Scheduling Scheduling : is the process of converting a project action plan into an operating time table. Why scheduling ? To answer the following questions: If each activity goes according to plan , then when will the project be completed? Which tasks are most critical to ensure the timely completion of the project? Which tasks can be delayed , if necessary , without delaying project completion and by how much? More specifically , at what times should each activity begin and end? At any given time during the project, how much money should have been spent? Is it worthwhile to incur extra costs to accelerate some of the activities? If so, then which ones?

Network Techniques PERT CPM PERT/CPM is based on a diagram that represents the entire project as a network of arrows and nodes. Two most popular approaches are : AOA : activity on arrow ( PERT ) AON : activity on node ( CPM )

Project Representation A network is a form of project representation schemes that use arrows and nodes to represent activities and their relationships. A 3 days 1 5

Rules for constructing a network Arrow represents the activity Circles represents time event ( start, finish) Any activity can be represented by one arrow only All activities having no predecessor should start at the same “start node” of the network. All activities having no successors should finish in one “finish node” in the network. Two nodes can only represent one activity

Notes for constructing a network

Forward Path Calculation Early Start ( ES ) Early Finish ( EF ) The earliest possible start time of an activity leaving a node equals the maximum of the early finish time of all activities entering that node EF = ES + duration

Backward Path Calculation Late Finish ( LF ) Late Start ( LS ) The latest possible finish time of an activity entering a node equals the minimum of the late start time of all activities leaving that node LS = LF - duration

4 questions must be answered to begin modeling process: What are the major project activities? What are the sequencing requirements or constraints for these activities? Which activities can be conducted simultaneously? What are the estimated time requirements for each activity?

Estimating the duration of project activities The length of each activity should be approximately in the range 0.5% to 2% of the length of the project.( 1 year -> between a day and week) If the number of activities is very large ( above 250 ) then the project should be divided into subprojects.

Two approaches are used for estimating the length of an activity Deterministic approach Past data If not exist : Modular approach Benchmark job technique approach Parametric technique ( cause-effect analysis , reg. analysis ) Stochastic approach Expected time estimation for an activity depends on: a: Optimistic time : which will be required if execution goes extremely well m:most likely time, which will be required if execution is normal b: pessimistic time , which will be required if everything goes badly. Et(A) = ( a + 4 m + b ) / 6

Difference Between PERT and CPM PERT used the arrow to represent an activity and CPM used the node. PERT used three estimates ( Opti, Pess. and Most likely ) of an activity’s required time, whereas CPM used just a single, best-time estimate.

The Top Level Project Tasks Brainstorm the Major Tasks C Establish Work Flow B G A D E F

Define Top Level Tasks Canoe Example Site Preparation Build Dock Build Building Finish and Ready for Business

Sequence Top Level Tasks Build Dock Site Preparation Finish Build Building

Sub-Tasks Detailed Tasks C G B A D E F Develop Work Sequence Detailed

Brainstorm Sub-Tasks Site Preparation Build Dock Build Building Finish Dock Site Install Pilings Foundation Order Canoes Frame Landscape Building Site Build Dock Roof Assemble Canoes Power Siding Open for Business Paint

Work Breakdown Structure Top Level Task 2nd Level Task 2nd Level Task 2nd Level Task 2nd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task 3rd Level Task Lower Level Tasks

Sequence Sub-Tasks Task Description Immediate Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canoes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M

Build Network Diagram (PERT Chart) (Activities on Arrows) 1 Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M

Build Network Diagram (PERT Chart) 1 3 Prep Dock Site Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M

Build Network Diagram (PERT Chart) 2 J Order Canoes A 1 3 Prep Dock Site Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M

Build Network Diagram (PERT Chart) 2 J Order Canoes A 1 3 Prep Dock Site B Task Predecessor Prepare Hut Site A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M 4 D Hut Foundation 6

Build Network Diagram (PERT Chart) 2 J Order Canoes A C E 1 3 5 9 Prep Dock Site Install Pilings Build Dock B Task Predecessor Prepare Hut Site A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M 4 D Hut Foundation 6

Build Network Diagram (PERT Chart) 2 J Order Canoes A C E 1 3 5 9 Prep Dock Site Install Pilings Build Dock B Task Predecessor Prepare Hut Site A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M G Power To Hut 4 D Hut Foundation 6

Build Network Diagram (PERT Chart) 2 L J Order Canoes Assemble Canoes A C E 1 3 5 9 Prep Dock Site Install Pilings Build Dock B Task Predecessor Prepare Hut Site A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M G Power To Hut 4 D Hut Foundation 6

Build Network Diagram (PERT Chart) 2 L J Order Canoes Assemble Canoes A C E 1 3 5 9 Prep Dock Site Install Pilings Build Dock B Task Predecessor Prepare Hut Site A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M G Power To Hut Roof 4 I D Hut Foundation F 6 7 Frame Hut

Build Network Diagram (PERT Chart) Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M Build Network Diagram (PERT Chart) 2 L J Order Canoes Assemble Canoes A C E 1 3 5 9 Prep Dock Site Install Pilings Build Dock B Prepare Hut Site G Power To Hut Roof Paint Hut K 4 I D Hut Foundation F H 6 7 8 Frame Hut Side Hut

Build Network Diagram (PERT Chart) Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M Build Network Diagram (PERT Chart) 2 L J Order Canoes Assemble Canoes A C E M N 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B Prepare Hut Site G Power To Hut Roof Paint Hut K 4 I D Hut Foundation F H 6 7 8 Frame Hut Side Hut

Build Network Diagram (PERT Chart) Canoe Example Add Times Task Description Time A Prepare Dock Site 3 d B Prepare Hut Site 4 d C Install Dock Pilings 6 d D Foundation for Hut 3 d E Build Dock 4 d F Frame Hut 3 d G Power to Hut 2 d H Side the Hut 2 d I Roof the Hut 3 d J Order Canoes 2 d K Paint Hut 4 d L Assemble Canoes 10 d M Finish Landscaping 4 d NOpen for Business 2 d 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Build Network Diagram (PERT Chart) Task Predecessor A Prepare Dock Site - B Prepare Hut Site - C Install Dock Pilings A D Foundation for Hut B E Build Dock C F Frame Hut D G Power to Hut D H Side the Hut F I Roof the Hut F J Order Canoes and Receive Canes - K Paint Hut H L Assemble Canoes J M Finish Landscaping L,I,K,E,G N Open for Business M Build Network Diagram (PERT Chart) 2 L J Order Canoes Assemble Canoes A C E M N 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B Prepare Hut Site G Power To Hut Roof Paint Hut K 4 I D Hut Foundation F H 6 7 8 Frame Hut Side Hut

Build Network Diagram (PERT Chart) Canoe Example Add Times Task Description Time A Prepare Dock Site 3 d B Prepare Hut Site 4 d C Install Dock Pilings 6 d D Foundation for Hut 3 d E Build Dock 4 d F Frame Hut 3 d G Power to Hut 2 d H Side the Hut 2 d I Roof the Hut 3 d J Order Canoes 2 d K Paint Hut 4 d L Assemble Canoes 10 d M Finish Landscaping 4 d NOpen for Business 2 d 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Determining Project Length Option 1: Sum all the task durations: A Prepare Dock Site - 3 d B Prepare Hut Site - 4 d C Install Dock Pilings A 6 d D Foundation for Hut B 3 d E Build Dock C 4 d F Frame Hut D 3 d G Power to Hut D 2 d H Side the Hut F 2 d I Roof the Hut F 3 d J Order Canoes and Receive Canoes - 2 d K Paint Hut H 4 d L Assemble Canoes J 10 d M Finish Landscaping L,I,K,E,G 4 d N Open for Business M 2 d Sum = 52 days Anything wrong with this approach?

Determining Project Length Option 2: Determine duration of each network path

Network Diagram Project Paths A-C-E-M-N = 19 days Network Diagram Project Paths 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Network Diagram Project Paths A-C-E-M-N = 19 days B-D-F-H-K-M-N = 22 days Network Diagram Project Paths 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Network Diagram Project Paths A-C-E-M-N = 19 days B-D-F-H-K-M-N = 22 days B-D-F-I-M-N = 18 days Network Diagram Project Paths 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Network Diagram Project Paths A-C-E-M-N = 19 days B-D-F-H-K-M-N = 22 days B-D-F-J-M-N = 18 days B-D-G-M-N = 15 days Network Diagram Project Paths 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Network Diagram Project Paths A-C-E-M-N = 19 days B-D-F-H-K-M-N = 22 days B-D-F-J-M-N = 18 days B-D-G-M-N = 15 days J-L-M-N = 18 days Network Diagram Project Paths 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) J (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Critical Path The Critical Path is the Longest Path Through the Network.

Network Diagram Canoe Example Critical Path Paths: A-C-E-M-N = 19 days B-D-F-H-K-M-N = 22 days B-D-F-J-M-N = 18 days B-D-G-M-N = 15 days J-L-M-N = 18 days Network Diagram Canoe Example Critical Path 2 L (10) J (2) Order Canoes Assemble Canoes A (3) C (6) E (4) M (4) N (2) 1 3 5 9 10 11 Prep Dock Site Install Pilings Build Dock Finish Landscape Open for Business B (4) Prepare Hut Site G (2) Power To Hut Roof Paint Hut 4 K (4) I (2) D (3) Hut Foundation F (3) H (2) 6 7 8 Frame Hut Side Hut

Completed Task Timetable Task Description Immediate Predecessor Time ES LS EF LF A Prepare Dock Site - 3 d 0 3 3 6 B Prepare Hut Site - 4 d 0 0 4 4 C Install Dock Pilings A 6 d 3 6 9 12 D Foundation for Hut B 3 d 4 4 7 7 E Build Dock C 4 d 9 12 13 16 F Frame Hut D 3 d 7 7 10 10 G Power to Hut D 2 d 7 14 9 16 H Side the Hut F 2 d 10 10 12 12 I Roof the Hut F 3 d 10 13 13 16 J Order Canoes and Receive Canoes - 2 d 0 4 2 6 K Paint Hut H 4 d 12 12 16 16 L Assemble Canoes J 10 d 2 6 12 16 M Finish Landscaping L,I,K,E,G 4 d 16 16 20 20 N Open for Business M 2 d 20 20 22 22

Slack Time Total Slack = The length of time an activity can be delayed without affecting the project completion time. Total Slack = Late Start - Early Start Total Slack = Late Finish - Early Finish For Critical Activities Free Slack = The time a task can be delayed without delaying another task.

Slack Time Task Description Immediate Predecessor Time ES LS EF LF Slack A Prepare Dock Site - 3 d 0 3 3 6 3 B Prepare Hut Site - 4 d 0 0 4 4 0 C Install Dock Pilings A 6 d 3 6 9 12 3 D Foundation for Hut B 3 d 4 4 7 7 0 E Build Dock C 4 d 9 12 13 16 3 F Frame Hut D 3 d 7 7 10 10 0 G Power to Hut D 2 d 7 14 9 16 7 H Side the Hut F 2 d 10 10 12 12 0 I Roof the Hut F 3 d 10 13 13 16 3 J Order Canoes and Receive Canoes - 2 d 0 4 2 6 4 K Paint Hut H 4 d 12 12 16 16 0 L Assemble Canoes J 10 d 2 6 12 16 4 M Finish Landscaping L,I,K,E,G 4 d 16 16 20 20 0 N Open for Business M 2 d 20 20 22 22 0

Critical Path Tasks Critical Path = All tasks with slack = zero

Critical Path = B - D - F - H - K - M - N Critical Path Tasks Task Description Immediate Predecessor Time ES LS EF LF Slack A Prepare Dock Site - 3 d 0 3 3 6 3 B Prepare Hut Site - 4 d 0 0 4 4 0 *** C Install Dock Pilings A 6 d 3 6 9 12 3 D Foundation for Hut B 3 d 4 4 7 7 0 *** E Build Dock C 4 d 9 12 13 16 3 F Frame Hut D 3 d 7 7 10 10 0 *** G Power to Hut D 2 d 7 14 9 16 7 H Side the Hut F 2 d 10 10 12 12 0 *** I Roof the Hut F 3 d 10 13 13 16 3 J Order Canoes and Receive Canoes - 2 d 0 4 2 6 4 K Paint Hut H 4 d 12 12 16 16 0 *** L Assemble Canoes J 10 d 2 6 12 16 4 M Finish Landscaping L,I,K,E,G 4 d 16 16 20 20 0 *** N Open for Business M 2 d 20 20 22 22 0 *** Critical Path = B - D - F - H - K - M - N

CPM ( A-O-N) : Example CPM network for computer Design Project: Activity Designation Pred. Dura Design A - 21 Build prototype B 4 Evaluate equipment C 7 Test Prototype D 2 Write equipment report E C,D 5 Write methods report F 8 Write final report G E,F

C 7 F 8 A 21 G 2 B 4 E 5 D 2

Determine the Critical path Forward pass: ES : the earliest possible time the activity can begin. EF : the early start time the time needed to complete the activity. ( EF = ES + Dur ) Backwards pass