2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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.

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

11. 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

12. 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