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

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

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Critical Path Method A Linear Programming Approach 3

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ActivityImmediate Predecessors Expected Time (days) 1Walls and Ceiling25 2Foundation-3 3Roof Timbers12 4Roof Sheathing33 5Electrical Wiring14 6Roof Shingles48 7Exterior Siding85 8Windows12 9Paint6, 7, Inside Wall Board8, 53 The example description is modified from the exercises described in Moore and Weatherford, Decision Modelling, Pearson The Build-Rite Construction Company has identified the following ten activities that take place in building a house. Determine the critical path and the critical activities. Example Problem 4

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Solution Critical activities: 1, 2, 3, 4, 6, 9 Activity Early Start ScheduleLate Start Schedule Total Slacks ESEFLSLF The project manager should adjust accordingly the budgets and resource allocations to avoid any delay on these activities.

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

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Precedence Constraints PredecessorSuccessor Duration of the Predecessor Objective Function minimize the project duration. Constraints e.g. activity 6 precedes activity 9 Decision Variables start times of the activities A LP Model for CPM analysis 7

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Nodes Decision Variables Arcs Precedence Constraints Longest Path Optimal Solution AON network & LP Model Note that an alternative LP model can be derived from the AOA network. Critical activities can then be identified via sensitivity analysis. 8

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Parameters Activity Time (days) 1Walls and Ceiling5 2Foundation3 3Roof Timbers2 4Roof Sheathing3 5Electrical Wiring4 6Roof Shingles8 7Exterior Siding5 8Windows2 9Paint2 10Inside Wall Board3 Project Start Time 0 Precedence Constraints PredecesorSuccessor The start time of the project The (expected) times of the activities Precedence Relations of two activities 9

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A Linear Programming Approach for Critical Path Analysis A Spreadsheet Implementation Activity Time (days)Start timeFinish time 1Walls and Ceiling5-- 2Foundation Roof Timbers Roof Sheathing Electrical Wiring Roof Shingles Exterior Siding5-- 8Windows2-- 9Paint2-- 10Inside Wall Board3-- Project Start Time 0 Objective Value Start timeFinish time days 10

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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. ESEF LSLF

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Critical Activities Early Start/Late Start Schedule Total Slacks ActivityESEFLSLF 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. Critical activities: 1, 2, 3, 4, 6, 9 12

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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 13

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Crashing A Linear Programming Approach 14

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ActivityNormal Time Normal Cost Crash Time Crash Cost e.g. Cost for Activity 1 Build-Rite’s engineers have calculated the cost of completing each activity. Their results are given below. How much would it cost to complete the project within 22 days? 21 days? 20 days?... Example Problem 15

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Solution: Time-Cost Trade-Off Project Duration Project Cost 16 The normal schedule obtained using CPM each activity is performed at its lowest cost and at a normal 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.

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Notations crash Max. Crash Days 17

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

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Crashing Activity Crashing (days) Normal Time Normal Cost Crash Time Crash Cost Max. Crash Days Cost per Crash Day 1 ? ? ? ? ? ? ? ? ? ? Crash Cost? Project Cost? Obj. Value ? A Linear Programming Approach for Crashing A Spreadsheet Implementation Crashing (days)

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Demo 20

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Resource Leveling MS Project

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The example question is modified from Project Management (Shtub, Bard, Globerson) Exercise 10.1 ActivityImmediate Predecessors Expected Time (days) Work hours 1Walls and Ceiling25 30 hrs 2Foundation-3 22 hrs 3Roof Timbers12 8 hrs 4Roof Sheathing33 16 hrs 5Electrical Wiring14 6 hrs 6Roof Shingles48 4 hrs 7Exterior Siding85 6 hrs 8Windows12 12 hrs 9Paint6, 7, hrs 10Inside Wall Board8, 53 4 hrs The working hours requirements of the activities are estimated. They are described below. Example 22

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

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Demo 24

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1. Create a Project. Set the working hours per day. E.g. 8 hours. The durations of activities (or tasks) are fixed in our case. 1.File New Blank Project 2.File Options Schedule 25

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2. Input the task information 1.Task Gantt Chart 2.Input the task information 3.Select all the tasks and then press “Auto Schedule” 26

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

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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. 28

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

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5. Type in the resource usage Input the work hours of the activities Select the column right click Assign Resources Select “Manpower” Assign TaskWork hour 130 hrs 222 hrs 38 hrs 416 hrs 56 hrs 64 hrs 76 hrs 812 hrs 98 hrs 104 hrs 30

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

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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 ) 32 Smaller f frustration

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