Project Management Chapter 8 (Crashing)

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

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.

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?

Example – crashing (1) Max weeks can be crashed 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? Normal weeks 2 6(3) 5 (1) 3 1 5(0)

Example – crashing (1) 6(3) 5 (1) 5(0) 2 6(3) 5 (1) 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?

Example – crashing (1) 6(3) 5 (1) 5(0) 3(0) 4(0) 2 6(3) 5 (1) 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?

Example – crashing (1) Such as 6(3) 5 (1) 8(0) 2 6(3) 5 (1) 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?)

Example – crashing (1) Solution: 6(3) 5 (1) 8(0) 2 6(3) 5 (1) 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

Example – crashing (1) Solution: 4(0) 4(1) 6(3) 5 (1) 8(0) 3(0) OR 2 6(3) 5 (1) 3 1 8(0) 3(0) OR 5 (1) 6(3) 2 1 3 8(0) Now, paths 1-2-3 and 1-3 are both critical paths

AOA Network for House Building Project 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

Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5) Figure 8.19 The Project Network for Building a House

Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5) Table 8.4

Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5) Crash cost & crash time have a linear relationship: Figure 8.20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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

Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5) Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs

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

Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows Exhibit 8.16

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

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

Example Problem Formulation and Data (2 of 2) 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

Formulating as a Linear Programming Model 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: 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 i Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

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 y34  0 y34 + x4 - x3  0 y45  3 y45 + x5 - x4  4 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 Objective is to minimize the cost of crashing Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall