Report

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 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 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 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. 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 B 9 C 8 4 A F 12 10 2 D 7 E 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 B 10 C 8 4 A F 12 10 3 D 7 E Critical Paths: A,D,F; A,B,C,F; A,D,E,F. Earliest Start Times -- Forward Computation 5 2 10 2 6 7 3 9 7 2 1 2 Earliest Start Times -- Forward Computation Note: Early Finish Time = Early Start Time + Activity Time 5 5 17 10 0 2 15 2 2 9 3 38 1 29 6 7 22 7 2 31 2 Latest Finish Times -- Backward Computation Note: Late Start Time = Late Finish Time Activity Time 5 5 26 10 0 2 15 2 9 9 3 38 1 29 6 7 22 7 39 2 37 Early S (F) Time = Late S (F) Time for critical path arcs 2