1. DECISION MODELING WITH MICROSOFT EXCEL Chapter 14 Copyright 2001 Prentice Hall Publishers and Ardith E. Baker Part 1 andand PERT CPM

2. INTRODUCTION The task of ________major projects is an ancient and honorable art. In about 2600 B.C., the Egyptians build the Great Pyramid for King Khufu. The Greek historian Herodotus claimed that 400,000 men worked for 20 years to build this structure. Modern projects ranging from building a ________ shopping center to putting a man on the moon are amazingly large, complex, and costly. Completing such _______on time and within _________ is not an easy task.

3. Indeed, the complicated problems of ___________ such projects are often structured by the _______________of activities. Typically, certain ___________may not be initiated before others have been completed. Some key questions to be answered in this chapter are: 1. What is the expected project ____________ date? 2. What is the potential “________” in this date? 3. What are the scheduled ______and completion dates for each specific________?

4. 4. What activities are _________in the sense that they must be completed exactly as _________ in order to meet the _______for overall project completion? 5. How long can _________activities be delayed before a _____in the overall completion date is incurred? 6. How might _________be concentrated most effectively on activities in order to ______ project completion? 7. What ________can be exercised on the flows of expenditures for the various activities throughout the _______of the project in order that the overall budget can be adhered to?

5. To answer these questions, we will use the methods _______(Program Evaluation Review Technique) and ______(Critical Path Method). Both of these approaches to scheduling represents a project as a____________. When a project involves ___________elements, the representation of the project requires a __________ network. PERT was developed in the late 1950s by the Navy Special Projects Office in cooperation with the management consulting firm of Booz, Allen, and Hamilton. The technique was used in the engineering and development program of the Polaris missile.

6. Many firms and government agencies today require all contractors to use________. CPM differs from PERT in the details of how time and cost are_________. The implementation of PERT and CPM had an immediate impact on __________projects because it allowed the practice of “management by_________.” ______was developed in 1957 by J. E. Kelly of Remington Rand and M. R. Walker of Du Pont.

7. TYPICAL PROJECT: THE GLOBAL OIL CREDIT CARD OPERATION A Moving the Global Oil credit card operation to Des Moines, Iowa, from the home office in Dallas is an important project. Global’s board of directors has set a firm _______of 22 weeks for the move and has put the Operations Analysis Group in charge of the move. The move is difficult to ________because it involves many different ___________within the company. ________________must select one of three available office sites.

8. __________has to determine which employees from Dallas will move, how many new employees to hire, and who will train them. The ________group and the treasurer’s office must organize and implement the operating procedures and the __________arrangements for the new operation. The _________will have to design the interior space and oversee needed structural improvements. Office partitions,____________________, furnishings, and so on, must all be provided for the existing building.

9. A second complicating factor is the inter- dependence of ____________(i.e., some parts of the project cannot be started until other parts are____________). Consider two obvious examples: Global cannot construct the _______of an office before it has been designed. Global cannot hire new ___________until it has determined its personnel requirements. THE ACTIVITY LIST PERT and CPM are specifically designed for _______ of this sort. The first step is to define the __________in the project and to establish ____________relationships.

10. The first __________prepared for the move is shown below. This is the ______________part of any PERT or CPM project and must be a group effort so that no important activities are overlooked. Note that the columns labeled Time and Resources are ________________ of things to come.

11. Each activity (represented by a_________) is placed on a separate line. An activity’s ___________predecessors are recorded on the same line. An immediate predecessor is an _________that must be ____________prior to the start of the activity in question (e.g., Global cannot start activity C until activity B is completed).

12. THE GANTT CHART Before discussing PERT and CPM, let’s look at another graphical approach, the _____________ (developed by Henry L. Gantt in 1918). Activities Time (weeks)

13. Activities Time (weeks) The _____________axis is time while each activity is listed on the ___________axis. The beginning of the bar represents the ________ possible starting time for the activity. Each bar represents the anticipated as well as actual__________. As each activity is completed, the appropriate bar is_________.

14. At any point in time, it is clear which activities are on ____________and which are not. Activities Time (weeks) As of week 13, activities D, E, and H are ________ schedule. Activity G has actually been _____________and hence is ahead of schedule.

15. The previous example shows how the Gantt chart is mainly used as a _________________device for following the progression in time of the __________ of a project. With the Gantt chart, we can see which tasks are on, behind or ahead of____________. It is important to note that in the context of the Gantt chart, “on schedule” means “it has been __________ no later than the earliest possible completion time.” However, this is too simple a concept for whether an activity is on schedule. The appropriate point of view should be whether the ______________is being delayed in terms of a target completion date.

16. The Gantt chart also fails to reveal which activities are _________________________of other activities. We will now see that the ___________representation contains the immediate predecessor information that we need. This information is of vital importance in determining project ________________time. THE NETWORK DIAGRAM In a PERT network__________, each activity is represented by an arrow that is called a _________or arc. the beginning and end of each activity (an _______) is indicated by a circle that is called a_________.

17. When an _______is completed, the ________occurs. Constructing the Network Diagram The following network diagram shows activities A through C. 123 4 A B C Note that the _______assigned to the nodes are arbitrary. They are simply used to _________events and do no imply anything about _____________ relationships. In the network diagram, each activity must ______at the node in which its immediate predecessors ________. For example, activity C starts at node because its immediate predecessor, activity B, ended there. 3

18. Now we need to add activity D to the network. However, note that activities ____________are both immediate predecessors to activity D. Therefore, nodes and must be combined so that activity _____can start from it. 24 1 3 2 4 A B C5D E Note that activity E, which has only D as an immediate predecessor, can be ______ with no difficulty. However, adding activity F creates new___________.

19. Since F has C as an immediate predecessor, it would ________from node. However, this would imply that ____is also an immediate predecessor to F, which is incorrect. 3 The Use of Dummy Activities This dilemma is solved by introducing a_____________, which is represented by a _______line in the network diagram. The dummy activity is _________in the sense that it requires no time or____________. It merely provides a ________________device that enables us to draw a network representation that correctly maintains the ______________precedence relationships.

20. 1 2 3 5 A B C7DE 4 F 6 Here is the resulting network diagram with the dummy activity.

21. The procedure is generalized as follows: Suppose that we wish to add an activity A to the network starting at_________, but not all of the activities that enter node N are immediate ________________of activity A. Create a new node M with a ___________activity running from node M to node N. Take those activities that are __________entering node N and that are immediate predecessors of activity A and _________them to enter node M. Now, make activity A _________at node M.

22. This network diagram shows the complete activity list and all of the precedence relationships. 1 2 3 5 A B C 7 D E 4 F 6 8 H G J I Selectsite Plan Personnelrequirements Selectpersonnel FinancialarrangementsDesignConstruct Move HireTrain

23. 1 2 3 5 A B C 7 D E 4 F 6 8 H G J I Some computer programs may have difficulty with activities H and G since they both start at node and end at node. 6 7 These activities may be read by the computer program as one instead of two.

24. A dummy activity can be used to cure this condition. Select Site [3] Plan [5] Personnel Requirements [3] Select Personnel [2] Financial Arrangements [5] Design [4] Construct [8] Move[2] Hire [4] Train [3] 1 2 3 5 A B C 7 D E 4 F 6 9 HG J I 8

25. An Activity-on-Nodes Example The previous network was an example of an Activity- on-Arc (or________) approach. In the Activity-on-Nodes (_______) approach, the activities are associated with the _________of the network while the ______of the network display the precedence relationships. The Global Oil network would be represented as follows: AD B E J C F I H G

26. The activity list and an appropriate network diagram are useful ________for representing the precedence relationships among the __________in a project. T HE CRITICAL PATH - MEETING THE BOARD’S DEADLINE Recall that the board has set a firm goal of ___weeks for the overall project to be completed. The _____estimates must first be incorporated before we can tell if this goal can be reached. The PERT-CPM procedure requires management to produce an ________of the expected time it will take to complete each activity on the activity list.

27. These time estimates are given below: If you added up all of the __________activity times in the above table, the total working time required to complete all the _________activities would be THE CRITICAL PATH CALCULATION 3 + 5 + 3 + 4 + 8 + 2 + 4 + 2 + 5 + 3 = 39 weeks

28. However, this does not take into account those activities which can be performed_______________. For example, activities A (3 weeks) and B (5 weeks) can be _______at the same time. Therefore, the total time to complete both activities would be_________. To obtain a _________of the minimum calendar time required for overall project duration, we must find the ___________in the network. A _____is a sequence of connected activities that leads from the starting node to the completion node (e.g., path_____________). 1 9 To complete the project, the activities ___________ must be completed (all paths must be traversed).

29. The task is to _________the total amount of calendar time required for all paths to be traversed and to find the _________path from start to finish. The longest path through the network is called the __________and will determine the overall project duration (because no other path will be longer). The activities on the critical path are called critical _________of the project since if they are delayed, then the _______________will be delayed. It is this _________of activities that must be kept on schedule.

30. Earliest Start and Earliest Finish Times Now let’s look at the steps employed in finding a critical path. Fundamental in this process is the ___________time for each activity. To illustrate this idea, consider activity D, “design facility.” Now assume that the project starts at time _____and ask yourself: “What is the earliest time at which activity D can start?” Clearly, it _____________until activity A is complete (3 weeks). However, it also cannot start before the _________activity is complete (0 weeks). Since the dummy cannot start until ____________are complete (a total of 8 weeks), we see that D cannot start until _________have passed.

31. 1 2 3 5 A B C 7 D E 4 F 6 9 HG J I 8 In this calculation, it is crucial to note that activities A and B both start at time 0. Select Site [3] Plan [5] Personnel Requirements [3] Select Personnel [2] Financial Arrangements [5] Design [4] Construct [8] Move[2] Hire [4] Train [3]

32. Thus, after 8 weeks, both A and C are ________and D can start. In other words, earliest start for activity D = 8 weeks Another important concept is _______________time for each activity. If we let ES = earliest _______time for a given activity EF = earliest ________time for a given activity t = __________activity time for a given activity Then, for a given activity, the ___________between earliest start time and earliest finish time is EF = ES + t

33. Consider the following rule: Earliest Start Time Rule The ES time for an activity leaving a particular node is the __________of the EF times for all activities entering the_________.

34. Looking at nodes,,, and of the previous network, the result is shown in brackets below [ES, EF]. 1234 The ES rule says that the ES for activity D is equal to the larger EF for all activities entering node 2. Continuing to each node in a _______ pass through the entire network, the values [ES, EF] are then computed for each_________. 1 2 3 B [0,5] C [5,8] D [8,12] 4 F [8,10] I [5,10] A [0,3]

35. The network with the ES and EF values is given below: 1 2 3 5 A [0,3] B [0,5] C [5,8] 7 D [8,12] E [12,20] 4 F [8,10] 6 9 H[12,12] J [20,23] I [5,10] 8 G [10,14] Note that the _____________time for J is 23 weeks. Therefore, the earliest completion time for the entire project is__________. We have now answered the 1 st question.

36. Latest Start and Latest Finish Times We now proceed with a ___________calculation in order to identify possible start and completion dates, the activities on the____________, and how long ___________activities may be delayed without affecting the overall completion date (answering the 3 rd, 4 th, and 5 th questions). Now that we have the target completion date of 23 weeks, we can work _____________from this date, determining the _________date each activity can finish without delaying the entire project. The backward pass begins at the completion node, node. Then, trace back through the network computing the __________time and ____________ time for each activity. 9

37. The relation between these quantities is LS = latest start time for a given activity LF = latest finish time for a given activity LS = LF - t The general rule is Latest Finish Time Rule The LF time for an activity entering a particular node is the ________________of the LS times for all activities leaving that node.

38. The complete network with the LS and LF values (given below the [ES,EF] values) is shown below: 1 2 3 5 A [0,3] B [0,5] C [5,8] 7 D [8,12] E [12,20] 4 F [8,10] 6 9 H[12,12] J [20,23] I [5,10] 8 G [10,14] [5,8] [0,5] [8,12] [12,20] [14,16] [5,8] [18,23] [20,23] [18,20] [16,20]

39. Slack and the Critical Path The next step of the ___________is to identify the amount of______, or free time, associated with each activity. Slack is the amount of _______an activity can be ________without affecting the completion date for the ___________project. Slack is the same concept covered in linear programming and is the __________that could be spent on that path without affecting the _________of the critical path. For each activity, the slack is computed as: Slack = LS – ES = LF – EF For example, the slack for activity G is: Slack for G = LS for G – ES for G = 16 – 10 = 6 weeks

40. Every activity on the critical path should have a slack of____. This means that the activity cannot be ___________without affecting the entire__________. Therefore, any activity with a slack of 0 is a _______ activity and is on the critical_______. The critical path activities are those with 0 slack.

41. Spreadsheet Approach for the Network The spreadsheet solution of this problem is most easily done with an activity-on-the-node (AON) approach.

42. We have now answered the following questions: 1. What is the _____________project completion date? 3. What are the __________start and completion dates for each specific activity? Answer:_________________ Answer: An activity may be scheduled to start at any date between “_______ start” and “_______start.” The scheduled completion ______will be “start date + expected activity time.”

43. 4. What activities are _________in the sense that they must be completed exactly as _________ in order to meet the target for overall project completion? 5. How long can _________activities be delayed before a delay in the overall completion date is incurred? Answer: The activities on the critical path are:________________. Answer: Any activity may be started as late as the “____________” date without delaying the overall project completion. The remaining questions will be answered later.

44. It is clear from the critical path analysis that we have a________. The board of directors wants to start operating in Des Moines in 22 weeks, and with the current plan 23 weeks are required. There are two basic approaches to ________the time required to complete a project: WAYS OF REDUCING PROJECT DURATION 1. A ________________: Here the analyst asks: “Does this project have to be done the way it is currently_____________?” In particular, “Do all of the activities on the critical path have to be done in the specified _________?” Can we make arrangements to accomplish some of these activities in a different way not on the critical path?

45. 2. A ___________: In this approach, the analyst assumes that the current diagram is _____________and works at reducing the time of certain activities on the critical path by devoting more _____________to them. The current expected times assume a certain ___________of resources. For example, the 8 weeks for construction (activity E) assumes a regular 8-hour workday. The contractor can complete the job more rapidly by working overtime, but at increased costs. The tactical approach takes into consideration _____ models, which will be discussed later. For now, let’s focus on the so-called strategic questions.

46. A Strategic Analysis This analysis is analogous to “__________?” analysis done with spreadsheets. After reviewing the network, it is discovered that the current network assumes that________, the training of new employees, must be carried out in the new building (after E is_________), and after records and key personnel have been moved (after H is complete). Perhaps these requirements can be___________. First, J can be accomplished ________________of H. Moreover, an alternative training facility can be secured by arranging to use ___________classroom space in Des Moines at a minimal cost. The new employees can be trained and ready to start the moment that construction ends.

47. On the other hand, a new __________will have to be added to the activity list: secure a training facility (activity K). All of these changes to the network may have created a new ___________with a still unsatisfactory minimum time (i.e., one greater than 22 weeks).

48. Spreadsheet Output for the Redefined Network This redefined activity list is shown in the form of the activity-on-the-arc (AOA) diagram. 1 2 3 5 A B C 7 D E 4 F 9 H G J I 8 6 K Select Site [3] Plan [5] Personnel Requirements [3] Select Personnel [2] Financial Arrangements [5] Design [4] Construct [8] Move [2] Hire [4] Train [3] Secure Training [3]

49. Here is the same network using the Activity-on-the- Node (AON) approach. AD B E J C F IH G K

50. The modified spreadsheet is shown below: Note that the redefined project completion time is 20 weeks and the new critical path is B-C-D-E.

51. End of Part 1 Please continue to Part 2