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ENCE 603 Management Science Applications in Project Management Lectures 5-7

Project Management LP Models in Scheduling, Integer Programming

Spring 2009 Instructor: Dr. Steven A. Gabriel www.eng.umd.edu/~sgabriel

1 Copyright 2008, Dr. Steven A. Gabriel

Outline

• • • • • • Project Scheduling Critical Path Method (CPM) AON and AOA methods Project Crashing Precedence Diagramming Method (PDM) Gantt Charts

2 Copyright 2008, Dr. Steven A. Gabriel

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Project Networks

• • • • • • • Project activities described by a network Can use the activity-on-node (AON) model Nodes are activities, arrows (arcs) indicate the precedence relationships Could also consider the activity-on-arc (AOA) model which has arcs for activities with nodes being the starting and ending points AON used frequently in practical, non-optimization situations, AOA is used in optimization settings First AON, then AOA Main idea for both is to determine the critical path (e.g., tasks whose delay will cause a delay for the whole project)

3 Copyright 2008, Dr. Steven A. Gabriel

Project Networks

• • • Sample project network (AON) (read left to right) Dashed lines indicate dummy activities Key: Activity, Duration (days)

4 Copyright 2008, Dr. Steven A. Gabriel

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Network Analysis

• • • • • • • Network Scheduling: Main purpose of CPM is to determine the “critical path” Critical path determines the minimum completion time for a project Use forward pass and backward pass routines to analyze the project network Network Control: Monitor progress of a project on the basis of the network schedule Take correction action when required • “Crashing” the project • Penalty/reward approach

5 Copyright 2008, Dr. Steven A. Gabriel

Activity on Node (AON) Representation of Project Networks

6 Copyright 2008, Dr. Steven A. Gabriel

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Project Networks

A: Activity identification (node) ES: Earliest starting time EC: Earliest completion time LS: Latest starting time LC: Latest completion time...