Predecessor Activity Predecessor Activity An activity that immediately precedes the one being considered An activity that immediately precedes the one being considered Successor Activity Successor Activity An activity that immediately follows the one being considered An activity that immediately follows the one being considered Descendent Activity Descendent Activity An activity restricted by the one under consideration An activity restricted by the one under consideration Antecedent Activity Antecedent Activity An activity that must precede the one being considered An activity that must precede the one being considered Source: Badiru & Pulat, 1995

Definitions (Cont’d) Source: Badiru & Pulat, 1995 Merge Point Merge Point Exists when two or more activities are predecessors to a single activity (the merge point) Exists when two or more activities are predecessors to a single activity (the merge point) Burst Point Burst Point Exists when two or more activities have a common predecessor (the burst point) Exists when two or more activities have a common predecessor (the burst point) Network Network Graphical portrayal of the relationship between activities and milestones in a project Graphical portrayal of the relationship between activities and milestones in a project Path Path A series of connected activities between any two events in a network A series of connected activities between any two events in a network

Outline Objective Objective Bar Chart Bar Chart  Network Techniques  CPM

Critical Path Method (CPM) DuPont, Inc., and UNIVAC Division of Remington Rand DuPont, Inc., and UNIVAC Division of Remington Rand Scheduling Maintenance Shutdowns in Chemical Processing Plants Scheduling Maintenance Shutdowns in Chemical Processing Plants ~1958 ~1958 Construction Projects Construction Projects Time and Cost Control Time and Cost Control Deterministic Times Deterministic Times

CPM Objective Determination of the critical path: the minimum time for a project Determination of the critical path: the minimum time for a project

CPM Precedence Source: Badiru & Pulat, 1995 Technical Precedence Technical Precedence Caused by the technical relationships among activities (e.g., in conventional construction, walls must be erected before roof installation) Caused by the technical relationships among activities (e.g., in conventional construction, walls must be erected before roof installation) Procedural Precedence Procedural Precedence Determined by organizational policies and procedures that are often subjective with no concrete justification Determined by organizational policies and procedures that are often subjective with no concrete justification Imposed Precedence Imposed Precedence E.g., Resource Imposed (Resource shortage may require one task to be before another) E.g., Resource Imposed (Resource shortage may require one task to be before another)

CPM: AOA & AON Source: Feigenbaum, 2002 Newitt, 2005  Activity-on-Arrow  Activity-on-Node Excavate Footings Mobilize Clear & Grub Fabricate Forms Footings Fabricate Rebar Footings Form Footings Start Finish 1 Start Form Footings 5 7 Excavate Footings 6 Fabricate Footings Forms at Site Workshop Clear & Grub 2 3 Mobilize 4 Fabricate Rebar Footings 8 Finish Arc Arrow Activity Dummy Activity Event Dummy Activity

CPM Calculations Source: Hegazy, 2002 Hendrickson and Au, 1989/2003 Forward Pass Forward Pass Early Start Times (ES) Early Start Times (ES) Earliest time an activity can start without violating precedence relations Earliest time an activity can start without violating precedence relations Early Finish Times (EF) Early Finish Times (EF) Earliest time an activity can finish without violating precedence relations Earliest time an activity can finish without violating precedence relations

Forward Pass - Intuition It’s 8am. Suppose you want to know the earliest time you can arrange to meet a friend after performing some tasks It’s 8am. Suppose you want to know the earliest time you can arrange to meet a friend after performing some tasks Wash hair (5 min) Wash hair (5 min) Boil water for tea (10 min) Boil water for tea (10 min) Eat breakfast (10 min) Eat breakfast (10 min) Walk to campus (5 min) Walk to campus (5 min) What is the earliest time you could meet your friend? What is the earliest time you could meet your friend?

CPM Calculations Source: Hegazy, 2002 Hendrickson and Au, 1989/2003 Backward Pass Backward Pass Late Start Times (LS) Late Start Times (LS) Latest time an activity can start without delaying the completion of the project Latest time an activity can start without delaying the completion of the project Late Finish Times (LF) Late Finish Times (LF) Latest time an activity can finish without delaying the completion of the project Latest time an activity can finish without delaying the completion of the project

Backward Pass - Intuition Your friend will arrive at 9am. You want to know by what time you need to start all things Your friend will arrive at 9am. You want to know by what time you need to start all things Wash hair (5 min) Wash hair (5 min) Boil water for tea (10 min) Boil water for tea (10 min) Eat breakfast (10 min) Eat breakfast (10 min) Walk to campus (5 min) Walk to campus (5 min) What is the latest time you should start? What is the latest time you should start?

Slack or Float It’s 8am, and you know that your friend will arrive at 9am. How much do you have as free time? It’s 8am, and you know that your friend will arrive at 9am. How much do you have as free time? Wash hair (5 min) Wash hair (5 min) Boil water for tea (10 min) Boil water for tea (10 min) Eat breakfast (10 min) Eat breakfast (10 min) Walk to campus (5 min) Walk to campus (5 min)

CPM Example Source: Badiru & Pulat, 1995 Draw AON network

A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start Forward Pass Source: Badiru & Pulat, ES EF

A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start Source: Badiru & Pulat, 1995 Forward Pass

A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start Source: Badiru & Pulat, 1995 Backward Pass 11 LS LF LF(k) = Min{LS(j)} j S(k) LF(k) = Min{LS(j)} j S(k) LS(k) = LF(k) – D(k) LS(k) = LF(k) – D(k) 

A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start Source: Badiru & Pulat, 1995 Backward Pass

Slack or Float The amount of flexibility an activity possesses The amount of flexibility an activity possesses Degree of freedom in timing for performing task Degree of freedom in timing for performing task Source: Hendrickson and Au, 1989/2003 A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start

Total Slack or Float Total Slack or Float (TS or TF) Total Slack or Float (TS or TF) Max time can delay w/o delaying the project Max time can delay w/o delaying the project TS(k) = {LF(k) - EF(k)} or {LS(k) - ES(k)} TS(k) = {LF(k) - EF(k)} or {LS(k) - ES(k)} A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start TS = 4

Free Slack or Float Free Slack or Float (FS or FF) Free Slack or Float (FS or FF) Max time can delay w/o delaying successors Max time can delay w/o delaying successors FS(k) = Min{ES(j)} - EF(k) j S(k) FS(k) = Min{ES(j)} - EF(k) j S(k) A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start FS = 3 

Independent Slack or Float Independent Slack or Float (IF) Independent Slack or Float (IF) Like Free float but assuming worst-case finish of predecessors Like Free float but assuming worst-case finish of predecessors IF(k) = Max { 0, ( Min(ES(j)) - Max(LF(i)) – D(k) ) } j S(k), i P(k) IF(k) = Max { 0, ( Min(ES(j)) - Max(LF(i)) – D(k) ) } j S(k), i P(k) A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start IF = 1  

CPM Analysis Adapted from: Badiru & Pulat, 1995 ActivityDurationESEFLSLFTSFSIFCritical A B C Yes D E F G Yes

Critical Path The path with the least slack or float in the network The path with the least slack or float in the network Activities in that path: critical activities Activities in that path: critical activities For algorithm as described, at least one such path For algorithm as described, at least one such path Must be completed on time or entire project delayed Must be completed on time or entire project delayed Determines minimum time required for project Determines minimum time required for project Consider near-critical activities as well! Consider near-critical activities as well!

A2A2 F4F4 B6B6 C4C4 D3D3 G2G2 E5E5 End Start Critical Path Source: Badiru & Pulat, 1995 If EF i = ES j, then activity i is a critical activity (here, activity i is an immediate predecessor of activity j

Path Criticality = minimum total float = maximum total float = total float or slack in current path Rank paths from more critical to less critical Rank paths from more critical to less critical

Source: Badiru & Pulat, 1995 Calculate Path Criticality Calculate Path Criticality α min = 0, α max = 5 α min = 0, α max = 5 Path 1: [(5-0)/(5-0)](100 %) = 100 % Path 1: [(5-0)/(5-0)](100 %) = 100 % Path 2: [(5-3)/(5-0)](100 %) = 40 % Path 2: [(5-3)/(5-0)](100 %) = 40 % Path 3: [(5-4)/(5-0)](100 %) = 20 % Path 3: [(5-4)/(5-0)](100 %) = 20 % Path 4: [(5-5)/(5-0)](100 %) = 0 % Path 4: [(5-5)/(5-0)](100 %) = 0 % Path Criticality - Example