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

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Objectives of project scheduling Produce an optimal project schedule in terms of cost, time, or risk. Usually, it is difficult to optimize the 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.

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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.

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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.

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PERT/CPM Node Arrow Predecessor SuccessorMerge point Burst point

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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.

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Recap - purpose of CPM Critical path Earliest starting timeES Earliest completion timeEC Latest starting timeLS Latest completion timeLC ActivityCapital letter Duration t

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Example ActivityPredecessorDuration A-2 B-6 C-4 DA3 EC5 FA4 GB, D, E2

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Activity on Node Network

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Forward pass analysis

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Backward pass analysis

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Slack Time in Triangles

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Critical path

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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.

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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.

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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.

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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

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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

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Variation of Task Completion Time Task A 2 4 6 4 Task B 3 4 5 4 Average44

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

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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, T e Calculate the variance of the project duration by summing up the variances of the activities on the critical path.

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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

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A PERT Example Activity Predecessor a m bt e s 2 A -1 2 42.17 0.2500 B -5 6 76.00 0.1111 C -2 4 53.83 0.2500 D A1 3 42.83 0.2500 E C4 5 7 5.17 0.2500 F A3 4 5 4.00 0.1111 G B, D, E1 2 3 2.00 0.1111

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What do T e & S 2 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)

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Probability of finishing the project in 10 days T e = 11S 2 = V[C] + V[E] + V[G] = 0.25 + 0.25 + 0.1111 = 0.6111 S= 0.7817 P( T<=T d ) = P(T<=10) = P(z<= ( 10-T e ) S ) = P(z<= (10-11) 0.7817 ) = P(z<= -1.2793) = 0.1003 About 10% probabilty fo finishing the project within 10 days

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Probability of finishing the project in 13 days T e = 11S 2 = V[C] + V[E] + V[G] = 0.25 + 0.25 + 0.1111 = 0.6111 S= 0.7817 P(T<=T d ) = P(T<=10) = P(z<= ( 13-T e ) S ) = P(z<= (13-11) 0.7817 ) = P(z<= 2.5585) = 0.9948 About 99% probabilty of finishing the project within 13 days

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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.

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Gantt Chart A B C D E F G 1234567891011

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Gantt Chart Variations Linked Bars Progress - monitoring Milestone Task - combinations Phase-Based Multiple-Projects Project-Slippage-tracking

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Linked Bars Gantt Chart A B C D E F G 1234567891011

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