Dynamic Scheduling Techniques for Heterogeneous Computing Systems
Chapter 6 - Techniques of Scheduling
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Transcript of Chapter 6 - Techniques of Scheduling
1/24/2011
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TECHNIQUES OF O
PLANNING & SCHEDULING
Introduction...
The techniques used for project scheduling will vary depending upon the project;
SizeComplexityDurationPersonnelOwner requirements
Introduction...
The Project Manager must choose a scheduling technique that is simple to use and is easily interpreted by all project participants.
Techniques...
Methods that are commonly used:Gantt Chart (Bar chart)Critical Path Method (CPM or network analysis)Precedence Diagram Method (PDM)gProgram Evaluation Review Technique (PERT)
Other methods:Line of BalanceTime Grid Diagram
?
GANTT CHARTGANTT CHART
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Gantt Chart...Widely acceptedA simple presentation that shows how major work activities are scheduled (the simplest form).For small project and few activities (non complex project).Can be developed from CPMMust be accompanied by detailed work program.
Gantt Chart...
Visual representation can help when a project manager needs an overview:
September October November December
User InterfacePrototype
RegistrationPersistence
Code to Gen. Password MD5
…etc…
RegistrationDialog
…etc…
Gantt Chart... Gantt Chart Schedule (Bar Chart)
Gantt Chart with Milestone Added Gantt Chart with Milestone Added
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Gantt Chart of a Sample Project A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST, LST, EFT, and LFT
A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource Requirements
NETWORK ANALYSIS
Introduction...
A planning method for a project which analysis will be done to all the activities involved.
Produce a network which is connected among the activities.
It is to optimize the resources needed, progress report and project monitoring.
To determine the critical path in a project.
Types of Network Analysis...
1. CPM
2. PDM
3. PERT
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CPM...
Commonly used in the engineering and construction industry (widely used in Project Management techniques).
E h ti it i i d ifi d ti d Each activity is assigned a specific duration and calculations through the network provide a single, specific duration for the project as a whole.
Provides interrelationships of activities and scheduling of costs and resources.
CPM...This method calculates the minimum completion time for a project along with the possible start and finish times for the project activities.
The duration of the critical path is the sum of the activities pdurations along the path
The duration of the critical path represents the minimum time required to complete a project.
Any delays along the critical path would imply that additional time would be required to complete the project
CPM...The CPM is a systematic scheduling method for a project network and involves four main steps:
1. A forward path to determine activities early‐start (ES) times
2. A backward path to determine activities late‐finish (LF) times
3. Float calculations
4. Identifying critical activities
Types of CPM...
1. Activity On Arrow (AOA) or “arrow diagram”
2. Activity On Node (AON) or “precedence diagram”
Logic Diagram Definitions...
NODE = a node is any closed geometric figure such as CIRCLE, SQUARE or DIAMOND.
ARROW = an arrow is a line connecting 2 nodes and having an arrowhead at one end. h d h h
gThe arrow designates that the activity is a predecessor to the one at the head of the arrow.
ACTIVITY = an activity is a time consuming effort required to perform a part of the project.
Logic Diagram Definitions...
EVENT= a point in time when an activity is started or completed. It does not consume time. BB
BURST ACTIVITY = an activity that has more than one activity immediately following it (more than one dependency arrow flowing from it).
D
A CA
D
C
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Logic Diagram Definitions...
MERGE ACTIVITY = an activity that has two or more preceding activities on which it depends. AA
PARALLEL (CONCURRENT) ACTIVITIES = Activities that can occur independently and, if desired, not at the same time.
C
DBB D
C
Logic Diagram Definitions...
RESTRAINT = a precedence relationship that establishes the sequence of activities. When one activity must be completed before a second activity can begin, the first is considered to be a restraint or restriction on the second. The arrow between that activity A is a restriction on activity y yB.
DUMMY = a dummy node is used to indicate a restraint relationship that requires no time. A dummy is denoted by a dashed symbol. It is treated as an activity with a zero (0) time duration.
Logic Diagram Definitions...
FORWARD PASS = calculates “earliest start” time and “ earliest finish” time for each activity.
BACKWARD PASS = calculates “latest start” time and “latest finish” time for each activity.
CRITICAL PATH = a scheduling technique using arrow, precedence, or PERT diagrams to determine the length of a project and to identify the activities and constraints on the critical path.
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 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.
5. Looping is not allowed.
6. Conditional statements are not allowed.
7. Use common start and stop nodes.
ACTIVITY – ON – ARROW(AOA)
Activity‐On‐Arrow (AOA)
Model basic = Activity On Arrow (AOA)Tail of the arrow = starting of the activityHead of the arrow = finishing or completing of the activitythe activity
Events are in circles called ‘node’.Activities represented by lines or arcs
Start End
Activity
Duration 1 2
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Activity‐On‐Arrow (AOA)
ACTIVITY EVENT
ERECTION OF STEEL COLUMN
AOA Network Fundamentals
6–32
Exercise ‐ Network Information
6–33
TABLE 6.2
Example of AOA
Exercise of AOA
• Activity A (predecessor) must be completed before Activity B & C (successors) start
AOA with DURATIONS & CRITICAL PATH
Network diagram with durations & critical path added
Activities if delayed will delay the whole project (the activities with the longest path)
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Rules of AOA...
No activity can start before its predecessors are complete.
Arrows imply logic only – direction or length may have no meaning.
Each activity has a different activity number, no duplicates allowed.
Activity...
Task or set of tasksUse resources
Milestones...Events that mark significant progress
Path...Series of connected activities between two events
Event...
To show the starting / ending of the activity
Normally stated in number
First and last eventsFirst event has no predecessorsLast event has no successorsAll networks have a first and last event
Dummy...Fault activity to connect the logic
Duration of the dummy activity is 0.
Used to maintain logic
Example:Activity C is depends on the completion of activity A and B, but activity D is only depends on the completion of the activity B. Therefore this type of network needs dummy.
B
A
D
C
Dummy
Dummy Activities...
Required due to AOA rule that each task is represented by one arrow, which connects two events.
Parallel tasks have different durationIf terminated on one event (instant in time), implication is that they both have the same durationNot generally the caseCannot change the schedule if one event slips without revising the diagram.
Example of Dummy
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Example of Dummy Example of Dummy
Example of Dummy Critical Path...
Critical path is directly continues for all the critical activities from project start until the project complete.
For critical activities, normally the earliest time start and the latest time start is same.
Float / Slacks...
‘Spare time’ in a network.
Float is the range of allowable time between when a task can be started and when it must be started.
Once float is used up, the finish date of the project is affected.Can show non‐critical activities
Float...
0 10
6 Days
Activity Float
6 Days
Activity Duration 6 Days Float Time 4Days
Available Time 10 Days
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Float / Slacks...
4 types of float:
1. TOTAL FLOAT (TF)
2. FREE FLOAT (FF)
3. INTERFERRING FLOAT (IF)
4. INDEPENDENCE FLOAT
Total Float (TF)...MAXIMUM additional duration / period in an activity that can be delayed without affect the completion date of the activity.
The amount of time an activity can exceed its early finish date without affecting the project end date or other imposed datesimposed dates.
The amount of float available to all activities on a given sub path of a network.
Total float of activities on the critical path is zero.
Total Float (TF) = LS – ES or LF – ES ‐ duration
Free Float (FF)...Total of duration / period of the activity can be delayed without affect start time for the next activity.
Activities not on the critical oath can be delayed without affecting the start time of succeeding tasks.
The amount o time that the activity can slip without affecting its successors.
The amount of time by which an activity can exceed its early finish date without affecting the early start date of any of its successors.
Free float = ES – EF or EF – ES ‐ Duration
Total Float vs Free Float C ‐Free Float for D
4 days ‐Total Float for D
‐Free Float ‐Total Float for CB for B D
2 days 2 days 3 days 3 days
A F
2 days 3 days
E
10 days
FF and TF with all activites in the Early Start Position
C ‐Free Float for C
4 days 3 days
‐Total Float For B B D
5 Days 2 days 3 days
A F
2 days 3 days
E
10 days
FF and TF with all activites in the Late Start Position
Activity Time Calculations...Early Start (ES)
The earliest possible time an activity can begin based on network logic.
Late Start (LS)The latest possible time an activity can start without delaying project completionproject completion.
Early Finish (EF)The earliest possible time an activity can finish based on network logic.EF = ES + Duration
Late Finish (LF)The latest possible time an activity can finish without delaying project completion.LF = LS + Duration
Network Computation ProcessForward 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 TimesHow 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)
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Stage 1 of a Sample AOA Network
Stage 2 of a Sample AOA Network
A Completed Sample AOA Network
A Completed Sample AOA Network Showing the Use of a Dummy Task
A Completed Sample AOA Network Showing the Use of a Dummy Task
A Sample Problem for Finding the Critical Path and Critical Time
Activity Predecesso Durationa -- 5 days b -- 4 c a 3d a 4 e a 6 f b, c 4 g d 5 h d, e 6 i f 6 j g, h 4
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Stage 1 of a Sample Network A Complete Network
The Critical Path and Time for Sample Project
An MSP Version of PERT/CPM Network
A Modified Version of MSP Network
ACTIVITY – ON – NODE ACTIVITY ON NODE (AON)
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Activity‐On‐Node (AON)...
A network scheduling method, similar to AOA, which allows overlapping activities.
Allow interrelationships to be represented in FINISH – START, START – FINISH, START –START, and FINISH – FINISH, making this method more representative of the real life construction process
Activity‐On‐Node (AON)...
Use a technique of Activity On Node (AON).
Activities represented by boxers or nodes.
Precedence consists of two parts:RelationshipsLag value or constraint
Activity A Activity B
Activity‐On‐Node (AON)...
Activity box = show the activities involved, activity number and duration.
Start symbol = show the starting activity in a Start symbol = show the starting activity in a project network.
End symbol = show the end activity on a project network.
ES
Duration
Activity
LFLS
EF
Activity–On–Node (AON)...
Activity‐on‐Node Fundamentals
FIGURE 6.2
Activity‐on‐Node Fundamentals
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Exercise ‐ Network Information Koll Business Center—Partial Network
Koll Business Center—Complete NetworkActivity Notation...
ES 12E9 EF
Activity Identifier
LS 17314 LF
Duration
The ES, EF, LS and LF are calculated by a FORWARD PASS and BACKWARD PASS.
Calendar Conventions...
To illustrate, assume that activities begin on the morning of the scheduled start date end and end in the evening of the scheduled finish date, and that an event or milestone occurs on the
f h d l d f h devening of the day its last predecessor finished.
17 18 20 21 22 23 2419
30
H24
23
17F 23G18
624 29
Calendar Conventions...
Four (4) factors to be considered:Activities involvedActivities durationResources‘Logic’ relationship‘Logic’ relationship
‘Logic’ conventionsSTART–to‐START (SS)FINISH–to‐FINISH (FF)START–to‐FINISH (SF)FINISH–to‐START (FS)
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‘Logic’ Conventions...
FINISH–to‐START (FS)Latter activity cannot begin until preceding activity is complete.
A B
FS ‐ S
Finish – to – Start lag
Example of Laddering Using F‐S Relationship
‘Logic’ Conventions...
START–to‐START (SS)Latter activity cannot begin until preceding has started
A B
Start –To – Start lag
SS ‐ S
‘Logic’ Conventions...
FINISH–to‐FINISH (FF)Latter activity cannot be completed until preceding has completed.
A
B
FF‐S
Finish‐to‐Finish lag
‘Logic’ Conventions...
START–to‐FINISH (SF)Latter activity cannot finish until preceding activity has started
A B
SF‐S
Start –to – Finish lag
Use of Lags
Finish‐to‐Finish Relationship
Start‐to‐Finish Relationship
CombinationRelationship
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Network Using Lags A Sample Set of Project Activities and Precedence
Task Predecessor a -- b -- c a d b e b f c, d g e
Stage 1 of a Sample AON Network
Stage 2 of a Sample AON Network
Use of Lags
Finish‐to‐Start Relationship
Start‐to‐Start Relationship
Use of Lags
Finish‐to‐Finish Relationship
Start‐to‐Finish Relationship
CombinationRelationship
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A Completed Sample AON Network
An MSP Version of a Sample Problem Network
A Pert/CPM Network for the Day Care Project
An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00
A Progress Report on a Day Care Project Showing Actual Progress Versus Baseline
Activity‐on‐Node Network
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Activity‐on‐Node Network Forward PassForward Pass ComputationAdd 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.
Activity‐on‐Node Network Backward PassBackward 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.
Determining Free Slack / FloatFree 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.
SensitivityThe 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.
Activity‐on‐Node Network with Slack
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Free Slack Example Using Microsoft Project
Using Microsoft Project to create a schedule is easy:Step 1: Enter the tasks:Enter the task nameEnter the task nameEnter the start timeEnter either the duration or expected end timeEnter dependencies, if any
Step 1...Enter the Tasks Using Microsoft Project
MS Project generates the Gantt chart for you automatically, on the right:
Using Microsoft Project
MS Project allows you to change dates whenever you wantThus, you can push back the start date if the project is delayedThe entire schedule is shifted over in responseThe entire schedule is shifted over in responseYou can add/change dependencies as you wish as wellNext to tasks is a space for resourcesHere is one place where you could put in persona namese.g. Java developer I
Using Microsoft Project