1. Slide 8.1 4E1 Project Management Network Representation and Critical Path Analysis - Part 1

2. Slide 8.2 Key Concepts Networks Building networks, possible problems, scheduling objectives Critical path (analysis) Calculating the critical path, possible complications, handling constraints Project planning software Project Evaluation and Review Technique (PERT) Using simulation with PERT Project plan

3. Slide 8.3 Structure of Session Developing a project schedule to build a garage Starting point: specification and info on resources From this you will create: a WBS a task list an arrow diagram network of the project a precedence diagram of the project (homework) We will then examine the concept of critical path You will determine the critical path through the network We will look briefly at PERT We will conclude with a summary of the plan We will consider some of the software tools available to help

4. Slide 8.4 Specification 8m x 5m garage Concrete base Wooden trussed & sheeted roof Double wooden doors No windows Side fascia boards Side gutter system which drains to a soakaway trench containing a drainage pipe Doors and trusses will need to be made up All exterior woodwork and doors to be painted Brick walls; no plastering required Reinforced steel joist (RSJ) required for the door You have all materials including bricks, wood, sand, cement, aggregate, ready- made guttering and grills plus nails, screws etc. and a full set of tools (mixer, spades, saws, etc.) and labour Assume that drainage is into an open pond and needs no connection to a main system

5. Slide 8.5 Exercise 1 Draw up a work breakdown structure From this, draw up a task list

6. Slide 8.6 Building a Garage RSJ lintel Gutter Fascia Boards Drain (under ground) Sheeted roof Wooden Double Doors Truss Beams Brick walls Ridge beam Door Frame

7. Slide 8.7 Extract from Possible WBS 1.Base 2.Drainage 3.Walls 4.Doors 4.1 Make door frame 4.1.1Cut frame timbers 4.1.2Prime frame timbers 4.1.3Assemble frame 4.1.4Paint frame 4.2 Make doors 4.2.1Cut door timbers 4.2.2Prime door timbers 4.2.3Assemble doors 4.2.4Fit hinges 4.2.5Hang doors 4.2.6Paint doors 4.2.7Fit bolt 5.Roofing…

8. Slide 8.8 Some Network Concepts We will first consider information-on-arrow representation Information-on-arrow networks can be used to represent various problems e.g.: Shortest route Flow capacity Projects The following terminology is used in networks: Nodes Sources/starts Sinks/ends Links/arcs Directed and undirected Loops Circuits Paths

9. Slide 8.9 Example: Shortest Route Problem 1 11 6 5 4 3 2 12 7 8 9 10 20 70 30 40 20 120 50 80 100 60 70 110 90 70 80 90 30 110 20 80 50 90 40 70 100 Start Finish Find the shortest route through this network where numbers are distances in kilometers – have fun!

10. Slide 8.10 Project Networks Arrows/links represent a task or activity and its duration - hence “Activity on Arrow” (AOA) conventionally run left-right One and only one starting node completion node link between each pair of nodes (why?) At least one path from start to completion No circuits or loops May be multiple paths from start to completion special activities, and thus links, with zero duration Project networks have some specific characteristics:

11. Slide 8.11 No. Task IDTaskDurationPredecessorsResources 1STARTProject start0 2G0102Dig foundation81Labourer 3G0103Make, prime door frame61Skilled 4G0104Dig soakaway, trench21Labourer 5G0107Make doors11Skilled 6G0110Cut roof timbers11Skilled 7G0205Concrete foundations22Labourer 8G0305Position door frame13Skilled 9G0411Lay underground pipe14Labourer, Skilled 10G0508Build main brick walls107, 8Skilled, Labourer 11G0509Lay concrete base27Labourer 12G0713Prime the doors15Skilled 13G0810Fit RSJ lintel110Skilled, Labourer 14G0913Lay floor screed111Skilled 15G1012Fit roof timbers26, 13Skilled 16G1016Case lintel, parapets213Skilled, Labourer 17G1115Fill draining trench19Labourer 18G1214Fit fascia boards115Skilled 19G1216Fit roof sheets115Skilled 20G1317Hang doors110, 12, 14Skilled, Labourer 21G1417Fit gutters and pipes19, 18Skilled 22G1518Concrete over trench117Labourer 23G1618Seal the roof216, 19Skilled 24G1718Paint all woodwork320, 21Skilled 25FINISHFinish project022, 23, 24 Exercise 2: Draw This Network

12. Slide 8.12 Solution… A D B E C G F H I J M L N Dig foundation 8 Cut roof Timbers 1 Dig trench 2 Make& Prime door frame 6 Make doors 1 Position d/frame 1 Concrete fdns 2 Lay under- ground pipe 1 Build walls 10 Concrete base 2 Prime doors 1 Fit RSJ 1 Lay floor screed 1 P O Fit roof timbers 2 Case lintel and parapets 2 K Fill Trench 1 Fit fascia boards 1 Fit roof sheets 1 Hang Doors 1 R S Fit gutters and pipes 1 Concrete over trench 1 Seal Roof 2 Paint Wood 3 Q FINISHFINISH STARTSTART

13. Slide 8.13 Project Network Features Slack Typical task has earliest start and latest completion times Slack = LC - ES Critical path If all tasks on a path from start to completion have zero slack, the path is on the critical path Free float Activities that can start late or finish early have free float Activities on the critical path have no free float Interfering float An activity that can only be delayed in its float at the expense of some other activity’s float has an interfering float Other types of float exist Sub-critical activities Activities with a small free float are sub-critical activities

14. Slide 8.14 Critical Path Network Objectives May be > 1 objective e.g. To minimise: Total project time Total project cost Cost for a given time Time for a given cost Idle resources CPA methods used as: planning tools control tools Many software packages can calculate the path May be > 1 critical path

15. Slide 8.15 Critical Path Method (CPM) To find the critical path three steps are required Requires care and thought Easy to make a mistake 1.Forward pass Traverse network from start, calculating earliest possible completion time of each task. This will give you a total time for the project. 2.Backward pass Working backwards from end, calculate latest completion time needed to complete each activity’s preceding task. 3.Identify critical path Nodes where the forward earliest completion time equals the backward latest completion lie on the critical path. Also single pass method

16. Slide 8.16 Example 1: Simple Project Network What is the critical path through this network? 1 6 5 4 3 2 3 0 2 3 7 2 2 5 6 3 Finish Start 0 2 e.g. Task (4,6). Duration 5 days

17. Slide 8.17 1 6 5 4 3 2 3 0 2 3 7 2 2 5 6 3 0 0 3 6 19 6 2 13 2 Start Finish Step 1: Forward Pass

18. Slide 8.18 1 6 5 4 3 2 3 0 2 3 7 2 2 5 6 3 0 0 3 6 6 2 2 13 19 3 0 6 13 4 6 Start Finish Step 2: Backward Pass

19. Slide 8.19 1 6 5 4 3 2 3 0 2 3 7 2 2 5 6 3 Start 0 0 3 6 6 2 2 13 19 30 6 13 4 6 Start Finish Step 3: Critical Path

20. Slide 8.20 Exercise 3: Given the Following… 1 2 367 8 9 5 4 11 10 3 a b c 7 4 d 5 d1d1 d2d2 0 0 0 d3d3 2 1 m l k 3 j 4 3 e 2 f i 9 8 h 1 g Find the critical path through this network

21. Slide 8.21 Exercise 3: Forward Pass 1 2 367 8 9 5 4 11 10 3 4 0 0 0 2 1 3 4 3 2 9 8 1 0 3 8 16 20 23 24 5 7

22. Slide 8.22 1 2 367 8 9 5 4 11 10 3 4 0 0 0 2 1 3 4 3 2 9 8 1 0 3 8 16 20 23 24 23 20 16 8 14 13 3 0 24 5 7 Exercise 3: Backward Pass

23. Slide 8.23 Exercise 3: Critical Path 1 2 367 8 9 5 4 11 10 3 4 5 0 0 0 2 1 3 4 3 2 9 8 1 0 3 8 16 20 23 24 23 20 16 8 14 13 3 0 24 7

24. Slide 8.24 Exercise 4 Find the critical path for the garage project Ignore labour constraints and non-working days A D B E C G F H I J M L N Dig foundation 8 Cut roof Timbers 1 Dig trench 2 Make& Prime door frame 6 Make doors 1 Position d/frame 1 Concrete fdns 2 Lay under- ground pipe 1 Build walls 10 Concrete base 2 Prime doors 1 Fit RSJ 1 Lay floor screed 1 P O Fit roof timbers 2 Case lintel and parapets 2 K Fill Trench 1 Fit fascia boards 1 Fit roof sheets 1 Hang Doors 1 R S Fit gutters and pipes 1 Concrete over trench 1 Seal Roof 2 Paint Wood 3 Q FINISHFINISH STARTSTART 1 6 10 20 21 8 10 12 20 21 23 24 25 28 2 3 4 26 24 9 10 21 24 25 20 23 10 8 0 0 27 23 21 23 24 23