CHAPTER 9: PROJECT MANAGEMENT The aim is to coordinate and plan a single job consisting lots of tasks between which precedence relationships exist Project planning Most popular planning tools are utilized in project management GANTT chart CPM (critical path method) PERT (program evaluation and review technique) 2 1
Project planning network The project consists of well-defined activities or tasks The activities have precedence relationships and must be performed in the proper order 3 Network drawing characteristics A circle represents a node. An arrow represents an activity. A dashed arrow represents a dummy activity. Arrows, or activities leaving a node, cannot be started until all activities incoming the node have been completed The completion of all activities incoming to a node is considered an event The length of an arrow has no significance A dummy activities are used to represent precedence relationshiphs 4 2
Example 9.1 (project of installing a precision rain gauge/wind sensor station) 5 Network drawing of example 9.1 6 3
Critical Path Method CPM offers a systematic procedure for selecting the critical path through the network The amount of slack or free time on noncritical paths may be determined Knowing the slack on noncritical paths may permit us to trade off manpower and equipment resources from noncritical activities in order to shorten the critical path 7 CPM forward and backward pass Notation t activity duration TE earliest event occurence time TL latest allowable event occurence time ES earliest activity start time EF earliest activity finish time LS latest allowable activity start time LF latest allowable activity finish time S total activity slack 8 4
Forward pass The forward pass provide the following information: The earliest event time (TE) The earliest activity start time (ES) The earliest activity finish time (EF) 9 Forward pass calculations The forward pass calculations start with the first activity (or activities) TE 0 0 (initial event occurence time is 0) Each activity begins as soon as its predecessor event (node) occurs, that is TE ES, thus EF ES + t TE +t The earliest event (node) occurence time is the largest of the earliest finish times of the incoming acivities, TE max{ef 1,EF 2,...,EF n } 10 5
Backward pass The backward pass provide the following information: The latest allowable event time (TL) The latest allowable activity start time (LS) The latest allowable activity finish time (LF) 11 Backward pass calculations The backward pass calculations start with the last node The latest allowable event time of the terminal (last) node is set to the earliest event time, TE TL The latest allowable finish time for an activity is its successor event s latest allowable occurence time, LF TL, thus LS LF t TL t The latest allowable time for an event is the smallest of the latest allowable start times of the leaving activities, TL min{ls 1,LS 2,...,LS n } 12 6
Example 9.2 a)determine the critical path b)what is the total slack time of the activity D? 13 Solution (forward pass) 14 7
Solution (backward pass) Critical path is defined as the sequence of the activities having no slack time (ES LS and EF LF) and TE TL for each node Critical path is as follows: Activities C and G or Nodes 1, 4 and 7 15 Solution (slack time) Total activity slack time Latest finish Earliest finish S D LF EF 35 26 9 days Delaying the start of activity D up to 9 days does not change the completion of the project 16 8
Program Evaluation and Review Technique PERT utilizes a project network, a critical path and total slack time PERT requires three estimated activity times: Optimistic time (a minimum time) Most likely time (an average time) Pessimistic time (a maximum time) PERT is used in managing projects involving uncertainty in the durations 17 Notation and formulations t o optimistic time t m most likely time t p pessimistic time to + 4tm + t p te, t e expected time 6 t p to St, S 6 t standard deviation of t V t 2 t p to 6, V t variance of t 18 9
Example for time distribution t o 7 days t m 9 days t p 13 days t e t o + 4t 6 m + t p V t 7 + 4(9) + 13 9.33 6 t p t 6 o 2 2 13 7 6 1 19 Parameters for a selected path T V e t e all activities along the path T V t all activities along the path, T e expected time of the path, V T total variation of the path 20 10
Standard normal distribution z x µ σ µ expected value of the distribution σ standard deviation 21 Example 9.3 Example 9.2 is copied for precedence relationships between tasks Tasks durations are presented in the form of PERT Your objective is to find out the probability of accomplishing the project within 47 days 22 11
Task durations 23 Critical path 24 12
Parameters of critical path T e t e C, G V T V t C, G 33+ 10 43 16.000 + 2.778 18.778 S T 18.778 4.333 S T standard deviation along the path 25 Probability of T e 47 x µ z σ x Te S T 47 43 0.923 4.333 F(z) F(0.923) 0.8212 (from table) 26 13