To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 17 Project Management Part (a)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Elements Of Project Management Project team –individuals from different departments within company Matrix organization –team structure with members from different functional areas depending on skills needed Project manager –leader of project team

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Planning Statement of work –written description of goals, work & time frame of project Activities require labor, resources & time Precedence relationship shows sequential relationship of project activities

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Simplified Project Network 132 Construct formsPour concrete

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Elements Of Project Planning Define project objective(s) Identify activities Establish precedence relationships Make time estimates Determine project completion time Compare project schedule objectives Determine resource requirements to meet objective

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Control Two phases –1. planning –2. control Work breakdown structure (WBS) –determine subcomponents, activities & tasks

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Gantt Chart Popular tool for project scheduling Graph with bar for representing the time for each task Provides visual display of project schedule Also shows slack for activities –(amount of time activity can be delayed without delaying project)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Month   Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work A Gantt Chart

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. CPM/PERT Critical Path Method (CPM) –DuPont & Remington-Rand (1956) –deterministic task times –activity-on-node network construction Project Eval. & Review Technique (PERT) –US Navy, Booz, Allen & Hamilton –multiple task time estimates –activity-on-arrow network construction

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Project Network Network consists of branches & nodes 132 Branch Node

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Network Construction In AON, nodes represent activities & arrows show precedence relationships In AOA, arrows represent activities & nodes are events for points in time An event is the completion or beginning of an activity A dummy shows precedence for two activities with same start & end nodes

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Concurrent Activities Dummy Lay foundation 2 3 Lay foundation Order material Incorrect precedence relationship Correct precedence relationship

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Network Convention: Activity-on- Arc (AOA) a b ca b c a b c d a b c Dummy activity

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Network Convention: Activity-on- Node (AON)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 1 Management Decision Systems (MDS) is a consulting company specializing in the development of decision support systems. MDS has just obtained the contract to develop a computer system to assist the management of a large company in formulating its capital expenditure plan. The project leader has developed the list of activities and immediate predecessors as shown in the table. Construct the precedence network (AOA and AON) for this problem.

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 1 - Solution Activity-On-Arc (AOA)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 1 - Solution Activity-On-Node

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Critical Path A path is a sequence of connected activities running from start to end node in network The critical path is the path with the longest duration in the network Project cannot be completed in less than the time of the critical path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. PERT and CPM By utilizing project planning and control techniques (such as PERT and CPM), a variety of important questions can be answered, such as: –When will the project be completed? –Which activities are most critical regarding the projects completion time? –How long can individual tasks be delayed without causing the project itself to be delayed?

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. PERT and CPM: Solution Approaches Enumerating all Paths in the Project Network. By Calculating Early Start, Early Finish, Late Start, Late Finish, and Total Slack.

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Example Project Network For Building A House Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Selec t carpe t Select paint Build house

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Solution: All Possible Paths A: = 9 months (36 weeks); the critical path B: = 8 months (32 weeks) C: = 8 months (32 weeks) D: = 7 months (28 weeks)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. End of Part (a)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 17 Project Management Part (b)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Definitions Early Start (ES), the earliest time an activity can start Early Finish (EF), the earliest time an activity can finish EF = ES + Activity Time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Definitions Late Start (LS), the latest time the activity can finish and not delay the project Late Finish (LF), the latest time the activity can finish and not delay the project LS = LF – Activity Time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Definitions Total Slack (TS) or Slack Time is: TS = LS – ES or TS = LF – EF

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Definitions A path is a sequence of connected activities running from start to end node in network The Critical Path (CP) is the path with the longest duration in the network. Also, it is the path in the network along which the activities have a zero total slack value. Project cannot be completed in less than the time of the critical path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Algorithm Forward Pass: Calculate the Early Finish Time for Each Activity Backward Pass: Calculate the Late Start for Each Activity Determine the Total Slack for Each Activity Identify the Critical Path for the project

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 2 For the given activities and their immediate predecessors, draw the precedence diagram. Then find the early start, early finish, late start, and late finish for each activity. Also, determine the length of the critical path and the activities along the critical path.

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 2 – Precedence Diagram (AON) B A C E D F G H J I K

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 2 – Precedence Diagram (AOA)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

Problem 2 – Precedence Diagram (AOA)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

End of Part (b)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 17 Project Management Part (c)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Probabilistic Time Estimates Reflect uncertainty of activity times Beta distribution is used in PERT b - a 6 ( ) Variance:  2 = a = optimistic estimate m = most likely time estimate b = pessimistic time estimate Where, 2 Mean (expected time): a + 4m + b 6 t =

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Example Beta Distributions m = t ba P (time) ba tm b mta

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. PERT Example Manual Testing Dummy System Training Dummy System Testing Orientation Position recruiting System development Equipment installation Equipment testing and modification Final debugging System changeover Job training

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Activity Information Time estimates (wks)Mean Time Variance Activityambt  2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Early And Late Times Activityt  2 ESEFLSLFTS

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Network With Times ( ) ES=8, EF=8 LS=9, LF=9 ( ) ES=6, EF=9 LS=6, LF=9 ( ) ES=3, EF=5 LS=14, LF=16 ( ) ES=0, EF=3 LS=2, LF=5 ( ) ES=0, EF=6 LS=0, LF=6 ( ) ES=0, EF=8 LS=1, LF= ( ) ES=3, EF=7 LS=5, LF=9 4 ( ) ES=9, EF=13 LS=12, LF=16 ( ) ES=9, EF=13 LS=9, LF=16 ( ) ES=13, EF=13 LS=16 LF=16 ( ) ES=13, EF=25 LS=16 LF=25 ( ) ES=13, EF=25 LS=16 LF=25 ( ) ES=8, EF=13 LS=16 LF=21

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Critical Path and Project Variance The Length of the Critical Path: 25 The Critical Path: 1-3, 3-5, 5-7, 7-9. Project variance is the sum of variances on the critical path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Probabilistic Network Analysis Determine probability that project is completed within specified time where  = t p = project mean time  = project standard deviation x = proposed project time Z = number of standard deviations x is from mean Z = x -  

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Distribution Of Project Time  = t p Timex ZZ Probability

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Probabilistic Analysis Example What is the probability that the project is completed within 30 weeks?

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Determining Probability From Z Value Z …  = 25 Time (weeks) x = 30 P( x<= 30 weeks) =

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. What is the probability that the project is completed within 22 weeks?  = 25 Time (weeks) x = 22 P( x<= 22 weeks) =0.1271

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Crashing Crashing is reducing project time by expending additional resources Crash time is an amount of time an activity is reduced Crash cost is the cost of reducing the activity time Goal is to reduce project duration at minimum cost

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 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

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time-Cost Trade- offs Cost ($) Project Duration Crashing Total cost Indirect cost Direct cost Time Minimum cost = optimal project time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time-Cost Trade-offs: Crashing Trial and Error Approach for small size problems (which is described and used for Problem 3) Mathematical Procedures (for example, Linear Programming Formulation) for large size problems

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Advantages of PERT/CPM Forces managers to organize Provides graphic display of activities Identifies – Critical activities – Slack activities Build A A Done Build B B Done Build C C Done Build D Ship JANFEBMARAPRMAYJUN On time!

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Limitations of PERT/CPM Important activities may be omitted Precedence relationships may not be correct Estimates may include a fudge factor 200 weeks

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 Office Automation, Inc., has developed a proposal for introducing a new computerized office system that will improve word processing and interoffice communications for a particular company. Contained in the proposal is a list of activities that must be accomplished in order to complete the new office system project. Information about the activities is shown below. Times are in weeks and costs are in thousands of dollars.

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 Show the network for the project. Develop the activity schedule for the project. What are the critical path activities and what is the expected project completion date? Assume that the company wishes to complete the project in 26 weeks. What crashing decisions would be recommended in order to meet the completion date at least possible cost. Work through the network and attempt to make crashing decisions. Develop an activity schedule for the crashed project. What is the added project cost to meet the 26-week completion date?

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Project Network - AON

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Activity Schedule Based on Normal Time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Based on the activity schedule, it can be determined that the critical path is along activities A-B-C-F and the length of the critical path is 31 weeks. Hence, the Expected Project Completion Date is in 31 weeks

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Also, from the project network it can easily be seen that there are 2 Paths in the network. They are: –Path 1: A-B-C-F with a length of 31 weeks –Path 2: A-D-E-F with a length of 30 weeks How do we get to complete the project in 26 weeks?

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Determine the potential Crash Cost per time period (weeks) for each activity Crash Cost per time period for activity i = K i = Total Crash Cost – Total Normal Cost Normal Time – Crash Time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution First crash activities on the Critical Path Note that by crashing critical path activities will lead to other paths with the same completion time (and thus will also become critical)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution 1.Activity B has the lowest crash cost on the critical path, A-B-C-F. Crash activity B by 1 week since the maximum crash weeks for Activity B are 2 weeks. The length of critical path = 30 weeks. Added cost = $15, Now, there are two critical paths. Reduce a common activity or a combination of activities from each path, which ever is the lowest.

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution 3.Next, reduce the common activity to both paths, activity A by 2 weeks (one week at a time). The length of the critical path = 28. Added cost = $20,000 + $20,000 4.Next, reduce activities B and D by 1 week each. The length of the critical path = 27. Added cost = $15,000 + $10,000 5.Next, reduce activities C and E by 1 week each. The length of the critical path = 26. Added cost = $20,000 + $12,500

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution 6.The desired completion time for the project of 26 weeks has been achieved. 7.The total added cost = $112,500

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 3 - Solution Revised Activity Schedule based on Crashing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. THE END