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IE 2030 Lecture 5: Project Management Drawing Gantt Charts

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: Project Management Drawing Gantt Charts

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  1. IE 2030 Lecture 5: Project ManagementDrawing 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

  2. 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

  3. 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 • Doesn’t deal with variability or uncertainty

  4. 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.

  5. IE 2030 Lecture 5: PERT/CPMHow 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

  6. 9 B C 8 4 A F 12 10 2 D E 7 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

  7. 10 B C 8 4 A F 12 10 3 D E 7 Critical Paths: A,D,F; A,B,C,F; A,D,E,F.

  8. Exponentially many paths

  9. Earliest Start Times -- Forward Computation 1 9 5 3 10 2 2 6 7 2 2 7 Algorithm to handle Exponentially many paths

  10. Earliest Start Times -- Forward Computation Note: Early Finish Time = Early Start Time + Activity Time 5 17 38 1 9 5 3 10 2 0 15 29 2 6 7 2 2 2 22 7 31 Algorithm to handle Exponentially many paths

  11. Latest Finish Times -- Backward Computation Note: Late Start Time = Late Finish Time - Activity Time 5 26 38 1 9 5 3 10 2 0 15 29 39 2 6 7 2 2 9 22 7 37 Algorithm to handle Exponentially many paths Early S (F) Time = Late S (F) Time for critical path arcs

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