# CRITICAL-PATH ANALYSIS FOR NETWORK SCHEDULING

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1 CRITICAL-PATH ANALYSIS FOR NTWORK SCHULING From studying this section, you will be able to: - Perform CPM and PM analyses for AOA and AON networks; - Calculate the early / late times that an activity can start / finish; - etermine the total project duration, activity floats, and the path of critical activities; - Represent the schedule using ar charts (Gantt charts); - Use Microsoft Project Software to schedule projects; and - xperiment with a spreadsheet model for network analysis. Scheduling = Planning +. The schedule is very important for the contractor to know when and how much labor is needed; vendors to know when to deliver materials; and subcontractors to know when they can do their work. Critical-Path Method (CPM) for AOA Networks The CPM is a systematic scheduling method for AOA network. The CPM involves 4 main steps: - A forward pass to determine activities early-start times; - A backward pass to determine activities late-finish times; - Float calculations; and - Identifying critical activities. Forward Pass & ackward Pass The forward pass determines the early-start times of activities, while the backward pass determines the late-finish (LF) times. () 5 d A () C (4) 9 (5) (6) d 7 Float Calculations A C uration (d) Results of Forward & ackward Pass Calculations of Other s Total Float & Criticality Calculations (S) (LF) LS = LF - d F = S + d TF = LF- S - d Critical (Y/N) 47

2 i Name duration = d i S LF S a) is early d F=S+d TF b) is late LS=LF-d TF d LF Total time available for the activity = LF - S Total Float (TF) = Total Slack = LF F = LS S = LF S d Another type of float often used in network analysis is the Free Float, which can be calculated as: Free Float = s (of succeeding activity) F (of activity in question) The free float defines the amount of time that an activity can be delayed without taking float away from any other activity. With free float available for an activity, a project manager knows that the float can be used without changes the status of any non-critical activity to become critical. Identifying Critical Activities Critical activities are the ones having TF = 0. They form a continuous path of the critical activities that is the longest in the network (Critical Path). Precedence iagram Method (PM) for AON Networks Sequence Step () A () C (4) (5) (6) 48

3 Schedule Presentation A C d= S = 0 d= TF= S= d=4 TF= S= d=6 S= S=9 d=5 arly ar Chart A C d= LF= TF= d= TF= d=4 d=6 LF=9 LF=9 LF=9 d=5 LF=4 Late ar Chart A C Labor amount / day Using ar Chart to Accumulate Resources Total labors 6 4 Profile of the labor resource demand

4 xample Solved xample Perform PM calculations for the small AON network shown here. Pay special attention to the different relationships and the lag times shown on them. 0 A () 0 SS= 4 or or (4-+) 0+= 5 () C (4) 7 9 (6) 4 0 -=0 5, 7 or (9+-5) FF= 7 (5) 7 Criticisms to Network Techniques - Assume all required resources are available - Can result in large resource fluctuations - Ignore project deadline - Ignore project costs - Use deterministic durations - o not consider realistic productivity factors 50

5 ack to Our Case Study Project We need to do the following: - Calculate S, LF, & TF for all activities. Identify critical ones. raw a Late ar Chart for the project. - What is the effect of delaying activity H by two days on project duration? Solution: uration S LF TF=LF-S-d Critical A 4 6 C 8 4 F 0 G 6 H 8 I 6 J 6 K 0 ACTIVITY A C F G H I J K 5

6 Critical Path Model on a Spreadsheet elay S F LS LF elay A S LS A LS F LF A elay C S C LS 4 F C LF elay S LS 5 F LF elay S F LS 6 LF The spreadsheet file ( CPM.xls ) represents a template for CPM analysis with one row for each activity. The data for an activity are represented in columns. The shaded cells include formulas while the white cells are user inputs pertaining to the activity I, Name, uration, Cost, Is of predecessors, Is of successors, and a elay value. The total project duration ( days) is also included in a separate cell at the top of the spreadsheet. Any change in the duration of any activity or the logical relationships automatically changes the project duration along with all the CPM data regarding the activities early and late times as well as the total floats, which identify critical and non-critical activities. xperiment with different option and see their impact on the schedule. 5

7 SCHULING RPTITIV & LINAR PROJCTS Repetitive Projects: Highways, Multiple Houses, Multiple ridge Maintenance, etc. Characteristics: Multiple locations, complex, many resources Challenges: - Crew Work Continuity - Learning Phenomenon - Representing the large amount of data New Representation: How to esign the Schedule: - How many crews needed to meet deadline? - How to arrange the crew assignment to maintain work continuity? Crew Synchronization Calculations: Crews (C) = () x (R) 5

8 Calculating a esired Progress Rate (R): Units n... R Advanced Scheduling Options Options. Use of interruption to save project time Unit. ach activity has up to methods of construction (e.g., normal work, overtime, or subcontractor) with associated time, cost, and crew constraints. The model can then be used to select the proper combination of methods that meet the deadline, cost, and crew constraints;. Activities can have non-standard durations and costs at selected units; and Saved 4. Conditional methods of construction can be specified by the user. Unit No Work proceeds forward from station to 8 only. Work proceeds from station to 8 only, with interruption at station 5. A C Crew Crew Crew Crew No work at station 8. Crew Crew Crew Small quantity at Station 4. Low productivity at Station (Large duration). Top crew works from station 9 to 5, while bottom crew works from station to 4. 54

9 xample: For this small project, the work hours and the number of workers for each activity are shown. if you are to construct these tasks for 5 houses in days, calculate the number of crews that need in each activity. raw the schedule and show when each crew enters and leaves the site. Use asyplan & compare your solution. Step : CPM Calculation. Sanit. Main 48 hrs, W. Footing 64 hrs, W A. xcavation 48 hrs, W C. Footing 64 hrs, W. Wall 7 hrs, W F. Wall 7 hrs, W Step : LO Calculations eadline T L = ; T = ; n = 5 uration () Total Float (TF) esired Rate (R) (n-) / (T L -T +TF) Min. Crews (C) = x R Actual Crews (C a ) Actual Rate (R a ) = C a / A C F Step : raw the Schedule raw the critical path

10 Assume: - Same no. of Crews - A in unit has double the duration - Unit 4 does not need excavation ack to the Case Study Project onsider that the project involves 5 typical units. The owner wants the contractor to finish all the work in 50 days. Compare manual solution to that of asyplan. A(4) (6) C() (8) (4) F(0) G(6) H(8) I(6) J(6) K(0) Step : Step : CPM Calculations LO Calculations uration () Total Float (TF) esired Rate (R) = (n-) / (T L -T +TF) Required Crews (C) = x R Actual Crews (C a ) Actual Rate (R a ) = C a / A * C F *G H I J *K T L = deadline duration = 50 days; T = CPM duration of a single unit; * = Critical activity 56

11 Step : raw the Schedule The Critical Path -G-K 8 C J K Path C-J-K Path A---I 6 44 F H I Path -F-H-I 57

12 Highway xample A three-kilometer highway stretch is divided to ten sections for planning purposes. ach section is 00 meters. The cross section is shown below along with activities details..8 m 0 m 0.9 m.5 m Total excavation thickness: Middle = 500mm; and Shoulders = 00 mm. Activities estimates are as follows:. xcavation. Sub-base. ase 4. inder 5. Asphalt 6. Curbs 7. Lighting 8. Sidewalks stimate stimate stimate Cost (\$),000 7,800 7,000 0,000 4,400,00 9,45 0,950 (days) 0. Cost (\$) 0,000 80,000 8,000 5,000 (days) 8 Cost (\$) 00,000 (days) 5 The logical relationships are shown. Also, for all activities, seasonal productivity factors are: Winter = 0.65; Spring =.0; and Fall = Requirements: - Use the Repetitive Schedule feature of asyplan to develop an optimum schedule. - eadline = 0 days and the project starts June, How will your plan differ if you start the whole project on Feb., 006? - How will your plan differ if you have a maximum of crews for each activity? - How will your plan differ if you start the whole project from one side as opposed to employing half the crews from each side? 58

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