Project Management L4W6 PDF

# Module 4: Project Scheduling & Control ## Types of Project | Methods well defined | Goals well defined | Type of Project | |---|---|---| | No | No | Type 3: R&D and Organizational Change Project | | No | Yes | Type 4: Product Development Project | | Yes | No | Type 2: Applications Softw...

# Module 4: Project Scheduling & Control ## Types of Project | Methods well defined | Goals well defined | Type of Project | |---|---|---| | No | No | Type 3: R&D and Organizational Change Project | | No | Yes | Type 4: Product Development Project | | Yes | No | Type 2: Applications Software Development Project | | Yes | Yes | Type 1: Engineering Project | ## Project Management Processes - Scope Management - Time Management - Cost Management - Quality Management - Human Resource Management - Communications Management - Risk Management - Procurement Management ## Project Scheduling & Control **Assign and track the project schedule using CPM. (CLO3)** **Demonstrate and apply engineering management and economic principles in multidisciplinary environments as an individual or as a leader in a team. (PLO11)** ## Project Scheduling & Control - **LEARNING OUTCOMES** - Able to arrange the activities appropriately. - Able to produce a realistic time scheduling. - Able to produce a resources estimation and planning. - Able to implement time and cost controlling. - Able to ease the contract administration. - Able to develop network diagram for a project. - Able to perform resources leveling for a project. ## Introduction to Scheduling - **Why We Need a Schedule:** - Contractual obligation - To establish a sequence of work and timeframe for performance of construction activities - To provide a communication tool between contractors, owner, A/E, subs, and suppliers - To document modifications ("as-planned" versus “as-built") - To show the impact of productivity-related problems on project completion (weather, strikes, delays) - Determine when to order and deliver materials and equipment ## Scheduling Techniques - **Planning, Scheduling And controlling Techniques:** - Bar Charts - Progress Curve or S-Curves - Linear Balance Method - Matrix Schedules - Critical Path Method (CPM) ## Types of Schedules - **Bar Chart** - Often called Gantt Chart - **Network Diagrams** - Arrow Diagram (AOA) - Precedence Diagram (AON) - Often called Critical Path Method (CPM) ## Formats of Schedules - **Summary schedule** - Shows major work elements, such as sitework, masonry, carpentry, electrical, plumbing, etc. - **Detailed schedule** - Work should be broken down into activities that comprise not more than 5% of total project - **Short-interval schedule** - Identifies work for upcoming 2-3 weeks - Usually prepared by superintendent ## Bar Chart - **Developed by Henry Gantt** - Often called a Gantt Chart - **Definition** - A graphical description of a project consisting of well-defined collection of tasks ## Bar Chart - **Activities are represented by bars in proportion to their duration** - An activity is a task or closely related group of tasks whose performance contributes to the completion of the overall project. - Example: Excavate foundation - **Activities are represented by bars in proportion to their duration** - **Bar chart is usually graphed on a calendar** - **Can be as simple or detailed as necessary** ## Example Bar Chart | No. | Description | Month | |---|---|---| | 1 | Mobilization | 1 | | 2 | Foundation Excavation | 1, 2 | | 3 | Diversion Stage | 3, 4 | | 4 | Foundation Grouting | 4 | | 5 | Dam Concrete | 5, 6, 7, 8, 9 | | 6 | Install Outlet Gates | 6 | | 7 | Install Trash Racks | 7 | | 8 | Prestress | 8, 9 | | 9 | Radial Gates | 9 | | 10 | Spillway Bridge | 9 | | 11 | Curtain Grout | 10 | | 12 | Dismantle Plant, Clean Up | 10 | * **Note**: The table in the image above shows a bar chart for a concrete gravity-arch dam, indicating the original schedule and actual progress with different tasks. ## Constructing a Bar Chart - **When constructing a bar chart, the following questions must be answered:** - What time units should be used? (days, weeks, months) - Should work days or calendar days be used? - How do I schedule non-continuous work? - **Additional information may be added to the basic bar chart:** - Cost of activity ("cost-loaded schedule") - Labor required for each activity (“man-loaded") - Materials required for each activity ("resource-loaded") ## Steps to Construct a Bar Chart 1. Break the job down into activities 2. Establish the sequence of work 3. Estimate activity duration ## 1. Break the Job Down Into Activities - Use the Work Breakdown Structure (WBS) from the cost estimate - Add activities as necessary - **Rule of thumb:** no activity should comprise more than 5% of the total scope of work - **Rule of thumb:** activity duration should range from 1 day to 15 days ## 2. Establish the Sequence Of Work - Sequencing needs to take into account the relationships between activities - There are four types of relationships that need to be taken into account. ## 2. Establish the Sequence Of Work (continued) 1. **Physical:** - Exists between two or more activities when one cannot start until another is partially or totally complete (i.e., cannot pour footings until they have been formed) 2. **Safety:** - Exists when simultaneous performance of two activities can result in a safety hazard (i.ê., in multi-story construction it is at times unsafe for crews to be working under one another) 3. **Resource:** - Due to limited resource availability, two activities may not be able to use a resource at the same time (i.e., a crane cannot be used for both pouring walls and erecting steel) 4. **Preferential:** - How the contractor wishes certain activities to be sequenced ## 3. Estimate Activity Duration - **How to estimate duration:** - From company's historic records - From asking superintendent or foreman - From standard estimating guide - From calculation using the Labor Hour Productivity equation ## 3. Estimate Activity Duration (continued) - **Labor-Hour Productivity Method** - **Total labor-hours required for an activity = (labor-hours/Unit) x (no. of units)** - **Total days = total labor hours / labor-hours / day** - **Total days = total labor hours / crew size x hrs/day** ## Using a Bar Chart for Planning and Progress - **Assume the progress of the activity as a direct linear function of the elapsed time** - **Example:** | No | Activity | Duration (Days) | Quantity Amount | Units | 3/30 | 4/6 | 4/13 | 4/20 | 4/27 | 5/4 | 5/11 | 5/18 | 5/25 | 6/1 | 6/8 | 6/15 | 6/22 | 6/24 | 7/6 | 7/13 | 7/20 | 7/27 | 8/3 | |---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| | 1 | Move-in | 5 | | | | | | | | | | | | | | | | | | | | | | | | | 2 | Clear & Grub | 20 | | SF | | | | | | | | | | | | | | | | | | | | | 3 | Earth moving | 60 | | CY | | | | | | | | | | | | | | | | | | | | 4 | Site Grading | 45 | | SF | | | | | | | | | | | | | | | | | | | 5 | Subbase | 45 | | | | | | | | | | | | | | | | | | | | | 6 | Base | 25 | | | | | | | | | | | | | | | | | | | | 7 | Paving | 25 | | | | | | | | | | | | | | | | | | | **Note:** The table in the image above shows a bar chart with a "Week Ending" column divided in 100% total and marked with planned, and completed works. ## Bar Chart Progress Schedule - **Bar chart progress schedule should satisfy the following minimum requirements:** - Include activities that describe essential features of the work. - Include start, duration, and completion date for each activity. - Include quantity and the estimated daily production rate for controlling items of work. ## Bar Charts | | Advantages | Disadvantages | |---|---|---| | | - Simple graphical - Easy for general comprehension - Wide spread used in industry - Mostly used in small project - Fairly broad planning and scheduling tools, so they require less revision and updating than more sophisticated systems | - Very cumbersome as the number of line activities, or bars increases - Logical interconnections and constraints of the various activities is not expressed - Difficult to use it for forecasting the effects that changes in a particular activity will have on the overall schedule | ## Example 1: Bar Chart - A project consist of six activités that should be done in a period of time. Try to create a bar chart to ease the project planning and scheduling. - Activity A: 1 week, starting from 1 Oct 2021 - Activity B: 2 week, starting from 5 Oct 2021 - Activity C: 3 week, starting from 15 Oct 2021 - Activity D: 2 week, starting from 25 Oct 2021 - Activity E: 2 week, starting from 29 Oct 2021 - Activity F: 1 week, starting from 5 Nov 2021 - **Start Date = 1/10** - **End Date = 12/11** - **Project Duration = 6 weeks** ## Example 1: Bar Chart | | Activity | Duration | Week | |---|---|---|---| | 1 | A | 1 | 1/10 | | 2 | B | 2 | 8/10 | | 3 | C | 3 | 15/10 | | 4 | D | 2 | 22/10 | | 5 | E | 2 | 29/10 | | 6 | F | 1 | 5/11 | | | | | 12/11 | **Note**: The table in the image above shows a bar chart for a project consisting of six activities that should be done in a period of time. The start date is 1/10 and the end date is 12/11. The project duration is 6 weeks. ## Example 2: Bar Chart - Data of a project consist of five activities with their duration and also amount of people needed for this project. Create a modificed bar chart according to the given data. | No | Activity | Duration (week) | Starting Date | Human Resources (people) | Successor | |---|---|---|---|---|---| | 1 | G | 1 | 01 October 2021 | 5 | H, I | | 2 | H | 2 | 08 October 2021 | 8 (4+4) | J | | 3 | I | 3 | 10 October 2021 | 15 (4+5+5+1) | K | | 4 | J | 2 | 22 October 2021 | 4 (2+2) | K | | 5 | K | 2 | 05 November 2021 | 3 | - | - **Start Date = 1/10** - **End Date = 12/11** - **Project Duration = 6 weeks** ## Example 2: Bar Chart | | Activity | Duration | People | Week | |---|---|---|---|---| | 1 | G | 1 | 5 | 1/10 | | 2 | H | 2 | 8 | 8/10 | | 3 | I | 3 | 15 | 15/10 | | 4 | J | 2 | 4 | 22/10 | | 5 | K | 1 | 3 | 29/10 | | | | | | 5/11 | | | | | | 12/11 | * **Note**: The table in the image above shows a bar chart for a project containing five activities with their duration and also the amount of people needed for this project. ## Progress Curve (S-Curve) - **Step by step to make s-curve** - Calculate cost for each activity - Calculate total cost for all activity - Calculate the progress ratio between cost for each activity and total cost - Divide those progress ratio equally for each activity according to its duration - Add the progress ratio which already divided for each unit of time - Calculate the cumulative progress ratio - Draw S-Curve as a relationship between cumulative progress ratio and duration of a project ## Combination between S-Curve & Bar Chart | No. | Description | Month | |---|---|---| | 1 | Mobilization | 1 | | 2 | Foundation Excavation | 1, 2 | | 3 | Diversion Stage | 3, 4 | | 4 | Foundation Grouting | 4 | | 5 | Dam Concrete | 5, 6 | | 6 | Install Outlet Gates | 6 | | 7 | Install Trash Racks | 7 | | 8 | Prestress | 8, 9 | | 9 | Radial Gates | 9 | | 10 | Spillway Bridge | 9 | | 11 | Curtain Grout | 10 | | 12 | Dismantle Plant, Clean Up | 10 | * **Note**: This table shows a combination of bar chart and S-curves for a project containing 12 activities showing original schedule and the actual progress marked with 100% progress along the curve. ## Example 3 : S-Curve - **Example 3**: As a bar chart is created in Example 1, draw a progress or S-Curve of the project with additional data given: | No | Activity | Duration | Cost (RM) | Total Cost | |---|---|---|---|---| | 1 | A | 1 | 1,600 | 1,600 | | 2 | B | 2 | 420 | 1,000 | | 3 | C | 3 | | 2,000 | | 4 | D | | 1,380 | 2,400 | | 5 | E | 2 | 1,800 | 1,800 | | 6 | F | 1 | | 2,000 | | | Total | | | 20,000 | ## Example 3 : S-Curve - **Convert cost from RM to % of total cost.** | No | Activity | Duration | Cost (%) | Total Cost | |---|---|---|---|---| | 1 | A | 1 | 8 | 8 | | 2 | B | 2 | 2.1 | 5 | | 3 | C | 3 | 10 | 10 | | 4 | D | 2 | 6.9 | 12 | |5 | E | 2 | 9 | 9 | | 6 | F | 1 | 10 | 10 | | | Total | | | 100 | ## Example 3: S-Curve | | Activity | Duration | Week | |---|---|---|---| | 1 | A | 1 | 1/10 | | 2 | B | 2 | 8/10 | | 3 | C | 3 | 15/10 | | 4 | D | 2 | 22/10 | | 5 | E | 2 | 29/10 | | 6 | F | 1 | 5/11 | | | | | 12/11 | - **Work Progress Ratio (%)**: 10.1, 5, 12.9, 16.9, 31, 24.1 - **Cumulative WPR (%)**: 10.1, 15.1, 28, 44.9, 75.9, 100 * **Note**: The table in the image above shows a chart with a "Work Progress Ratio" column. For example, for the first week, the WPR is 10.1%, the cumulative WPR is 10.1%, and so on. ## Example 3: S-Curve | | Activity | Duration (week) | Progress Ratio (%) | Week | |---|---|---|---|---| | 1 | A | 1 | 8 | 1/10 | 8/10 | 15/10 | 22/10 | 29/10 | 5/11 | 6 | 100 | | 2 | B | 2 | 10 | | | | | | | | 100 | | 3 | C | 3 | 30 | | | | | | | | 100 | | 4 | D | 2 | 24 | | | | | | | | 50 | | 5 | E | 2 | 18 | | | | | | | | | | 6 | F | 1 | 10 | | | | | | | | | - **Work progress ratio (%)**: 10.1, 5, 12.9, 16.9, 31, 24.1 - **Cumulative wok progress ratio (%)**: 10.1, 15.1, 28, 44.9, 75.9, 100 * **Note**: The table in the image above shows a table with a "Column Work Progress Ratio" with 100% cumulative progress. ## Linear Balance Method - **Facts about linear balance method** - Also called as Vertical Production Method (VPM) - Apply best to linear and repetitive operations, such as tunnels, pipelines, highways etc. * **Note**: The image above shows a line graph with 10 distinct activities and their time steps for a project with 100% progress shown along the y-axis. ## Matrix Schedule - **Facts about matrix schedules** - Fairly common used on high-rise buildings with successive floors repeating essentially the same plan. - The vertical correlation of floors to rows is immediately obvious to anyone and requires no explanation. - The chronological, left-to-right flow of each floor’s operations is easy to see. - The logical interrelationships among operations are also more obvious than in a bar chart - With some forethought, the vertical columns can be made to correspond to the specialty subcontractors ## Matrix Schedule - **Sequence of operations on each floor** * **Note**: The image above shows a matrix schedule. The matrix has three columns: "Building floor numbers," "Intermediate Operations," and "Install suspended ceiling, Paint and carpet." The matrix is used to track the progress of construction on each floor of a building. ## Network Diagrams - **Definition** - A network consists of two basic elements, nodes and links between these nodes - **Activities on arrows (AOA) - arrow diagram** - Activities are represented by two nodes and one link - **Activities on nodes (AON) - precedence diagram** - Activities represented by nodes and links represent the relationship ## Basic Rules of Network Logic (Precedence Diagram) - **Rule 1: Eliminate redundant linkages** * **Note**: The two diagrams in the image above show a precedence diagram, illustrating that a redundant linkage (left) should be replaced with a simple connection (right). ## Basic Rules of Network Logic - **Rule 2: Close the network to give single beginning and ending nodes** * **Note**: The diagram in the image above shows a closed network with single starting nodes (Initial Event) and ending nodes (Terminal Event). ## Basic Rules of Network Logic - **Rule 3: Before an activity may begin, all activities preceding it must be completed (activities with no predecessors are self-actuating when the project begins).** - **Rule 4: All relationships are assumed to be finish to start.** - **Rule 5: Event numbers must not be duplicated in a network.** - **Rule 6: No two events may be directly connected by more than one arrow.** ## Activities Relationships - **a) Finish-to-start relationship** - (Start of B must lag 5 days after the finish of A) - **b) Start-to-start relationship** - (Start of B must lag 3 days after the start of A) - **c) Finish-to-finish relationship** - (Finish of B must lag 3 days after the finish of A) - **d) Start-to-finish relationship** - (Finish of B must lag 45 days after start of A) ## Sequencing and Numbering * **Note**: The diagram in the image above illustrates a sequence of six activities organized by time. Each activity is represented by a box with its duration and a number. ## Constructing a Network Diagram 1. Create activity list and eliminate redundancies 2. Construct arrow/precedence diagram 3. Arrange activities in a sequential order. ## Time Values Associated With Each Activity 1. ESD -> Early Start Date 2. EFD -> Early Finish Date 3. LSD -> Late Start Date 4. LFD -> Late Finish Date ## Scheduling Computations (Forward Pass Rules) - **Four rules of completing a Forward Pass:** - Rule 1: The initial project event is assumed to occur at time zero. - Rule 2: All activities are assumed to start as soon as possible, that is, as soon as all the predecessor activities are completed. - Rule 3: The early finish time of an activity is merely the sum of its early start date and the estimated activity duration. - **EFD₁= ESD₁ + T₁** ## Scheduling Computations (Forward Pass Rules) – cont. - Rule 4: At merge points, the early start is the largest value of the preceding early finish time. * **Note**: The diagram in the image above illustrates a forward pass, showing the early finish date (EFD) and the early start date (ESD) of a project. The EFD is the earliest time an activity can be finished, and the ESD is the earliest time an activity can be started. ## Scheduling Computations (Backward Pass Rules) - **Three rules of completing a Backward Pass:** - Rule 1: The late finish date of the last activity is equal to its early finish date. - Rule 2: The late start date for any activity is found by subtracting the activity duration from its late finish date. - **LSD₁= LFD₁ - T₁** ## Scheduling Computations (Backward Pass Rules) - cont. - Rule 3: In the backward pass, the late finish date of an activity is the smallest late start value of the following activities. * **Note**: The diagram in the image above explains a backward pass, showing the late start date (LSD), late finish date (LFD) and the late finish date (LFD) of a project. The LSD is the latest time an activity can be started, and the LFD is the latest time an activity can be finished. ## The Float Concept - **What is "float"?** - Float or slack is the amount of scheduling leeway that a network activity has - **What is "total float"?** - That time span in which the completion of an activity may occur and not delay the completion of the project - **Equation for total float (TF):** - **TF₁ = LFD - EFD₁** - **= LSD, - ESD₁** ## The Float Concept (cont.) - **What is "free float"?** - The time span in which the completion of an activity may occur and not delay the finish of the project or delay the start of any following activity - **What is a link lag?** - The difference between the early start date of an activity and the early finish date of the preceding activity - **Lagi;= ESD; - EFD;** ## The Float Concept (cont.) - **How to determine free float:** - Free float is the minimum value of the link lags of the link that follows an activity. - **FF 20 = Min {Float 20-25 Float 20-30 {6 1 = Min {6 1 = 1** ## Critical Path Example * **Note**: The diagram in the image above shows a critical path example with 8 activities. The critical path is a path in a project network that has the longest duration. This is the path that must be worked on to meet the project deadline. ## Network Diagram - **Note**: - The image above shows a circle representing a network diagram. It contains the following elements: ESD, T (Activity), EFD, LSD, NO, and LFD. ## Critical Path Method | | Advantages | Disadvantages | |---|---|---| | | Networks can much more concisely represent large numbers of activities The logical interrelationships and dependencies among activities is really shown Much more useful for forecasting and control It identify the most critical elements in the project schedule Easy to adjust if any delay is happen in the project | A little bit difficult to understand the network system | ## Types of CPM - Arrow Diagram Method (ADM) - Precedence Diagram Method (PDM) ## ADM vs. PDM | Item | ADM | PDM | |---|---|---| | Activity | | | | | | Event | | | * **Notes**: The tables in the image above show a comparison between ADM and PDM methods. ADM is the Arrow Diagram Method, where activities are represented by arrows, and events are represented by nodes, and PDM is the Precedence Diagram Method, where activities are represented by nodes, and events are represented by arrows. ## ADM vs. PDM (cont.) | Item | ADM | PDM | |---|---|---| | Dummy Activity | | | | | * **Notes**: The tables in the image above provides further understanding of the differences between ADM and PDM methods. In the table, the image compares dummy activities. In the ADM method, a dummy activity can be used to show a relationship between activities where one event is used to show the relationship between more than one activity. In the PDM method, dummy activities are not used. ## ADM vs. PDM (cont.) | Item | ADM | |---|---| | Dummy Activity | | | **False**: - A - B **True**: - A - B * **Notes**: The figure for the false diagram illustrates the use of dummy activities. The dummy activity D indicates that activity A is independent of activities B and C, while activity C depends on activity B and D. The figure for the true diagram shows that activity D is independent of activities A, B, and C while activity E depends on activities A and B. ## ADM vs. PDM (cont.) | Item | ADM | |---|---| | Dummy Activity | | | **False**: - A - B - C **True**: - A - B - C * **Notes**: The figure for the false diagram illustrates the use of dummy activities. The dummy activity D indicates that activity A is independent of activities B and C, while activity C depends on activity B and D. The dummy activity F indicates that activity B is independent of activities A and D, while activity F depends on activity A and D. The figure for the true diagram shows that activity D is independent of activities A, B, and C while activity E depends on activities A and B. The dummy activity F is independent of activities A, B, and C while activity F depends on activities B and C. ## ADM vs. PDM (cont.) | Item | ADM | PDM | |---|---|---| | Relationship | F - S | F - F - S - S - F - S | | Critical path | | | * **Notes**: The tables in the image above compares the two methods by explaining the relationship between the activities in each approach. The ADM method has a single relation between activities, which is called a finish-to-start relationship. While the PDM method uses a more complex relationship, which includes a finish-to-start, finish-to-finish, and start-to-finish relation between activities. ## ADM vs. PDM (cont.) | Item | ADM | PDM | |---|---|---| | Total float | | | | Estimating duration | | | * **Notes**: The tables on the page above explain the main differences in the two methods, the ADM, and the PDM. In the table, the image explains the total float and the estimation of project duration in each approach. ## Arrow Diagram Method - **Estimating Project Duration using Arrow Diagram Method (ADM)** * **Note**: The image above shows a diagram illustrating the forward pass, backward pass and the formula to calculate the project duration. ## Example 4: Arrow Diagram Method | Activity | Successor | Duration (week) | |---|---|---| | A | B, C | 2 | | B | D | 3 | | C | E | 2 | | D | F | 4 | | E | G | 5 | | F | H | 2 | | G | H | 3 | | H | - | 1 | - Estimate the total project duration. - Calculate the total float for each activity in the project - Draw the bar chart according to your calculation ## Example 4: Arrow Diagram Method - **Activity** - B, C - D - E - F - G - H - - - **Duration (week)** - 2 - 3 - 2 - 4 - 5 - 2 - 3 - 1 * **Notes**: The image above shows an arrow diagram method with 8 activities with their duration and successors. The arrow diagram is a graphical representation of a project network, where activities are represented by arrows and events are represented by nodes. ## Example 4: Arrow Diagram Method | Event | Activity | Duration | ES | LS | EF | LF | Float | |---|---|---|---|---|---|---|---|---| | 1-2 | A | 2 | 0 | 0 | 2 | 2 | 0* | | 2-3 | B | 3 | 2 | 2 | 5 | 5 | 0* | | 2-4 | C | 2 | 2 | 3 | 4 | 5 | 1 | | 3-5 | D | 4 | 5 | 5 | 9 | 9 | 0* | | 4-6 | E | 3 | 4 | 5 | 7 | 8 | 1 | | 5-7 | F | 2 | 9 | 9 | 11 | 11 | 0* | | 6-7 | G | 3 | 7 | 8 | 10 | 11 | 1 | | 7-8 | H | 1 | 11 | 11 | 12 | 12 | 0* | | | | | | | | | * **Notes**: The table in the image above shows a table of activities with their details, such as duration, early start (ES), late start (LS), early finish (EF), late finish (LF), and total float. ## Example 4: Arrow Diagram Method | No | Act. | Week | |---|---|---| | 1 | A | 1, 2 | | 2 | B | 2, 3, 4 | | 3 | C | 2, 3 | | 4 | D | 4, 5, 6, 7, 8 | | 5 | E | 4, 5, 6 | | 6 | F | 7, 8, 9, 10 | | 7 | G | 7, 8 | | 8 | H | 9, 10, 11, 12 | * **Critical Path = A-B-D-F-H** * **Notes**: The table in the image above shows the chart for the activities with 12 weeks, marking their start time. The chart clearly reflects the project's critical path. The critical path is the longest path in a project network, and it is the path that must be worked on to meet the project deadline. ## Example 5: Arrow Diagram Method | Activity | Predecessor | Duration (week) | |---|---|---| | A | - | 2 | | B | - | 1 | | C | - | 3 | | D | A | 1 | | E | B | 3 | | F | C | 2 | | G | D | 4 | | H | D, E | 1 | | I | D, E, F | 2 | | J | G | 1 | | K | H | 2 | | L | I | 3 | | | | | - Estimate the total project duration. - Calculate the total float for each activity in the project - Draw the bar chart according to your calculation ## Example 5: Arrow Diagram Method * **Notes**: The image above shows an arrow diagram with durations and their predecessors. ## Example 5: Arrow Diagram Method | No | Activity | Total Float | Week | |---|---|---|---|---| | 1 | A | 2 | 1, 2 | | 2 | B | 1 | 2, 3 | | 3 | C | 0 | 3, 4 | | 4 | D | 2 | 4, 5 | | 5 | E | 1 | 4, 5, 6, 7 | | 6 | F | 0 | 5, 6 | | 7 | G | 2 | 6, 7, 8, 9 | | 8 | H | 3 | 7, 8, 9 | | 9 | I | 0 | 8, 9 | | 10 | J | 2 | 9, 10 | | 11 | K | 3 | 10, 11