Transcript crashing1
Project Management Chapter 8 (Crashing) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-1 Project Crashing Basic Concept In last lecture, we studied on how to use CPM and PERT to identify critical path for a project problem Now, the question is: Question: Can we cut short its project completion time? If so, how! Chapter 8 - Project Management 2 8-2 Project Crashing Solution! Yes, the project duration can be reduced by assigning more resources to project activities. But, doing this would somehow increase our project cost! How do we strike a balance? ■ Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time. 3 8-3 Trade-off concept Here, we adopt the “Trade-off” concept We attempt to “crash” some “critical” events by allocating more resources to them, so that the time of one or more critical activities is reduced to a time that is less than the normal activity time. How to do that: Question: What criteria should it be based on when deciding to crashing critical times? 4 8-4 Example – crashing (1) Max weeks can be crashed Normal weeks 5 (1) 2 6(3) 3 1 5(0) The critical path is 1-2-3, the completion time =11 How? Path: 1-2-3 = 5+6=11 weeks Path: 1-3 = 5 weeks Now, how many days can we “crash” it? 5 8-5 Example – crashing (1) 5 (1) 2 6(3) 3 1 5(0) The maximum time that can be crashed for: Path 1-2-3 = 1 + 3 = 4 Path 1-3 = 0 Should we use up all these 4 weeks? 6 8-6 Example – crashing (1) 4(0) 5 (1) 3(0) 2 6(3) 3 1 5(0) If we used all 4 days, then path 1-2-3 has (5-1) + (6-3) = 7 completion weeks Now, we need to check if the completion time for path 1-3 has lesser than 7 weeks (why?) Now, path 1-3 has (5-0) = 5 weeks Since path 1-3 still shorter than 7 weeks, we used up all 4 crashed weeks Question: What if path 1-3 has, say 8 weeks completion time? 7 8-7 Example – crashing (1) Such as 5 (1) 2 6(3) 3 1 8(0) Now, we cannot use all 4 days (Why?) Because path 1-2-3 will not be critical path anymore as path 1-3 would now has longest hour to finish Rule: When a path is a critical path, it will not stay as a critical path So, we can only reduce the path 1-2-3 completion time to the same time as path 1-3. (HOW?) 8 8-8 Example – crashing (1) Solution: 5 (1) 2 6(3) 3 1 8(0) We can only reduce total time for path 1-2-3 = path 1-3, that is 8 weeks If the cost for path 1-2 and path 2-3 is the same then We can random pick them to crash so that its completion Time is 8 weeks 9 8-9 Example – crashing (1) Solution: 4(0) 5 (1) 2 4(1) 6(3) 3 1 8(0) OR 5 (1) 1 2 3(0) 6(3) 3 8(0) Now, paths 1-2-3 and 1-3 are both critical paths 10 8-10 The Project Network AOA Network for House Building Project Figure 8.6 Expanded Network for Building a House Showing Concurrent Activities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-11 Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5) Figure 8.19 The Project Network for Building a House Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-12 Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5) Table 8.4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-13 Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5) Crash cost & crash time have a linear relationship: Total Crash Cost $2000 Total Crash Time 5 weeks $400 / wk Figure 8.20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-14 Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (2 of 2) Figure 8.23 The Time-Cost Trade-Off Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-15 Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5) Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-16 Project Crashing and Time-Cost Trade-Off Example Problem (5 of 5) As activities are crashed, the critical path may change and several paths may become critical. Figure 8.22 Revised Network with Activity 1 Crashed Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-17 Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 8.16 8-18 Formulating as a Linear Programming Model AOA Network for House Building Project Figure 8.6 Expanded Network for Building a House Showing Concurrent Activities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-19 Formulating as a Linear Programming Model Example Problem Formulation and Data (1 of 2) Figure 8.24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-20 The CPM/PERT Network Example Problem Formulation and Data (2 of 2) Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7 subject to: x2 - x1 12 x3 - x2 8 x4 - x2 4 x4 - x3 0 x5 - x4 4 x6 - x4 12 x6 - x5 4 x7 - x6 4 xi, xj 0 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-21 The CPM/PERT Network Formulating as a Linear Programming Model The objective is to minimize the project duration (critical path time). General linear programming model with AOA convention: Minimize Z = xi subject to: i xj - xi tij for all activities i j xi, xj 0 Where: xi = earliest event time of node i xj = earliest event time of node j tij = time of activity i j Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-22 Project Crashing with Linear Programming Example Problem – Model Formulation Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46 + 200y56 + 7000y67 subject to: y12 5 y12 + x2 - x1 12 x7 30 y23 3 y23 + x3 - x2 8 xi, yij ≥ 0 y24 1 y24 + x4 - x2 4 Objective is to y34 0 y34 + x4 - x3 0 minimize the y45 3 y45 + x5 - x4 4 cost of crashing y46 3 y46 + x6 - x4 12 y56 3 y56 + x6 - x5 4 y67 1 x67 + x7 - x6 4 xi = earliest event time of node i xj = earliest event time of node j yij = amount of time by which activity i j is crashed Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 8-23