Project Management ______________________________________ Operations Research Jan Fábry
Project Management Ø Project Activity 5 Activity 2 Activity 1 Activity 7 Activity 3 Activity 4 Activity 6 ______________________________________ Operations Research Jan Fábry
Project Management NETWORK – graphical representation of the project Activity Node Activity 5 Activity 2 Activity 1 Activity 7 Activity 3 Activity 4 Activity 6 ______________________________________ Operations Research Jan Fábry
Project Management NETWORK – graphical representation of the project Activity Arc 1 ACT 2 2 AC T 3 3 4 3 5 5 9 9 T T AC AC 1 2 5 5 T T AC AC 1 T AC ACT 4 ACT 6 4 6 ACT 10 AC T 7 6 ACT 8 7 6 8 AC T 11 2 ______________________________________ Operations Research Jan Fábry
Project Management Ø Event Activity A Design a car 1 Start point of A Activity B Make a prototype 3 2 Finish point of A Start point of B Finish point of B ______________________________________ Operations Research Jan Fábry
Project Management Activity A Design a car 1 Activity B Make a prototype 2 3 Activity A immediately PRECEDES activity B Activity B immediately SUCCEEDS activity A ______________________________________ Operations Research Jan Fábry
Project Management ty B type i tiv oto Ac pr 3 a Activity A ke Design a car Ma 1 2 Com Acti put vity C er p 4 rese nta tion Activity A is the predecessor of Activity B and C ______________________________________ Operations Research Jan Fábry
Project Management 5 Pr ot A ot ct yp iv e p ity re D se nt at ion ty B type i tiv oto Ac pr 3 a Activity A ke Design a car Ma Dummy activity 1 2 Activity E Prototype test Com Activi ty C pute 4 r pr esen tatio n Activity E (Prototype test) follows Activity B Activity D (Prototype presentation) follows Activity B and C ______________________________________ Operations Research Jan Fábry
Project Management Activity Requirements - time - money (cost) - material - machines - people ______________________________________ Operations Research Jan Fábry
Project Management Phases of Project Management Ø Planning Network Ø Scheduling Start and finish times for each activity Finish time of project Ø Controlling Periodic progress reports ______________________________________ Operations Research Jan Fábry
Project Management Methods Deterministic time Critical Path Method (CPM) Probabilistic time Program Evaluation Review Technique (PERT) ______________________________________ Operations Research Jan Fábry
Project Management CPM ______________________________________ Operations Research Jan Fábry
Project Management CPM Ø Finish time of the project Ø Start and finish times of each activity Ø A critical path consisting of critical activities Ø Non-critical activities and their possible delay ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Ø Christmas compilation of Czech carols Ø 11 activities: 1) Songs Selection 2) Mastering 3) Promotion Material Elaborating ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Ø 11 activities: 4) Customers Analysis 5) Promotion Material Production 6) Make CD Copies 7) Customers Selection ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Ø 11 activities: 8) Data to Printing House 9) Promotion Material to Printing House 10) Laser Print 11) Mailing ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Activity Description Duration Predecessors A Songs Selection 15 None B Mastering 8 A C Promotion Material Elaborating 6 A D Customers Analysis 7 A E Promotion Material Production 4 C, D F Promotion Material to PH 5 E G Customers Selection 3 D ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Activity Description Duration Predecessors H Make CD Copies 12 B, D I Data to PH 3 G J Laser Print 9 F, I K Mailing 8 H, J Ø All the envelopes have to be delivered until December 12 Ø Objective: set the starting date of the project ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Solution - CPM 1) Construct the network 2) Event analysis - forward pass - backward pass 3) Activity analysis - critical activities - noncritical activities ______________________________________ Operations Research Jan Fábry
Project Management CPM 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 ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 1) Construct the network i j 3 2 i < j 2 3 ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Activity Description Duration Predecessors A Songs Selection 15 None B Mastering 8 A C Promotion Material Elaborating 6 A D Customers Analysis 7 A E Promotion Material Production 4 C, D F Promotion Material to PH 5 E G Customers Selection 3 D ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. Activity Description Duration Predecessors H Make CD Copies 12 B, D I Data to PH 3 G J Laser Print 9 F, I K Mailing 8 H, J ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. H 9 4 B 1 A D 2 C 3 D 2 G 7 I D 1 5 K 10 J 8 F E 6 ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 12 4 8 1 15 7 2 6 9 3 7 3 0 5 10 9 0 3 8 8 5 4 6 ______________________________________ Operations Research Jan Fábry
Project Management CPM 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 ETj ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 2) Event analysis - forward pass Ascending order: ET 1 ET 2 ET 3 … ETn The earliest event time for completing a project is the earliest time of the last event. T = ETn ______________________________________ Operations Research Jan Fábry
Project Management CPM 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 LTi ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 2) Event analysis - backward pass Descending order: LT 1 LT 2 LT 3 … LTn 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. LTn = T = ETn or LTn = TPL > T ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 3) Activity analysis Total float: i ETi LTi tij j ETj LTj ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 3) Activity analysis Critical activity: TFij = 0 if LTn = T = ETn TFij = TPL - T if LTn = TPL > T Noncritical activity: TFij > 0 if LTn = T = ETn TFij > TPL - T if LTn = TPL > T ______________________________________ Operations Research Jan Fábry
Project Management CPM Example - Music DM, Inc. 3) Activity analysis Critical path: 1 A 4 B D 2 C 3 D 2 G H 7 9 I D 1 5 K 10 J 8 F 6 E ______________________________________ Operations Research Jan Fábry
Project Management CPM 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 ______________________________________ Operations Research Jan Fábry
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