Project Management and scheduling Objectives of project scheduling

Project Management and scheduling • Objectives of project scheduling • Network analysis • Scheduling techniques

Objectives of project scheduling • Produce an optimal project schedule in terms of cost, time, or risk. • Usually, it is difficult to optimize three variables at the same time. Thus, • setting an acceptable limit for two of the three varaibles and optimizing the project in terms of the third variable.

Critical Path Method (CPM) • Produce the earliest and lastest starting and finishing times for each task or activity. • Calculate the amount of slack associated with each activity. • Determine the critical tasks (Critical path). • Forward pass and backward pass computational procedures.

Network control • Track the progress of a project on the basis of the network schedule and taking corrective actions when necessary. • Evaluate the actual performance against expected performance.

PERT/CPM Node Merge point Successor Burst point Arrow Predecessor

Two models of PERT/CPM • Activity-on-Arrow (AOA): Arrows are used to represent activities or tasks. Nodes represent starting and ending points of activities. • Activity-on-Node (AON): Nodes are used to represent activities or tasks, while arrows represent precedence relationships.

Recap - purpose of CPM • • Critical path Earliest starting time ES Earliest completion time EC Latest starting time LS Latest completion time LC Activity Capital letter Duration t

Example • • Activity A B C D E F G Predecessor A C A B, D, E Duration 2 6 4 3 5 4 2

Activity on Node Network

Forward pass analysis

Backward pass analysis

Slack Time in Triangles

Critical path

Computational analysis of network • Forward pass: each activity begins at its earliest time. An activity can begin as soon as the last of its predecessors is finished. • Backward pass: begins at its latest completion time and ends at the latest starting time of the first activity in the project network.

Rules for implementation forward pass • The earliest start time (ES) for any node (j) is equal to the maximum of the earliest completion times (EC) of the immediate predecessors of the node. • The earliest completion time (EC) of any activity is its earliest start time plus its estimated time (its duration). • The earliest completion time of the project is equal to the earliest completion time the very last activity.

Rules for implementation backward pass • The latest completion time (LC) of any activity is the smallest of the latest start times of the activity’s immediate successors. • The latest start time for any activity is the latest completion time minus the activity time.

Calculate slack time for each activity • Slack time: the difference in time between the two dates at the beginning of a job or the two dates at the end of the job. Slack time represents the flexiblity of the job. • Thus, slack time = LS - ES or LC - EC

PERT • PERT is an extension of CPM. • In reality, activities are usually subjected to uncertainty which determine the actual durations of the activities. • It incorporates variabilities in activity duration into project entwork analysis. • The poetntial uncertainties in activity are accounted for by using three time estimates for each activity

Variation of Task Completion Time Task A Task B 2 3 4 4 6 5 4 4 Average 4 4

PERT Estimates & Formulas a+4 m+b te = 6 2 (b-a) s 2 = 36 a = optimistic time estimate m = most likely time estimate b = pessimistic time estimate (a < m < b) te = expected time for the activity s 2=variance of the duration of the activity

PERT • Calculate the expected time for each activity • Calculate the variance of the duration of each activity • Follow the same procedure as CPM does to calculate the project duration, Te • Calculate the variance of the project duration by summing up the variances of the activities on the critical path.

Sources of the Three Estimates • • • Furnished by an experienced person Extracted from standard time data Obtained from historical data Obtained from regression/forecasting Generated by simulation Dictated by customer requirement

A PERT Example • Activity Predecessor a m b te s 2 • • 1 5 2 1 4 3 1 2 6 4 3 5 4 2 4 7 5 3 2. 17 6. 00 3. 83 2. 83 5. 17 4. 00 2. 00 0. 2500 0. 1111 A B C D E F G A C A B, D, E

What do Te & 2 S tell us? • How likely to finish the project in a specified deadline. • For example, suppose we would like to know the probability of completing the project on or before a deadline of 10 time units (days)

Probability of finishing the project in 10 days S 2 = V[C] + V[E] + V[G] S= 0. 7817 = 0. 25 + 0. 1111 = 0. 6111 ( 10 -Te ) P( T<=Td ) = P(T<=10) = P(z<= ) S Te = 11 (10 -11) = P(z<= 0. 7817 = 0. 1003 ) = P(z<= -1. 2793) About 10% probabilty fo finishing the project within 10 days

Probability of finishing the project in 13 days S 2 = V[C] + V[E] + V[G] S= 0. 7817 = 0. 25 + 0. 1111 = 0. 6111 ( 13 -Te ) P(T<=Td ) = P(T<=10) = P(z<= ) S Te = 11 (13 -11) = P(z<= 0. 7817 = 0. 9948 ) = P(z<= 2. 5585) About 99% probabilty of finishing the project within 13 days

Gantt Chart • Gantt chart is a matrix of rows and columns. The time scale is indicated along the horizontal axis. Activities are arranged along the vertical axis. • Gantt charts are usually used to represent the project schedule. Gantt charts should be updated periodically.