# CPM, Crashing, Resource Leveling using MS Excel & MS Project

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CPM, Crashing, Resource Leveling using MS Excel & MS Project
12/4/2017 CPM, Crashing, Resource Leveling using MS Excel & MS Project David S.W. Lai Sept 24, 2013

Scope Critical Path Analysis Crashing Resource leveling
12/4/2017 Scope Critical Path Analysis Crashing Resource leveling Linear Programming (LP) approach MS Excel 2010 MS Project 2010

A Linear Programming Approach
Critical Path Method A Linear Programming Approach

Determine the critical path and the critical activities.
Example Problem 12/4/2017 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.

Solution Critical activities: 1, 2, 3, 4, 6, 9
12/4/2017 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.

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

A LP Model for CPM analysis
12/4/2017 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

AON network & LP Model Nodes Decision Variables Precedence Constraints
12/4/2017 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.

Precedence Constraints
12/4/2017 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

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

Early start schedule Late start schedule
EF 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

Early Start/Late Start Schedule
12/4/2017 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

Demo To enable the solver in EXCEL 2010 You may find the solver in
12/4/2017 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

A Linear Programming Approach
Crashing A Linear Programming Approach

SEEM3530 Tutorial 2 Project Management
12/4/2017 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?...

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.

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

A LP Model for Crashing with a fixed project due date
12/4/2017 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.

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

Demo

Resource Leveling MS Project 2010

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

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

Demo

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.

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

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

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.

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

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

6. Resource Graph Task  Gantt chart  Resource Graph
12/4/2017 6. Resource Graph Task  Gantt chart  Resource Graph Large frustration

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

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