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IE 2030 Lecture 5: Project Management Drawing Gantt Charts Time on horizontal axis, Activities on vertical axis. 1 bar per activity Length of bar = required activity time Left end of bar at ES=Earliest Start Time Concepts: –Slack Time – Earliest Start Time

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IE 2030 Lecture 5: Gantt Charts Slack time example 2 2 5 The first 2-time-unit activity has slack 0, and the second has a slack of 1. Either (but not both) could be delayed without delaying the project

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IE 2030 Lecture 5: Gantt Charts Gantt Chart Pros and Cons Easy to understand, visual Can show how large a staff is needed Good for small projects Poor at showing precedence relations Poor at showing ``practical slack Doesnt deal with variability or uncertainty

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IE 2030 Lecture 5: PERT/CPM How to draw PERT/CPM networks Concepts: Critical Path, Early Time, Late Time How to compute values. Why a good algorithmic method is needed. A model for dealing with uncertainty: PERT, Beta distribution, central limit theorem. Formulas that make assumptions.

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IE 2030 Lecture 5: PERT/CPM How to Draw Networks Each activity is represented by a unique arc (branch) Start node, Finish node Parallel arcs not permitted: 2 arcs may not share both head and tail nodes Use dummy arcs as needed for precedence Nodes may be thought of as events such as the end of an activity

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A D B E C F 4 9 8 1210 7 2 Critical Path: A,D,F. Early start time of D,F = Late time = 12 Early start time of B,C = 4; Late start time=5

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A D B E C F 4 10 8 1210 7 3 Critical Paths: A,D,F; A,B,C,F; A,D,E,F.

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5 10 26 Earliest Start Times -- Forward Computation 2 3 7 7 9 1 22

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0 5 2 15 17 22 29 38 31 5 10 26 Earliest Start Times -- Forward Computation Note: Early Finish Time = Early Start Time + Activity Time 2 3 7 7 9 1 22

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0 5 9 15 26 22 29 38 37 39 5 10 26 Latest Finish Times -- Backward Computation Note: Late Start Time = Late Finish Time - Activity Time 2 3 7 7 9 1 22 Early S (F) Time = Late S (F) Time for critical path arcs

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