1. CPM, Crashing, Resource Leveling using MS Excel & MS Project
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CPM, Crashing, Resource Leveling using MS Excel & MS Project
David S.W. Lai
Sept 24, 2013

2. Scope Critical Path Analysis Crashing Resource leveling
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Scope
Critical Path Analysis
Crashing
Resource leveling
Linear Programming (LP) approach
MS Excel 2010
MS Project 2010

3. A Linear Programming Approach
Critical Path Method
A Linear Programming Approach

4. Determine the critical path and the critical activities.
Example Problem
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The Build-Rite Construction Company has identified the following ten activities that take place in building a house.
Activity
Immediate Predecessors
Expected Time (days) 1
Walls and Ceiling 2 5
Foundation - 3
Roof Timbers 4
Roof Sheathing
Electrical Wiring 6
Roof Shingles 8 7
Exterior Siding
Windows 9
Paint
6, 7, 10 10
Inside Wall Board
8, 5
Determine the critical path and the critical activities.
The example description is modified from the exercises described in Moore and Weatherford, Decision Modelling, Pearson 2001.

5. Solution Critical activities: 1, 2, 3, 4, 6, 9
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Solution
Activity
Early Start Schedule
Late Start Schedule
Total Slacks ES EF LS LF 1 3 8 2 10 4 13 5 12 14 18 6 21 7 15 16 9 23
Critical activities: 1, 2, 3, 4, 6, 9
The project manager should adjust accordingly the budgets and resource allocations to avoid any delay on these activities.

6. Critical Path Method Step 1: Forward pass Step 2: Backward pass
Step 3: Calculating slacks
Early Start Schedule
Late Start Schedule
Slacks

7. A LP Model for CPM analysis
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Objective Function
minimize the project duration.
Precedence Constraints
Predecessor
Successor
Duration of the Predecessor 2 1 3 5 4 6 8 7 9 10
Constraints
e.g. activity 6 precedes activity 9
Decision Variables
start times of the activities

8. AON network & LP Model Nodes Decision Variables Precedence Constraints
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Nodes
Decision Variables
Precedence Constraints
Arcs
Optimal Solution
Longest Path 9 2 1 3 5 8 7 4 10 6
Note that an alternative LP model can be derived from the AOA network.
Critical activities can then be identified via sensitivity analysis.

9. Precedence Constraints
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Parameters
The start time of the project
The (expected) times of the activities
Precedence Relations of two activities
Activity
Time (days) 1
Walls and Ceiling 5 2
Foundation 3
Roof Timbers 4
Roof Sheathing
Electrical Wiring 6
Roof Shingles 8 7
Exterior Siding
Windows 9
Paint 10
Inside Wall Board
Project Start Time
Precedence Constraints
Predecesor
Successor 2 1 3 4 5 6 8 7 9 10

10. 12/4/2017
A Linear Programming Approach for Critical Path Analysis A Spreadsheet Implementation
Activity
Time (days)
Start time
Finish time 1
Walls and Ceiling 5 - 2
Foundation 3
Roof Timbers 4
Roof Sheathing
Electrical Wiring 6
Roof Shingles 8 7
Exterior Siding
Windows 9
Paint 10
Inside Wall Board
Project Start Time
Objective Value
Start time
Finish time 3 8 10 13 12 21 15 23
23 days

11. Early start schedule Late start scheduleEF 3 8 10 13 12 21 15 23
Early start schedule
Any activity will be started at its earliest start time.
Late start schedule
Any activity will be started at its latest start time. LS LF 3 8 10 13 14 18 21 16 23

12. Early Start/Late Start Schedule
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Critical Activities
Since the total slacks can be determined using the early start schedule and the late start schedule, the critical activities can be identified as well.
Early Start/Late Start Schedule
Total Slacks
Activity ES EF LS LF 1 3 8 2 10 4 13 5 12 14 18 6 21 7 15 16 9 23
Critical activities: 1, 2, 3, 4, 6, 9

13. Demo To enable the solver in EXCEL 2010 You may find the solver in
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Demo
To enable the solver in EXCEL 2010
File  Options Add-Ins  Select “Solver Add-in”  Go Select “Solver Add-in”  OK
You may find the solver in
Data  Solver
Objective Function
Decision Variables
Constraints
Use simplex method for
the LP models

14. A Linear Programming Approach
Crashing
A Linear Programming Approach

15. SEEM3530 Tutorial 2 Project Management
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Example Problem
Build-Rite’s engineers have calculated the cost of completing each activity. Their results are given below.
Activity
Normal
Time
Cost
Crash Time
Crash Cost 1 5 50 3 72 2 20 30 15 4 8 6 13 21 7 45 65 52 9 40 10 22 34
e.g. Cost for Activity 1
How much would it cost to complete the project within 22 days? 21 days? 20 days?...

16. Solution: Time-Cost Trade-Off
Project
Cost
The normal schedule obtained using CPM
each activity is performed at its lowest cost and at a normal duration.
Project Duration
The crashing process has revealed a relationship between the cost and the schedule of the project, which allows us to prepare our budget by considering the possible trade-offs between cost and time.

17. 12/4/2017
Notations
crash
Max. Crash Days
crash

18. A LP Model for Crashing with a fixed project due date
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A LP Model for Crashing with a fixed project due date
Minimize the cost for crashing
Precedence Constraints
Max. Clashed Days
No. of days to crash
Project due date
Start times of the activities.

19. 12/4/2017
A Linear Programming Approach for Crashing A Spreadsheet Implementation
Crashing
Activity
Crashing (days)
Normal Time
Normal Cost
Crash Time
Crash Cost
Max. Crash Days
Cost per Crash Day 1 ? 5 50 3 72 2 11 20 30 10 15 4 8 6 13 21 7 45 65 52 9 40 22 34 12
Project Cost
Obj. Value
Crashing (days) 2 1 4 84
288
372.1

20. Demo

21. Resource Leveling
MS Project 2010

22. Immediate Predecessors
Example
The working hours requirements of the activities are estimated. They are described below.
Activity
Immediate Predecessors
Expected Time (days)
Work hours 1
Walls and Ceiling 2 5
30 hrs
Foundation - 3
22 hrs
Roof Timbers
8 hrs 4
Roof Sheathing
16 hrs
Electrical Wiring
6 hrs 6
Roof Shingles 8
4 hrs 7
Exterior Siding
Windows
12 hrs 9
Paint
6, 7, 10 10
Inside Wall Board
8, 5
The example question is modified from Project Management (Shtub, Bard, Globerson) Exercise 10.1

23. Resource leveling
The reallocation of slacks in activities to minimize fluctuations in resource requirement profile.
The resource profile before leveling.
large resource fluctuation
Overallocation of resource
The resource profile after leveling.
Minimized resource fluctuation
No delay in the project

24. Demo

25. 1. Create a Project. File  New  Blank Project
File  Options  Schedule
Set the working hours per day. E.g. 8 hours.
The durations of activities (or tasks) are fixed in our case.

26. 2. Input the task information
Task  Gantt Chart
Input the task information
Select all the tasks and then press “Auto Schedule”

27. 3. Set the Project Start Date
Project  Project Information  Statistics

28. 3. Identify the critical path
Task  Gantt Chart  Network Diagram
Gantt chart  Add New Column  “total slack”
Note that the project can be finished within 23 days.

29. 4. Add a renewable resource
Task  Gantt Chart  Resource Sheet
In the first row, input
Resource Name: Manpower
Type: work
Max. Units: 100%
Examples of renewable resource
Manpower
Materials
Machines

30. 5. Type in the resource usage
Input the work hours of the activities
Select the column  right click  Assign Resources  Select “Manpower”  Assign
Task
Work hour 1
30 hrs 2
22 hrs 3
8 hrs 4
16 hrs 5
6 hrs 6
4 hrs 7 8
12 hrs 9 10

31. 6. Resource Graph Task  Gantt chart  Resource Graph
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6. Resource Graph
Task  Gantt chart  Resource Graph
Large frustration

32. 7. Resource Leveling
Resource  Leveling Options  tick “level only within available slack.
Resource  level all
Frustration is minimized.
No over-allocation
The project duration remains the same (total slacks are reduced )
Smaller f
frustration