Week 7-8 Scheduling PDF

Network Scheduling 1  Steps in the Network Model 1. Define activities 2. Determine physical constrains 3. Establish activity relationships 4. Draw a network diagram 5. Determine productivities and assign durations 6. Assign resources and costs 7. C...

Network Scheduling 1  Steps in the Network Model 1. Define activities 2. Determine physical constrains 3. Establish activity relationships 4. Draw a network diagram 5. Determine productivities and assign durations 6. Assign resources and costs 7. Calculate early and late start & finish times 8. Compute float values and identify critical path 2  Arrow Diagram Diagram is made out of arrows and nodes, plus letters and numbers for labeling and calculation purposes. The arrows represent the actual activity. The nodes represent the point in time (event) when activities start and finish. Also called I-J Diagram, Arrow Diagram or simply CPM. Formats Arrow Diagram Example Act. Description Duratio Depends n on A Construct wall footing 10 days - B Construct column 15 days - footing C Erect masonry walls 15 days A D Construct columns 15 days B E Erect roof girders 5 days C,D  Arrow Diagram Conventions Convention Correctly applied: Nonconsecutive nodes and arrow numbers Incorrectly applied:  Arrow Diagram Conventions Convention Correctly applied: J-Node number greater than I- node number Incorrectly applied:  Arrow Diagram Conventions Convention Correctly applied: Arrows point right, up or down, but not left Incorrectly applied:  Arrow Diagram Conventions Convention Correctly applied: Activity number greater than number of any precedent activity Incorrectly applied:  Arrow Diagram Conventions Convention Correctly applied: Activities have unique pair of node numbers Incorrectly applied:  Dummy activities Dummy activities or “pseudo-activities” have zero duration and do not consume resources. Used to: Split activities to assure unique activity designation. Show proper logic (as logical constraints) Change activity predecessors. Create single start or ending activities. Dummy activity used as activity splitter Dummy activity as a logical constraint Dummy activities used as single starting and ending activities Starting Dummy activities used as single starting and ending activities Ending CRITICAL PATH METHOD (Activity-On-Arrow) D = Activity Duration “Act.” = Activity Description I-J = Events/Nodes ES = Early Start EF = Early Finish LS = Late Start LF = Late Finish  Activity Times Early Start. The point in time that all activities preceding have been completed. Early Finish. The earliest all work started with an Early Start can be completed. It equals Early Start plus Duration. Late Finish. The point in time that all work involved in the activity must be completed in order to avoid delaying following activities. Late Start. The point in time by which activity must be started in order to avoid delay to following activities. Late Start equals Late Finish minus Duration.  CPM - Definitions D = Duration estimate of the mean duration time for an activity ES = Early Start earliest possible start time for an activity (from forward pass) EF = Early Finish earliest possible finish time for an activity (from forward pass) LS = Late Start latest possible start time to support project finish date (from backward pass) LF = Late Finish latest possible finish time to support project finish date (from backward pass) 18  Critical Path The critical path of a network is the path representing a combination of certain activities, any one of which if delayed, will cause a delay to the project. It is the longest path, in time, through the network. Project Duration. The aggregate combination of all durations of the activities along the critical path of the project. Critical Activities. Activities along the critical path. These activities have no Total Float.  Precedence Diagram (PDM) - AoN Activity Types Excavate Place Rebar Place Concrete Predecessors: Successors: Activities that must Activities that must precede an activity succeed an activity 20  Precedence Diagram (PDM) - AoN Activity-On-Node activity event 21  Precedence Diagram (PDM) - AoN Box/Rectangle: Represents Activity Lines with Arrows connect boxes: Represent logical relationships: Predecessor (Immediate Preceding Activity - IPA): controls the start or finish of another activity Successor: depends on the start or finish of another activity 22  Precedence Diagram (PDM) - AoN The Earliest Early The Earliest Start Time Activity Finish Time for the Times for the Activity Activity The The Activity Activity Descriptio Duration n The latest The latest Start Time Late Finish Time for the Activity for the Activity Times Activity  Forward Pass Develops the Early Dates: Project begins at end of day 0 (equivalent to beginning of day 1): E1 = 0 ESj = MAX [EFi] (always use latest of preceding early dates) EFi = ESi + Duration 24  Forward Pass Example ES Activity ID EF Activity LS Duration LF Usually start your calculations from the 0 0 0EF end of day 0. Start 0 ES = 0 (Project Start) Duration = 0 EF = ES + Duration = 0+0=0 25  Forward Pass Example 0ES 30 EF 15 ESj = Max [EFi] = 0 Duration = 15 Order & Deliver Piles EF = ES + Duration = 0 0 0 0 + 15 = 15 15 Start 0 ES 40 EF Move in 3 26  Forward Pass Example 0 30 15 ESj = Max [EFi] = 0 Duration = 15 Order & Deliver Piles EF = ES + Duration = 0 0 0 0 + 15 = 15 15 Start 0 ESj = Max [EFi] = 0 ES 0 40 EF 3 Duration = 3 Move in EF = ES + Duration = 0+3=3 3 27  Forward Pass Example ES 3 80 EF 6 ESj = Max [EFi] = 3 Prefabricate abutment Duration = 3 forms EF = ES + Duration = 0 40 3 3+3=6 3 Move in 3 ESj = Max [EFi] = 3 ES 3 90 EF 6 Duration = 3 Excavate Abutment EF = ES + Duration = 3+3=6 3 28  Forward Pass Example 5 70 12 ESj = Latest [EFi] = 18 Fabricate & Deliver Duration = 2 Footing Rebar EF = ES + Duration = 18 ES 40 20 EF 7 18 + 2 = 20 Forms & Rebar footing 2 15 110 18 Drive Piles abutment 3 29  Backward Pass Develops the Late Dates: LFlast : Option 1a: LFlast = Contract Date (the contractual project completion date). Option 1b: LFlast = EFlast (zero float option: the project finishes on the early finish of the last activity – forward pass) LFi = MIN [LSj] LSj = LFj - Duration 30  Backward Pass – Example 55 360 58 LFj = Min [LSi] = 60 Duration = 3 Guardrails LS = LF - Duration = 60 390 63 60 – 3 = 57 57 3 60 Cleanup LFj = Min [LSi] = 60 55 370 60 Duration = 5 LS LF 60 3 63 Paint LS = LF - Duration = 60 – 5 = 55 55 5 60 31  Backward Pass – Example LFj = Min [LSi] = 55 Duration = 3 55 360 58 LS = LF - Duration = 55 – 3 = 52 52 360 55 Guardrails 57 3 60 Strip Deck 52 LS 3 55 LF 55 370 60 Paint 55 5 60 32 PRECEDENCE TO ARROW PRECEDENCE TO ARROW PRECEDENCE TO ARROW PRECEDENCE TO ARROW PRECEDENCE TO ARROW PRECEDENCE TO ARROW  Example #1 Activity Precedes Duration(D ays) J … 14 I J 10 H J 8 G J 6 F I 5 E H, I 2 D G 12 C F, G 8 B E, F 15 A B, C, D 10 Example #1: PRECEDENCE (AON)  Example #1: PRECEDENCE “Forward Pass” (AON) ES = The EF = ES + D Biggest EF Number = Max {n1,n2, …,nn} n1 n2 nn The First Activity ES = 0  Example #1: PRECEDENCE “Forward Pass (AON) Calculation” 10 25 25 27 27 35 B E H 15 2 8 0 10 10 18 25 30 30 40 40 54 A C F I J 10 8 5 10 14 10 22 22 28 D G 12 6  Example #1: PRECEDENCE “Backward Pass”(AON) The last LF = EF for the last activity unless stated otherwise n1 n2 nn LF = The LS = LF - D Smallest LS Number = Min {n1,n2,…,nn}  Example #1: PRECEDENCE “Backward Pass(AON) Calculation” 10 25 25 27 27 35 B E H 10 15 25 28 2 30 32 8 40 0 10 10 18 25 30 30 40 40 54 A C F I J 0 10 10 17 8 25 25 5 30 30 10 40 40 14 54 10 22 22 28 D G 22 12 34 34 6 40  Float (Slack) Total Float (TF): the time an activity may be delayed without delaying the END of a PROJECT TF = LS - ES = LF – EF Free Float (FF): the time an activity may be delayed without delaying any other ACTIVITY FF = ESj - EFi 45  TOTAL FLOAT It is the total amount of time that the activity can be delayed without causing any delay in the project duration TF = LS – ES = LF - EF  FREE FLOAT It is the total amount of time that an activity can be delayed without causing any delay in the early start of the following activities. FF(of A) = ES (of activity B) – EF (of activity A)  Total Float Example Total Float TF = LF – EF = LS – ES 55 360 58 TF = 60-58 = 2 Guardrails TF = 57-55 = 2 57 3 60 WHAT DOES THIS MEAN? 55 370 60 TF = LF – EF = LS – ES TF = 60-60 = 0 Paint TF = 55-55 = 0 55 5 60 48  FREE FLOAT FF = Min {ES (of B,C, or D) – EF (of A)} FF= Min {( 54-43= 9), (45-43= 2), (49- 43= 6)} FF= 2  Free Float Example Free Float 10 260 35 43 260 45 Fabricate & Deliver Girders Set Girders 18 LS 25 43 LF 43 2 45 FF = ESj - EFi FF = 43- 35 = 8 50  EXAMPLE #1: PRECEDENCE (AON) Critical Path 0 0 3 0 5 5 10 25 25 27 27 35 B E H 10 15 25 28 2 30 32 8 40 0 0 7 4 0 0 0 0 0 0 0 10 10 18 25 30 30 40 40 54 A C F I J 0 10 10 17 8 25 25 15 30 30 10 40 40 14 54 12 0 12 12 10 22 22 28 D G 22 12 34 34 6 40  EXAMPLE #2 Duration(Day Activity Depends on s) A … 10 B A 15 C A 8 D A 12 E D 2 F D 5 G D 6 H B,C,E 8 I F,G 10 J B 14 K H,I 4 L H,J 15 M I 12 N K,L,M 10 EXAMPLE #2: PRECEDENCE (AON) EXAMPLE #2: PRECEDENCE (AON) B J L 15 14 15 H 8 A C E K N 10 8 2 4 10 D F I M 12 5 10 12 G 6  EXAMPLE #2: PRECEDENCE (AON) “Forward Pass 10 25 Calculation” 25 39 39 54 B J L 15 14 15 25 33 H 0 10 10 18 22 24 38 42 54 64 8 A C E K N 10 8 2 4 10 10 22 22 27 28 38 38 50 D F I M 12 5 10 12 22 28 G 6  EXAMPLE #2: PRECEDENCE (AON) “Backward Pass 10 25 Calculation” 25 39 39 54 B J L 10 15 25 25 14 39 39 15 54 25 33 H 0 10 10 18 22 24 38 42 54 64 31 8 39 A C E K N 0 10 10 23 8 31 29 2 31 50 4 54 54 10 64 10 22 22 27 28 38 38 50 D F I M 14 12 26 27 5 32 32 10 42 42 12 54 22 28 G 26 6 32  EXAMPLE #2: PRECEDENCE (AON) “Float Calculation” 0 0 0 0 0 0 10 25 25 39 39 54 B J L 10 15 25 25 14 39 39 15 54 6 5 25 33 0 0 13 7 7 1 12 12 0 0 H 0 10 10 18 22 24 38 42 54 64 31 8 39 A C E K N 0 10 10 23 8 31 29 2 31 50 4 54 54 10 64 4 0 5 1 4 0 4 4 22 27 28 38 38 50 10 22 F I M 27 5 32 32 10 42 42 12 54 D 14 12 26 4 0 22 28 G 26 6 32  SPECIAL RELATIONSHIPS Special Relationships in AON Start to Start (SS) Finish to Start (FS) Finish to Finish (FF) Start to Finish (SF) Could be represented by a lag or lead value (for example FS=0, SS=10, FF=1) ACTIVITY LEAD AND LAG Lag is the time that an activity follows or is delayed from the start or finish of its predecessor. Lead is the time that an activity precedes the start or finish of its successor. Lead can be considered the opposite of lag.  Finish to Start (FS) A B A must be completed before B Place Pour starts Rebar Concret Start B depends on e Finish of A 2 Days B may start 2 days A B after A finishes or Pour Strip B can not start Concret Footing e sooner than 2 days after A is finished Start to Start (SS) A C The start of B depends on the start of A or B B can not start until A has started Pouring concrete Place Rebar can not start until rebar has been Pour placed or Concrete Rebar must be placed before concrete can be  Start to Start (SS) SS is useful when start of one activity must lag the start of another House Framing Roughing-in cannot start until house framing has 3 Days been underway for at Rough-in least 3 days, or Plumbing At least 3 days of house framing work must be completed before roughing-in of plumbing can start  Finish to Finish (FF) Erection of masonry wall can not finish until one day after Erect Masonry Wall the conduits inside the wall have been 1 installed or Days At least 1 day must Install Conduit in Wall pass after the wall conduits are installed before erection of the masonry wall can  Finish to Start 35 43 47 59 Activity FS4 Activity A B 0/5 0/5 40 8 48 1252 64 ESB = EFA + Lag Value AB = 43 + 4 = 47 LFA = LSB - Lag Value AB = 52 - 4 = 48 TF = LF - EF = 64 - 59 or 48 - 43 = 5 FFA = ESB - Lag Value AB - EFA = 47 - 4 - 43 =0  Start to Start (SS) SS4 35 43 39 51 Activity Activity A B 0/13 0/13 48 8 56 1252 64 ESB = ESA + Lag Value AB = 35 + 4 = 39 LSA = LSB - Lag Value AB = 52 - 4 = 48 TF = LF - EF = 64 - 51 or 56 - 43 = 13 FFA = ESB - Lag Value AB - ESA = 39 - 4 - 35 =0  Finish to Finish (FF) 35 43 FF4 35 47 Activity Activity A B 0/17 0/17 52 8 60 1252 64 EFB = EFA + Lag Value AB = 43 + 4 = 47 LFA = LFB - Lag Value AB = 64 - 4 = 60 TF = LF - EF = 64 - 47 or 60 - 43 = 17 FFA = EFB - Lag Value AB - EFA = 47 - 4 - 43 =0  Start to Finish (SF) SF4 35 43 27 39 Activity Activity A B 0/25 0/25 60 8 68 1252 64 EFB = ESA + Lag Value AB = 35 + 4 = 39 LSA = LFB - Lag Value AB = 64 - 4 = 60 TF = LF - EF = 64 - 39 or 68 - 43 = 25 FFA = EFB - Lag Value AB - ESA = 39 - 4 - 35 =0 RESOURCE ALLOCATION AND LEVELING (SMOOTHING)  Importance of Allocating and Leveling Resources Resources need to be brought to the project in an organized and sustainable fashion. The shape of the resource curves should be positively sloping until they reach a peak, then they should be negatively sloping until that resource is removed from the project.  Importance of Allocating and Leveling Resources (Contd.) Worst case scenario is a resource curve with ups and downs throughout the project. This type of curve requires the same resource to be brought back onto the job, removed, and brought back later. This process is inefficient, expensive, and causes low morale among personnel.  Importance of Allocating and Leveling Resources (Contd.) To overcome this difficulties, either the logic of the project needs to be changed, or the start dates of those activities with float needs to be moved from the early start date to a date that maximizes the effective use of the impacted resource. Through this iterative process, the start and finish dates can be fine- tuned to develop a list of best start and finish dates.  Importance of Allocating and Leveling Resources (Contd.) Resource distribution is the primary tool that assists the Project Manager in determining the best time to start a specific activity. Activities on the critical path must begin and end on their required date. Activities with float can be shifted to help maximize the efficiency in the process. Resource Allocation and Leveling Resource Allocation deals with the allocation of resources that are limited. Resource Leveling deals with the efficient use of the required resources when the project duration cannot be altered. Example Activi Depends Durati Resourc ES EF LS LF TF ty On on es A … 2 0 2 0 2 0 0 B A 11 2 13 2 13 0 3 C A 3 2 5 8 11 6 4 D A 6 2 8 4 10 2 5 E C,D 4 8 12 11 15 3 6 F D 5 8 13 10 15 2 3 G E,F,H 3 15 18 15 18 0 1 H B,C 2 13 15 13 15 0 0 Early Start Histogram Early Start Histogram Late Start Histogram Late Start Histogram Resource Leveling FIXED PROJECT DURATION Resource Leveling FIXED PROJECT DURATION Resource Allocation LIMITED RESOURCES 20 +1 1 Resource Allocation LIMITED RESOURCES