1. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. Solution - CPM 1) Construct the network 2) Event analysis - forward pass - backward pass 3) Activity analysis - critical activities - noncritical activities CPM

2. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 1) Construct the network One start node & one end node Each activity  one arc Two nodes are connected maximally by one arc CPM

3. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 1) Construct the network i j i < j 2 3 3 2 CPM

4. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors A Songs Selection 15None BMastering8A C Promotion Material Elaborating 6A D Customers Analysis 7A E Promotion Material Production 4 C, D F Promotion Material to PH 5E G Customers Selection 3D CPM

5. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors H Make CD Copies 12 B, D I Data to PH 3G J Laser Print 9 F, I KMailing8 H, J CPM

6. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 1 2 4 3 5 6 9 7 10 8 A B D C D1D1 E FH D2D2 GI J KCPM

7. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 1 2 4 3 5 6 9 7 10 8 15 8 7 6 0 4 512 0 33 9 8CPM

8. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - forward pass The earliest event time for a node is the earliest time at which all the preceding activities have been completed. j ET j CPM

9. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - forward pass ET 1 ET 1  ET 2 ET 2  ET 3 ET 3 …  ET n Ascending order: The earliest event time for completing a project is the earliest time of the last event. T = ET n CPM

10. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - backward pass The latest event time for a node is the latest time at which the event can occur without delaying the determined completion time of the project. i LT i CPM

11. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - backward pass LT 1  LT 2  LT 3  …  LT n Descending order: The latest event time for completing a project can be set in the planning process or can be considered as the earliest event time for completing a project. LT n = T = ET n or LT n = T PL > T CPM

12. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Total float: i LT i ET i j ET j LT j t ij CPM

13. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Critical activity: TF ij = 0 TF ij = T PL - T if LT n = T = ET n if LT n = T = ET n if LT n = T PL > T if LT n = T PL > T Noncritical activity: TF ij > 0 TF ij > T PL - T if LT n = T = ET n if LT n = T = ET n if LT n = T PL > T if LT n = T PL > T CPM

14. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Critical path: 1 2 4 3 5 6 9 7 10 8 A B D C D1D1 E F H D2D2 GI J KCPM

15. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Noncritical activity 1) Start of the activity can be postponed 2) Duration of the activity can be extended 3) Combination of 1 and 2 CPM