Beni Asllani University of Tennessee at Chattanooga Chapter 9 Project Management Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III Beni Asllani University of Tennessee at Chattanooga Copyright 2006 John Wiley & Sons, Inc.

Lecture Outline Project Planning Project Scheduling Project Control CPM/PERT Probabilistic Activity Times Project Crashing and Time-Cost Trade-off Copyright 2006 John Wiley & Sons, Inc.

What is a Project? Project Examples unique, one-time operational activity or effort Examples constructing houses, factories, shopping malls, athletic stadiums or arenas developing military weapons systems, aircrafts, new ships launching satellite systems constructing oil pipelines developing and implementing new computer systems planning concert, football games, or basketball tournaments introducing new products into market Copyright 2006 John Wiley & Sons, Inc.

Project Elements Objective Scope Contract requirements Schedules Resources Personnel Control Risk and problem analysis Copyright 2006 John Wiley & Sons, Inc.

Project Management Process Project planning Project scheduling Project control Project team made up of individuals from various areas and departments within a company Matrix organization a team structure with members from functional areas, depending on skills required Project Manager most important member of project team Copyright 2006 John Wiley & Sons, Inc.

Project Scope Scope statement Statement of work a document that provides an understanding, justification, and expected result of a project Statement of work written description of objectives of a project Work breakdown structure breaks down a project into components, subcomponents, activities, and tasks Copyright 2006 John Wiley & Sons, Inc.

Work Breakdown Structure for Computer Order Processing System Project Copyright 2006 John Wiley & Sons, Inc.

Organizational Breakdown Structure a chart that shows which organizational units are responsible for work items Responsibility Assignment Matrix shows who is responsible for work in a project Copyright 2006 John Wiley & Sons, Inc.

Project Scheduling Steps Techniques Define activities Sequence activities Estimate time Develop schedule Techniques Gantt chart CPM PERT Microsoft Project Copyright 2006 John Wiley & Sons, Inc.

Gantt Chart Graph or bar chart with a bar for each project activity that shows passage of time Provides visual display of project schedule Slack amount of time an activity can be delayed without delaying the project Copyright 2006 John Wiley & Sons, Inc.

Example of Gantt Chart Month 0 2 4 6 8 10 | | | | | 1 3 5 7 9 | | | | | Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 0 2 4 6 8 10 Month 1 3 5 7 9 Copyright 2006 John Wiley & Sons, Inc.

Project Control Time management Cost management Quality management Performance management Earned Value Analysis a standard procedure for numerically measuring a project’s progress, forecasting its completion date and cost and measuring schedule and budget variation Communication Enterprise project management Copyright 2006 John Wiley & Sons, Inc.

CPM/PERT Critical Path Method (CPM) DuPont & Remington-Rand (1956) Deterministic task times Activity-on-node network construction Project Evaluation and Review Technique (PERT) US Navy, Booz, Allen & Hamilton Multiple task time estimates Activity-on-arrow network construction Copyright 2006 John Wiley & Sons, Inc.

Project Network Activity-on-node (AON) Node Activity-on-arrow (AOA) nodes represent activities, and arrows show precedence relationships Activity-on-arrow (AOA) arrows represent activities and nodes are events for points in time Event completion or beginning of an activity in a project 1 3 2 Branch Node Copyright 2006 John Wiley & Sons, Inc.

AOA Project Network for a House 3 2 1 4 6 7 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house Copyright 2006 John Wiley & Sons, Inc.

Concurrent Activities 2 3 Lay foundation Order material (a) Incorrect precedence relationship (b) Correct precedence relationship 4 Dummy Lay foundation 1 Copyright 2006 John Wiley & Sons, Inc.

AON Network for House Building Project 1 3 2 4 5 6 7 Start Design house and obtain financing Order and receive materials Select paint Select carpet Lay foundations Build house Finish work Copyright 2006 John Wiley & Sons, Inc.

Critical Path Critical path 4 2 7 1 Start 3 6 5 A: 1-2-4-7 3 + 2 + 3 + 1 = 9 months B: 1-2-5-6-7 3 + 2 + 1 + 1 + 1 = 8 months C: 1-3-4-7 3 + 1 + 3 + 1 = 8 months D: 1-3-5-6-7 3 + 1 + 1 + 1 + 1 = 7 months Critical path Longest path through a network Minimum project completion time Copyright 2006 John Wiley & Sons, Inc.

Activity Start Times 4 2 7 1 3 6 5 Start at 5 months Finish at 9 months Finish Copyright 2006 John Wiley & Sons, Inc.

Mode Configuration 1 3 Activity number Earliest start Earliest finish 3 Latest finish Activity duration Latest start Copyright 2006 John Wiley & Sons, Inc.

Forward Pass Start at the beginning of CPM/PERT network to determine the earliest activity times Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time EF= ES + t Copyright 2006 John Wiley & Sons, Inc.

Earliest Activity Start and Finish Times 1 3 2 5 4 6 8 7 9 Start Design house and obtain financing Select pain Lay foundations Select carpet Build house Finish work Order and receive materials Copyright 2006 John Wiley & Sons, Inc.

Backward Pass Determines latest activity times by starting at the end of CPM/PERT network and working forward Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors Copyright 2006 John Wiley & Sons, Inc.

Latest Activity Start and Finish Times 1 3 2 5 4 6 7 8 9 Start Design house and obtain financing Select pain Lay foundations Select carpet Build house Finish work Order and receive materials Copyright 2006 John Wiley & Sons, Inc.

Activity Slack Slack S EF LF ES LS Activity * Critical Path 9 8 *7 1 7 9 8 *7 1 7 6 5 *4 4 3 *2 *1 Slack S EF LF ES LS Activity Copyright 2006 John Wiley & Sons, Inc.

Probabilistic Time Estimates Beta distribution a probability distribution traditionally used in CPM/PERT a = optimistic estimate m = most likely time estimate b = pessimistic time estimate where Mean (expected time): t = a + 4m + b 6 Variance: 2 = b - a 2 Copyright 2006 John Wiley & Sons, Inc.

Examples of Beta Distributions P(time) Time a m t b m = t Copyright 2006 John Wiley & Sons, Inc.

Project Network with Probabilistic Time Estimates: Example Start Finish 2 3,6,9 3 1,3,5 1 6,8,10 5 2,3,4 6 3,4,5 4 2,4,12 7 2,2,2 8 3,7,11 9 2,4,6 10 1,4,7 11 1,10,13 Equipment installation System development Position recruiting Equipment testing and modification Manual testing Job Training Orientation System training System testing Final debugging System changeover Copyright 2006 John Wiley & Sons, Inc.

Activity Time Estimates 1 6 8 10 8 0.44 2 3 6 9 6 1.00 3 1 3 5 3 0.44 4 2 4 12 5 2.78 5 2 3 4 3 0.11 6 3 4 5 4 0.11 7 2 2 2 2 0.00 8 3 7 11 7 1.78 9 2 4 6 4 0.44 10 1 4 7 4 1.00 11 1 10 13 9 4.00 TIME ESTIMATES (WKS) MEAN TIME VARIANCE ACTIVITY a m b t б2 Copyright 2006 John Wiley & Sons, Inc.

Activity Early, Late Times, and Slack ACTIVITY t б ES EF LS LF S 1 8 0.44 0 8 1 9 1 2 6 1.00 0 6 0 6 0 3 3 0.44 0 3 2 5 2 4 5 2.78 8 13 16 21 8 5 3 0.11 6 9 6 9 0 6 4 0.11 3 7 5 9 2 7 2 0.00 3 5 14 16 11 8 7 1.78 9 16 9 16 0 9 4 0.44 9 13 12 16 3 10 4 1.00 13 17 21 25 8 11 9 4.00 16 25 16 25 0 Copyright 2006 John Wiley & Sons, Inc.

Earliest, Latest, and Slack Start Finish 1 8 9 3 2 5 4 13 16 21 6 7 14 12 10 17 Critical Path 2 6 5 9 3 8 16 7 11 25 Copyright 2006 John Wiley & Sons, Inc.

Total project variance 2 = б22 + б52 + б82 + б112 = 1.00 + 0.11 + 1.78 + 4.00 = 6.89 weeks Total project variance Copyright 2006 John Wiley & Sons, Inc.

Probabilistic Network Analysis Determine probability that project is completed within specified time where  = tp = project mean time  = project standard deviation x = proposed project time Z = number of standard deviations x is from mean Z = x -   Copyright 2006 John Wiley & Sons, Inc.

Normal Distribution Of Project Time  = tp Time x Z Probability Copyright 2006 John Wiley & Sons, Inc.

Southern Textile Example What is the probability that the project is completed within 30 weeks?  = 25 Time (weeks) x = 30 P(x  30 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = 1.91 x -   30 - 25 2.62 From Table A.1, (appendix A) a Z score of 1.91 corresponds to a probability of 0.4719. Thus P(30) = 0.4719 + 0.5000 = 0.9719 Copyright 2006 John Wiley & Sons, Inc.

Southern Textile Example What is the probability that the project is completed within 22 weeks?  = 25 Time (weeks) x = 22 P(x  22 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = -1.14 x -   22 - 25 2.62 From Table A.1 (appendix A) a Z score of -1.14 corresponds to a probability of 0.3729. Thus P(22) = 0.5000 - 0.3729 = 0.1271 Copyright 2006 John Wiley & Sons, Inc.

Project Crashing Crashing Crash time Crash cost Goal reducing project time by expending additional resources Crash time an amount of time an activity is reduced Crash cost cost of reducing activity time Goal reduce project duration at minimum cost Copyright 2006 John Wiley & Sons, Inc.

Project Crashing: Example 1 12 2 8 4 3 5 6 7 Copyright 2006 John Wiley & Sons, Inc.

Project Crashing: Example (cont.) $7,000 – $6,000 – $5,000 – $4,000 – $3,000 – $2,000 – $1,000 – – | | | | | | | 0 2 4 6 8 10 12 14 Weeks Normal activity Normal time Normal cost Crash time Crashed activity Crash cost Slope = crash cost per week Copyright 2006 John Wiley & Sons, Inc.

Normal Activity and Crash Data TOTAL NORMAL CRASH ALLOWABLE CRASH TIME TIME NORMAL CRASH CRASH TIME COST PER ACTIVITY (WEEKS) (WEEKS) COST COST (WEEKS) WEEK 1 12 7 $3,000 $5,000 5 $400 2 8 5 2,000 3,500 3 500 3 4 3 4,000 7,000 1 3,000 4 12 9 50,000 71,000 3 7,000 5 4 1 500 1,100 3 200 6 4 1 500 1,100 3 200 7 4 3 15,000 22,000 1 7,000 $75,000 $110,700 Copyright 2006 John Wiley & Sons, Inc.

FROM … TO… Project Duration: 36 weeks Project Duration: 31 weeks 12 2 8 3 4 5 6 7 $400 $500 $3000 $7000 $200 $700 Project Duration: 36 weeks FROM … 1 7 2 8 3 4 5 6 $400 $500 $3000 $7000 $200 $700 12 Project Duration: 31 weeks Additional Cost: $2000 TO… Copyright 2006 John Wiley & Sons, Inc.

Time-Cost Relationship Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Reduce project length as long as crashing costs are less than indirect costs Copyright 2006 John Wiley & Sons, Inc.

Minimum cost = optimal project time Time-Cost Tradeoff Cost ($) Project duration Crashing Time Minimum cost = optimal project time Total project cost Indirect cost Direct cost Copyright 2006 John Wiley & Sons, Inc.

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