1. Operations Research II Course,, September 20131 Operations Research II Part 1: Project Management Dr. Aref Rashad Part 2: Network Flow Part 3: Inventory Models Part 4: Queuing Models Part 5: Decision Models 413 I Part 6: Forecasting Models

2. Operations Research II Course,, September 20132 Operations Research II Introduction to Management Science, 8th Edition. By Bernard W. Taylor III References: Operations Research, 8th Edition. By Hamdy Taha An Introduction to Management Science, 6th Edition. By Anderson, Sweeney & Williams

3. Operations Research II Course,, September 20133 Sheet 1: Project Management Sheet 2: Network Flow Sheet 3: Inventory Models Sheet 4: Queuing Models Sheet 5: Decision Models Sheet 6: Forecasting Models Sheets & Assignments Assignment 1: Project Management.. To be submitted in Week 4 Assignment 2: Inventory Models …… To be submitted in Week 9

4. Operations Research II Course,, September 20134 Part 1: Project Management Operations Research II Dr. Aref Rashad

5. Operations Research II Course,, September 20135 The Elements of Project Management The Project Network CPM/PERT Activity-on-Node Networks Project Crashing and Time-Cost Trade-Off Microsoft Project Management Software Topics

6. Operations Research II Course,, September 20136 Elements of Project Management What Is a Project? A project is “A temporary and one-time endeavor undertaken to create a unique product or service, which brings about beneficial change or added value” A project ends when its objectives have been reached, or the project has been terminated. Projects can be large or small and take a short or long time to complete. *PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) (2004), p. 5.

7. Operations Research II Course,, September 20137 Project Attributes A project: Has a unique purpose. Is temporary. Is developed using progressive elaboration. Requires resources, often from various areas. Should have a primary customer or sponsor, which usually provides the direction and funding for the project. Involves uncertainty.

8. Operations Research II Course,, September 20138 Project 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

9. Operations Research II Course,, September 20139 The Triple Constraint Every project is constrained in different ways by its: Scope goals: What work will be done? Time goals: How long should it take to complete? Cost goals: What should it cost? Manage these or they will manage you! It is the project manager’s duty to balance these three often-competing goals.

10. Operations Research II Course,, September 201310 What is Project Management? Project management is : “The application of knowledge, skills, tools and techniques to project activities to meet project requirements.”* “Organizing and managing resources so the project is completed within defined scope, quality, time and cost constraints” *PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) (2004), p. 8. Successful project management is delivering a quality product that meets the customer’s requirements within time, scope, and budget.

11. Operations Research II Course,, September 201311  Scheduling  Project activities  Start & end times  Network Project Management Activities  Controlling  Monitor, compare, revise, action  Planning  Objectives  Resources  Work break-down schedule  Organization

12. Operations Research II Course,, September 201312 Project Planning, Scheduling, and Controlling BeforeStart of projectDuring projectTimelineproject

13. Operations Research II Course,, September 201313 Project Planning, Scheduling, and Controlling BeforeStart of projectDuring projectTimelineproject

14. Operations Research II Course,, September 201314 Project Planning, Scheduling, and Controlling BeforeStart of projectDuring projectTimelineproject

15. Operations Research II Course,, September 201315  Establishing objectives  Defining project  Creating work breakdown structure  Determining resources  Forming organization Project Planning

16. Operations Research II Course,, September 201316 Work Breakdown Structure “Project best understood by breaking it down into its parts” Work Breakdown Structure (WBS) powerful tool for doing this (not just a task list) fundamental to much of project planning & tracking Start at top, progressively break work down (tree structure) into work packages (Tasks/Activities) Roll up the packages for bottom up Packages give clear work assignments (Work Not in the WBS is Work Not in the Project)

17. Operations Research II Course,, September 201317 Work Breakdown Structure Level 1.Project 2.Major tasks in the project 3.Subtasks in the major tasks 4.Activities (or work packages) to be completed The next level decomposition of a WBS element (child level) must represent 100% of the work applicable to the next higher (parent) element. 100 % Rule

18. Operations Research II Course,, September 201318 Operations Research II Course,, September 201318

19. Operations Research II Course,, September 201319 WBS in Tabular Form 1.0 Concept 1.1 Evaluate current systems 1.2 Define Requirements 1.2.1 Define user requirements 1.2.2 Define content requirements 1.2.3 Define system requirements 1.2.4 Define server owner requirements 1.3 Define specific functionality 1.4 Define risks and risk management approach 1.5 Develop project plan 1.6 Brief web development team 2.0 Web Site Design 3.0 Web Site Development 4.0 Roll Out 5.0 Support

20. 20 USER DOCUMENTS Sample Partial WBS SOFTWARE PROJECT SOFTWARE SYSTEM TRAINING MATERIALS SYSTEM ANALYSIS PROJECT MGT MODULE 1MODULE 2MODULE 3 SYSTEM TEST CODINGTEST Level 1 Level 3 Level 2 Operations Research II Course,, September 2013 20

21. Operations Research II Course,, September 201321 Project Scheduling

22. Operations Research II Course,, September 201322 Purposes of Project Scheduling 1. Shows the relationship of each activity to others and to the whole project 2. Identifies the precedence relationships among activities 3. Encourages the setting of realistic time and cost estimates for each activity 4. Helps make better use of people, money, and material resources by identifying critical bottlenecks in the project Establish Project Network

23. Operations Research II Course,, September 201323 Project Network Techniques PERT CPM -Program Evaluation and ReviewTechnique - Developed by the US Navy with Booz Hamilton Lockheed on the Polaris Missile/Submarine program Critical Path Method Developed by El Dupont for Chemical Plant Shutdown Project- about same time as PERT Both use same calculations, almost similar Main difference is probabilistic and deterministic in time estimation Gantt Chart also used in scheduling

24. Operations Research II Course,, September 201324 Six Steps CPM & PERT 1. Define the project and prepare the work breakdown structure 2. Develop relationships among the activities - decide which activities must precede and which must follow others 3. Draw the network connecting all of the activities 4. Assign time and/or cost estimates to each activity 5. Compute the longest time path through the network – this is called the critical path 6. Use the network to help plan, schedule, monitor, and control the project

25. 1.When will the entire project be completed? 2.What are the critical activities or tasks in the project? 3.Which are the noncritical activities? 4.What is the probability the project will be completed by a specific date? 5.Is the project on schedule, behind schedule, or ahead of schedule? 6.Is the money spent equal to, less than, or greater than the budget? 7.Are there enough resources available to finish the project on time? 8.If the project must be finished in a shorter time, what is the way to accomplish this at least cost? Questions CPM & PERT Can Answer Operations Research II Course,, September 201325

26. Operations Research II Course,, September 201326 A branch reflects an activity of a project. Time duration of activities shown on branches A node represents the beginning and end of activities, referred to as events. Branches in the network indicate precedence relationships. When an activity is completed at a node, it has been realized. The Elements of Project Management The Project Network Network for Building a House

27. Operations Research II Course,, September 201327 Emphasis on Logic in Network Construction Construction of network should be based on logical or technical dependencies among activities Example - before activity ‘Approve Drawing’ can be started the activity ‘Prepare Drawing’ must be completed Common error – build network on the basis of time logic (a feeling for proper sequence ) see example below WRONG !!! CORRECT

28. Operations Research II Course,, September 201328 Activities can occur at the same time (concurrently). Two or more activities cannot share the same start and end nodes. A dummy activity shows a ence relationship but reflects no passage of time. Dummy activities have no resources (time, labor, machinery, etc) – purpose is to PRESERVE LOGIC of the network The Project Network Concurrent Activities 1 2 a b 1 2 3 a b

29. Operations Research II Course,, September 201329 EXAMPLES OF THE USE OF DUMMYACTIVITY Dummy RIGHT 1 1 2 Activity c not required for e a b c d e a b c d e WRONG !!! RIGHT Network concurrent activities 1 2 1 2 3 a WRONG!!! a b b WRONG ! RIGHT

30. Operations Research II Course,, September 201330 1 1 2 2 3 3 4 ad b e c f ad b e fc WRONG!!! RIGHT!!! a precedes d. a and b precede e, b and c precede f (a does not precede f) EXAMPLES OF THE USE OF DUMMYACTIVITY

31. Operations Research II Course,, September 201331 The Project Network Paths Through a Network Paths Through the House-Building Network

32. Operations Research II Course,, September 201332 The Project Network The Critical Path Alternative Paths in the Network Path A: 1  2  3  4  6  7, 3 + 2 + 0 + 3 + 1 = 9 months Path B: 1  2  3  4  5  6  7, 3 + 2 + 0 + 1 + 1+ 1 = 8 months Path C: 1  2  4  6  7, 3 + 1 + 3 + 1 = 8 months Path D: 1  2  4  5  6  7, 3 + 1 + 1 + 1 + 1 = 7 months Critical Path = Longest Path

33. Operations Research II Course,, September 201333 The Project Network Activity, duration, ES, EF, LS, LF 2 3 Activity Name Duration Build 15 Early Start Early Finish Late Start Late Finish The earliest time an activity can start The latest finish time The earliest start time plus the activity time latest finish time minus activity time 1 2 4 3

34. Operations Research II Course,, September 201334 ES is the earliest time an activity can start. ES ij = Maximum (EF i ) EF is the earliest start time plus the activity time. EF ij = ES ij + t ij The Project Network Activity Scheduling – Earliest Times EF= ES + 3 ES= Max ( 4, 5 )

35. Operations Research II Course,, September 201335 LS is the latest time an activity can start without delaying critical path time. LS ij = LF ij - t ij LF is the latest finish time. LF ij = Minimum (LS j ) The Project Network Activity Scheduling – Latest Times LS= LF -1 LF= Min ( 5, 6 )

36. Operations Research II Course,, September 201336 The Project Network Critical Path Earliest and Latest Activity Start and Finish Times Critical Activities where ES=LS & EF=LF Critical Path A: 1  2  3  4  6  7 EF=LF= 9 months

37. Operations Research II Course,, September 201337 Slack is the amount of time an activity can be delayed without delaying the project. Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal. Shared Slack is slack available for a sequence of activities. The Project Network Activity Slack 2 3 [ES=5, EF=9] [LS=8, LF=12] Activity 589 12 5 89 5 89 Duration C 4

38. Operations Research II Course,, September 201338 The Project Network Calculating Activity Slack Time (1 of 2) S= LS - ES LF= LF - EF Slack S = LS - ES or = LF - EF

39. Gantt Chart ActivityDuration123456789 1..23 2..32 2..41 4..51 4..63 5..61 6..71 Operations Research II Course,, September 201339 Critical Path Slack The Project Network Time Schedule

40. CPM Example: CPM Network a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 Operations Research II Course,, September 201340

41. CPM Example ES and EF Times a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 0 5 Operations Research II Course,, September 201341

42. CPM Example ES and EF Times a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 5 14 8 21 6 23 6 21 Operations Research II Course,, September 201342

43. CPM Example ES and EF Times a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 5 14 8 21 33 6 23 21 30 23 29 6 21 Project’s EF = 33 Project’s EF = 33 Operations Research II Course,, September 201343

44. CPM Example LS and LF Times a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 5 14 8 21 33 6 23 21 30 23 29 6 21 33 27 33 24 33 Operations Research II Course,, September 2013 44

45. CPM Example LS and LF Times a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 5 14 8 21 33 6 23 21 30 23 29 6 21 4 10 08 712 21 33 27 33 8 21 10 27 24 33 18 24 Operations Research II Course,, September 2013 45

46. CPM Example Float a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 5 14 8 21 33 6 23 21 30 23 29 6 21 3 9 08 712 21 33 27 33 8 21 10 27 24 33 9 24 3 4 3 3 4 0 0 7 7 0 Operations Research II Course,, September 2013 46

47. CPM Example Critical Path a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 Operations Research II Course,, September 201347

48. Operations Research II Course,, September 201348 Importance of Float (Slack) and Critical Path 1. Slack or Float shows how much allowance each activity has, i.e how long it can be delayed without affecting completion date of project 2. Critical path is a sequence of activities from start to finish with zero slack. Critical activities are activities on the critical path. 3. Critical path identifies the minimum time to complete project 4. If any activity on the critical path is shortened or extended, project time will be shortened or extended accordingly

49. Operations Research II Course,, September 201349 5. So, a lot of effort should be put in trying to control activities along this path, so that project can meet due date. If any activity is lengthened, be aware that project will not meet deadline and some action needs to be taken. 6.If can spend resources to speed up some activity, do so only for critical activities. 7.Don’t waste resources on non-critical activity, it will not shorten the project time. 8.If resources can be saved by lengthening some activities, do so for non-critical activities, up to limit of float. Importance of Float (Slack) and Critical Path (cont)

50. Operations Research II Course,, September 201350 Activity time estimates usually can not be made with certainty. PERT used for probabilistic activity times. In PERT, three time estimates are used: most likely time (m), the optimistic time (a), and the pessimistic time (b). These provide an estimate of the mean and variance of a beta distribution: mean (expected time): variance: Probabilistic Activity Times

51. Operations Research II Course,, September 201351 Probabilistic Activity Times Example (1 of 3) Network for Installation Order Processing System

52. Operations Research II Course,, September 201352 Probabilistic Activity Times Example (2 of 3) Activity Time Estimates

53. Operations Research II Course,, September 201353 Probabilistic Activity Times Example (3 of 3) Network with Mean Activity Times and Variances

54. Operations Research II Course,, September 201354 Probabilistic Activity Times Earliest and Latest Activity Times and Slack Earliest and Latest Activity Times

55. Operations Research II Course,, September 201355 Activity Earliest and Latest Times and Slack Probabilistic Activity Times Earliest and Latest Activity Times and Slack

56. Operations Research II Course,, September 201356 The expected project time is the sum of the expected times of the critical path activities. The project variance is the sum of the variances of the critical path activities. The expected project time is assumed to be normally distributed (based on central limit theorem). In example, expected project time (t p ) and variance (v p ) interpreted as the mean (  ) and variance (  2 ) of a normal distribution:  = 25 weeks  2 = 6.9 weeks Probabilistic Activity Times Expected Project Time and Variance

57. Operations Research II Course,, September 201357 Using normal distribution, probabilities are determined by computing number of standard deviations (Z) a value is from the mean. Value is used to find corresponding probability Probability Analysis of a Project Network

58. Operations Research II Course,, September 201358 Z value of 1.90 corresponds to probability of.4713 in Normal Distribuion Table. Probability of completing project in 30 weeks or less: (.5000 +.4713) =.9713.  2 = 6.9  = 2.63 Z = (x-  )/  = (30 -25)/2.63 = 1.90 Probability Analysis of a Project Network Example 1

59. Operations Research II Course,, September 201359 Z = (22 - 25)/2.63 = -1.14 Z value of 1.14 (ignore negative) corresponds to probability of.3729. Probability that customer will be retained is.1271 Probability Analysis of a Project Network Example 2

60. Operations Research II Course,, September 201360 Comparison Between CPM and PERT CPMPERT 1Uses network, calculate float or slack, identify critical path and activities, guides to monitor and controlling project Same as CPM 2Uses one value of activity timeRequires 3 estimates of activity time Calculates mean and variance of time 3Used where times can be estimated with confidence, familiar activities Used where times cannot be estimated with confidence. Unfamiliar or new activities 4Minimizing cost is more importantMeeting time target or estimating percent completion is more important 5Example: construction projects, building one off machines, ships, etc Example: Involving new activities or products, research and development etc

61. Operations Research II Course,, September 201361 BENEFITS OFCPM / PERT NETWORK Consistent framework for planning, scheduling, monitoring, and controlling project. Shows interdependence of all tasks, work packages, and work units. Helps proper communications between departments and functions. Determines expected project completion date. Identifies so-called critical activities, which can delay the project completion time.

62. Operations Research II Course,, September 201362 Identified activities with slacks that can be delayed for specified periods without penalty, or from which resources may be temporarily borrowed Determines the dates on which tasks may be started or must be started if the project is to stay in schedule. Shows which tasks must be coordinated to avoid resource or timing conflicts. Shows which tasks may run in parallel to meet project completion date BENEFITS OFCPM / PERT NETWORK (cont.)

63. Operations Research II Course,, September 201363 The project networks developed so far have used the “activity-on-arrow” (AOA) convention. “Activity-on-node” (AON) is another method of creating a network diagram. The two different conventions accomplish the same thing, but there are a few differences. An AON diagram will often require more nodes than an AOA diagram. An AON diagram does not require dummy activities because two “activities” will never have the same start and end nodes. Microsoft Project handles only AON networks. Activity-on-Node Networks

64. A Comparison of AON and AOA Network Conventions AON Activity AOA A comes before B, which comes before C (a) A B C BAC A and B must both be completed before C can start (b) A C C B A B B and C cannot begin until A is completed (c) B A C A B C Operations Research II Course,, September 201364

65. A Comparison of AON and AOA Network Conventions C and D cannot begin until both A and B are completed (d) A B C D B AC D C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA (e) CA BD Dummy activity A B C D Operations Research II Course,, September 201365 AON Activity AOA

66. A Comparison of AON and AOA Network Conventions B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA. (f) A C DB AB C D Dummy activity Operations Research II Course,, September 201366 AON Activity AOA

67. Operations Research II Course,, September 201367 This node includes the activity number in the upper left-hand corner, the activity duration in the lower left-hand corner, and the earliest start and finish times, and latest start and finish times in the four boxes on the right side of the node. Activity-on-Node Networks Node Structure Activity-on-Node Configuration

68. Operations Research II Course,, September 201368 Activity-on-Node Networks AON Network Diagram House-Building Network with AON

69. Operations Research II Course,, September 201369 Project duration can be reduced by assigning more resources to project activities. Doing this however increases project cost. Decision is based on analysis of trade-off between time and cost. Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time. Crashing achieved by devoting more resources to crashed activities. Project Crashing and Time-Cost Trade-Off Definition

70. Operations Research II Course,, September 201370 Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5) Network for Constructing a House

71. Operations Research II Course,, September 201371 Crash cost and crash time have linear relationship: total crash cost/total crash time = $2000/5 = $400/wk Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5) Time-Cost Relationship for Crashing Activity 1  2

72. Operations Research II Course,, September 201372 Normal Activity and Crash Data Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5)

73. Operations Research II Course,, September 201373 Network with Normal Activity Times and Weekly Activity Crashing Costs Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5)

74. Operations Research II Course,, September 201374 Revised Network with Activity 1  2 Crashed Project Crashing and Time-Cost Trade-Off Example Problem (5 of 5) As activities are crashed, the critical path may change and several paths may become critical.

75. Operations Research II Course,, September 201375 Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (1 of 2) Project crashing costs and indirect costs have an inverse relationship. Crashing costs are highest when the project is shortened. Indirect costs increase as the project duration increases. Optimal project time is at minimum point on the total cost curve.

76. Operations Research II Course,, September 201376 Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (2 of 2) A Time-Cost Trade-Off

77. Operations Research II Course,, September 201377 Benefits of PERT/CPM Useful at many stages of project management Mathematically simple Uses graphical displays Gives critical path & slack time Provides project documentation Useful in monitoring costs

78. Operations Research II Course,, September 201378 Advantages of PERT/CPM  Networks generated provide valuable project documentation and graphically point out who is responsible for various project activities  Applicable to a wide variety of projects and industries  Useful in monitoring not only schedules, but costs as well

79. Operations Research II Course,, September 201379 Assumes clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over-emphasis on critical path Limitations of PERT/CPM

80. Project Management Software There are several popular packages for managing projects  Primavera  MacProject  Pertmaster  VisiSchedule  Time Line  Microsoft Project Operations Research II Course,, September 201380

81. Using Microsoft Project Operations Research II Course,, September 2013 81

82. Using Microsoft Project Operations Research II Course,, September 201382

83. Using Microsoft Project Operations Research II Course,, September 201383

84. Using Microsoft Project Operations Research II Course,, September 201384

85. Using Microsoft Project Operations Research II Course,, September 201385

86. Using Microsoft Project Operations Research II Course,, September 201386

87. Using Microsoft Project Operations Research II Course,, September 201387

88. Gantt Chart Operations Research II Course,, September 201388

89. Operations Research II Course,, September 201389 Probability Analysis of a Project Network Example Problem – Excel Solution (1 of 3)

90. Operations Research II Course,, September 201390 Probability Analysis of a Project Network Example Problem – Excel Solution (3 of 3)

91. Operations Research II Course,, September 201391 Given the following data determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less. PERT Project Management Example Problem Problem Statement and Data

92. Operations Research II Course,, September 201392 PERT Project Management Example Problem Solution (1 of 4) Step 1: Compute the expected activity times and variances.

93. Operations Research II Course,, September 201393 PERT Project Management Example Problem Solution (2 of 4) Step 2: Determine the earliest and latest times at each node.

94. Operations Research II Course,, September 201394 PERT Project Management Example Problem Solution (3 of 4) Step 3: Identify the critical path and compute expected completion time and variance. Critical path (activities with no slack): 1  2  3  4  5 Expected project completion time (t p ): 24 days Variance: v = 4 + 4/9 + 4/9 + 1/9 = 5 days

95. Operations Research II Course,, September 201395 PERT Project Management Example Problem Solution (4 of 4) Step 4: Determine the Probability That the Project Will be Completed in 28 days or less. Z = (x -  )/  = (28 -24)/  5 = 1.79 Corresponding probability from Table A.1, Appendix A, is.4633 and P(x  28) =.9633.